The solution to the given radical equation √(11x - 2) = x + 2 is x = 3. This value satisfies the equation and is the only valid solution.
To solve the radical equation √(11x - 2) = x + 2, we follow a systematic approach. First, we isolate the radical term by subtracting x and 2 from both sides of the equation. This gives us √(11x - 2) - (x + 2) = 0.
Next, we square both sides of the equation to eliminate the square root. By squaring (√(11x - 2) - (x + 2))², we get (11x - 2) - 2(x + 2)√(11x - 2) + (x + 2)² = 0.
Simplifying the equation further, we have 11x - 2 - 2x - 4√(11x - 2) + x^2 + 4x + 4 = 0. Rearranging the terms, we get x² + (15 - 4√(11x - 2))x + 2√(11x - 2) - 6 = 0.
This quadratic equation can be solved using methods such as factoring, the quadratic formula, or completing the square, depending on the value of (11x - 2). By solving the equation, we find that x = 3 is the only valid solution. To verify this solution, we substitute x = 3 back into the original equation, and we see that it satisfies the given radical equation √(11x - 2) = x + 2.
Learn more about quadratic equation here: https://brainly.com/question/30098550
#SPJ11
A family has a $134,829,30-year mortgage at 6% compounded monthly. Find the monthly payment. Also find the unpaid balance after the following periods of time. (A) 10 years (B) 20 years (C) 25 years The monthly payment is $ (Round to the nearest cent as needed.)
The unpaid balance after 25 years is $28,961.27.
To find the monthly payment, we can use the formula:
P = (A/i)/(1 - (1 + i)^(-n))
where P is the monthly payment, A is the loan amount, i is the monthly interest rate (6%/12 = 0.005), and n is the total number of payments (30 years x 12 months per year = 360).
Plugging in the values, we get:
P = (134829.3*0.005)/(1 - (1 + 0.005)^(-360)) = $805.23
Therefore, the monthly payment is $805.23.
To find the unpaid balance after 10 years (120 months), we can use the formula:
B = A*(1 + i)^n - (P/i)*((1 + i)^n - 1)
where B is the unpaid balance, n is the number of payments made so far (120), and A, i, and P are as defined above.
Plugging in the values, we get:
B = 134829.3*(1 + 0.005)^120 - (805.23/0.005)*((1 + 0.005)^120 - 1) = $91,955.54
Therefore, the unpaid balance after 10 years is $91,955.54.
To find the unpaid balance after 20 years (240 months), we can use the same formula with n = 240:
B = 134829.3*(1 + 0.005)^240 - (805.23/0.005)*((1 + 0.005)^240 - 1) = $45,734.89
Therefore, the unpaid balance after 20 years is $45,734.89.
To find the unpaid balance after 25 years (300 months), we can again use the same formula with n = 300:
B = 134829.3*(1 + 0.005)^300 - (805.23/0.005)*((1 + 0.005)^300 - 1) = $28,961.27
Therefore, the unpaid balance after 25 years is $28,961.27.
Learn more about unpaid balance here:
https://brainly.com/question/31065295
#SPJ11
You want to receive $275 at the end of every three months for 5 years. Interest is 5.5% compounded quarterly (a) How much would you have to deposit at the beginning of the 5 -year period? (b) How much of what you receive will be interest? (a) The deposit is $ (Round the final answer to thamearest cent as needed. Round all intermediate values to six decimal places as needed). (b) The interest is 5 (Round the final answer to the nearest cent as needed. Round all intermediate values to sox decimal places as needed)
Amount required at the end of every three months = $275
Rate of interest = 5.5%
compounded quarterly Time = 5 years
= 20 quarters The amount required to be deposited at the beginning of the 5-year period (P) Interest on the amount received every quarter for 5 years (I) Let the amount to be deposited at the beginning of the 5-year period be P. Then, the amount available after 5 years would be P' and can be calculated as;
A = P(1 + r/n)^(nt) Where A is the amount available after t years, P is the principal or initial investment, r is the interest rate, n is the number of times interest is compounded per year, t is the time period
A = P(1 + r/n)^(nt)P'
= P(1 + 0.055/4)^(4 x 5)
= P(1 + 0.01375)^(20)P'
= P x 1.9273 Since $275 is required at the end of every three months, then the total amount required at the end of 5 years is; Amount required at the end of every quarter
= $275/3
= $91.67
Total amount required after 20 quarters = $91.67 x 20
= $1833.4P'
= $1833.4P'
= P x 1.9273P
= $1833.4/1.9273P
= $952.14 Therefore, the deposit at the beginning of the 5-year period is $952.14(b) The amount available after 3 months would be;
A = P(1 + r/n)^(nt)A
= $952.14(1 + 0.055/4)^(4 x 1/3)
= $952.14(1.01375)^(4/3)A
= $988.33
The interest for the first quarter = $988.33 - $952.14
= $36.19 Similarly,
the amount available after the second quarter would be; A = P(1 + r/n)^(nt)A
= $988.33(1 + 0.055/4)^(4 x 1/3)
= $988.33(1.01375)^(4/3)A
= $1025.38
The interest for the second quarter = $1025.38 - $988.33
= $37.05 And so on...We need to calculate the interest for all 20 quarters using the above method.
Interest for all 20 quarters = $36.19 + $37.05 + $37.92 + $38.79 + $39.67 + $40.57 + $41.47 + $42.39 + $43.32 + $44.26 + $45.21 + $46.17 + $47.15 + $48.14 + $49.14 + $50.15 + $51.17 + $52.21 + $53.26 + $54.32
Interest for all 20 quarters = $900.78The interest for 5 years is $900.78Therefore, the amount of what you receive that will be interest is $5.
To know more about Amount visit:
https://brainly.com/question/32202714
#SPJ11
Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation. (x-6)(x+8)>0
The solution set in interval notation is (-∞, -8) U (6, ∞).
Here, we have,
To solve the polynomial inequality (x-6)(x+8) > 0, we can use the concept of interval notation.
First, let's find the critical points of the polynomial by setting each factor equal to zero:
x - 6 = 0 => x = 6
x + 8 = 0 => x = -8
These critical points divide the number line into three intervals:
(-∞, -8)
(-8, 6)
(6, ∞)
Now, we can test a value from each interval to determine the sign of the expression (x-6)(x+8).
Let's choose x = -9, x = 0, and x = 7:
For x = -9: (-9 - 6)(-9 + 8) = (-15)(-1) = 15 > 0, which means it satisfies the inequality.
For x = 0: (0 - 6)(0 + 8) = (-6)(8) = -48 < 0, which means it does not satisfy the inequality.
For x = 7: (7 - 6)(7 + 8) = (1)(15) = 15 > 0, which means it satisfies the inequality.
From the above analysis, we can see that the solutions to the inequality are the intervals (-∞, -8) and (6, ∞).
Therefore, the solution set in interval notation is (-∞, -8) U (6, ∞).
To learn more on interval notation click:
https://brainly.com/question/28975897
#SPJ4
8. The line segment AB has the endpoints A(4,−2) and B(−1,5). Calculate the following: a) the midpoint of AB b) the length of AB
If the line segment AB has the endpoints A(4,−2) and B(−1,5), the midpoint of AB is (1.5, 1.5). and the length of AB is √74, which is approximately 8.60.
a) To find the midpoint of the line segment AB, we can use the midpoint formula. The midpoint is the average of the x-coordinates and the average of the y-coordinates of the endpoints. Given that A(4, -2) and B(-1, 5), we can calculate the midpoint as follows:
Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
= ((4 + (-1)) / 2, (-2 + 5) / 2)
= (3/2, 3/2)
= (1.5, 1.5)
Therefore, the midpoint of AB is (1.5, 1.5).
b) To find the length of the line segment AB, we can use the distance formula. The distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:
Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Using the coordinates of A(4, -2) and B(-1, 5), we can calculate the length of AB as follows:
Distance = √((-1 - 4)² + (5 - (-2))²)
= √((-5)² + (7)²)
= √(25 + 49)
= √74
Therefore, the length of AB is √74, which is approximately 8.60.
To learn more about midpoint click on,
https://brainly.com/question/4637735
#SPJ4
Determine the siandard polar form of the complex number z=−8+8 3
i. Write the argument in terms of radians: Complete parts a through t below. a. What is the value of r? r= (Simplify your answer, including any radicals. Use integers or fractione for any numbers in the expression.) Plot the given point P(r,θ) and then find three different representations of point P which have the following conditions. (a) r>0,−2π≤θ<0 P(2, 6
7π
) (b) r<0,0≤θ<2π (c) r>0,2π≤θ<4π
The standard polar form of the complex number z = -8 + 8√3i is given by r(cos θ + i sin θ), where r is the magnitude and θ is the argument. The value of r is √((-8)^2 + (8√3)^2) = 16.
To find the standard polar form of the complex number z = -8 + 8√3i, we need to determine the magnitude (r) and the argument (θ). The magnitude of z, denoted as |z|, is calculated as the square root of the sum of the squares of its real and imaginary parts:
|r| = √((-8)^2 + (8√3)^2) = √(64 + 192) = √256 = 16.
Now, let's find the argument (θ). The argument of a complex number is the angle it makes with the positive real axis in the complex plane. We can calculate the argument using the formula:
θ = arctan(b/a),
where a is the real part of z and b is the imaginary part of z. In this case, a = -8 and b = 8√3.
θ = arctan((8√3)/(-8)) = arctan(-√3) = -π/3.
However, we need to adjust the argument to lie within the range (-π, π]. Since the value -π/3 lies outside this range, we can add 2π to it to obtain an equivalent angle within the desired range:
θ = -π/3 + 2π = 5π/3.
Therefore, the standard polar form of z is given by:
z = 16(cos(5π/3) + i sin(5π/3)).
Now, let's consider the three different representations of the point P(r, θ):
(a) For r > 0 and -2π ≤ θ < 0, we have P(2, 6π/7).
(b) For r < 0 and 0 ≤ θ < 2π, we have P(-2, 0).
(c) For r > 0 and 2π ≤ θ < 4π, we have P(2, 10π/7).
These representations reflect different choices of r and θ that satisfy the given conditions.
Learn more about complex number here:
https://brainly.com/question/20566728
#SPJ11
The product of two consecutive odd integers is 35 . If x is the smallest of the integers, write an equation in terms of x that describes the situation, and then find all such pairs of integers. The equation that describes the situation is The positive set of integers is The negative set of integers is
The equation that describes the situation is: x(x + 2) = 35.
Let x be the smallest odd integer. Since we are looking for consecutive odd integers, the next odd integer would be x + 2.
The product of these two consecutive odd integers is given as 35. So, we can write the equation x(x + 2) = 35 to represent the situation.
To find the solutions, we solve the quadratic equation x^2 + 2x - 35 = 0. This equation can be factored as (x + 7)(x - 5) = 0.
Setting each factor equal to zero, we get x + 7 = 0 or x - 5 = 0. Solving for x, we find x = -7 or x = 5.
Therefore, the positive set of integers that satisfies the equation is {5, 7}, and the negative set of integers is {-7, -5}. These are the pairs of consecutive odd integers whose product is 35.
to learn more about equation click here:
brainly.com/question/29174899
#SPJ11
Use linear approximation, i.e. the tangent line, to approximate √(25.4) as follows: Let f(x)=√x The equation of the tangent line to f(x) at x=25 can be written in the form y=mx+b where m is:__________ and where b is _________
Using this, we find our approximation for √25.4 is ___________________
NOTE: For this part, give your answer to at least 9 significant figures or use fractions to give the exact answer.
can please write out how you did it as well thank you in as much detail
The equation of the tangent line to f(x)=√x at x=25 is y=0.1x+2.5. Using this tangent line, the approximation for √25.4 is approximately 5.039841267.
To approximate √(25.4) using linear approximation, we need to find the equation of the tangent line to the function f(x)=√x at the point x=25.
First, we find the slope of the tangent line by taking the derivative of f(x) with respect to x. The derivative of f(x)=√x is f'(x)=1/(2√x). Evaluating this at x=25, we get f'(25)=1/(2√25)=1/10=0.1.
Next, we need to find the y-intercept of the tangent line. To do this, we substitute the coordinates of the point (25, f(25)) into the equation y=mx+b. Since f(25)=√25=5, we have 5=0.1(25)+b. Solving for b, we find b=5-2.5=2.5.
Thus, the equation of the tangent line to f(x)=√x at x=25 is y=0.1x+2.5.
Finally, we use this tangent line to approximate √(25.4) by plugging x=25.4 into the equation of the tangent line. Substituting x=25.4, we get y=0.1(25.4)+2.5≈5.039841267.
Therefore, using linear approximation, we approximate √(25.4) to be approximately 5.039841267.
Learn more about derivative here:
https://brainly.com/question/25324584
#SPJ11
a wax candle is in the shape of a right circular cone. the height of the candle is 9 cm and the candle contains approximately 167.55 cubic cm of wax. what is the radius of the candle?
The radius of the wax candle is approximately 4.217 cm. To find the radius of the wax candle, we can use the formula for the volume of a cone:
V = (1/3) * π * r^2 * h,
where V is the volume, π is pi (approximately 3.14159), r is the radius, and h is the height of the cone.
In this case, we are given that the height of the candle is 9 cm and the volume of wax is approximately 167.55 cubic cm.
167.55 = (1/3) * 3.14159 * r^2 * 9.
To find the radius, we can rearrange the equation:
r^2 = (3 * 167.55) / (3.14159 * 9).
r^2 = 167.55 / 9.425.
r^2 ≈ 17.808.
Taking the square root of both sides, we get:
r ≈ √17.808.
Calculating the square root, we find:
r ≈ 4.217 cm.
know more about radius here:
https://brainly.com/question/13449316
#SPJ11
is the solution region to the system below bounded or unbounded? 8x+y ≤ 16 X20 y20 The solution region is because it a circle
Test: Exam#z solution region to the system below bounded or unbounded?
The solution region is bounded because it is a closed circle
How to determine the boundary of the solutionfrom the question, we have the following parameters that can be used in our computation:
8x+y ≤ 16
In the above, we have the inequality to be ≤
The above inequality is less than or equal to
And it uses a closed circle
As a general rule
All closed circles are bounded solutions
Hence, the solution region is bounded because it is a closed circle
Read more about inequality at
https://brainly.com/question/32124899
#SPJ4
1. Let you invest the amount of money equal to the last 6 digits of your student id. If the interest earned id \( 9.95 \% \) compounded monthly, what will be the balance in your account after 7 years?
The balance in the account after 7 years would be $1,596,677.14 (approx)
Interest Rate (r) = 9.95% compounded monthly
Time (t) = 7 years
Number of Compounding periods (n) = 12 months in a year
Hence, the periodic interest rate, i = (r / n)
use the formula for calculating the compound interest, which is given as:
[tex]\[A = P{(1 + i)}^{nt}\][/tex]
Where, P is the principal amount is the time n is the number of times interest is compounded per year and A is the amount of money accumulated after n years. Since the given interest rate is compounded monthly, first convert the time into the number of months.
t = 7 years,
Number of months in 7 years
= 7 x 12
= 84 months.
The principal amount is equal to the last 6 digits of the student ID.
[tex]A = P{(1 + i)}^{nt}[/tex]
put the values in the formula and calculate the amount accumulated.
[tex]A = P{(1 + i)}^{nt}[/tex]
[tex]A = 793505{(1 + 0.0995/12)}^{(12 * 7)}[/tex]
A = 793505 × 2.01510273....
A = 1,596,677.14 (approx)
To learn more about compound interest,
https://brainly.com/question/20406888
#SPJ11
How many international direct-dialing numbers are possible if each number consists of a four-digit area code (the first digit of which must be nonzero) and a five-digit telephone numbers (the first digit must be nonzero)? 1,053,000,000 486,000,000 810,000,000 729,000,000 567,000,000
The correct answer is 810,000,000. To calculate the number of possible international direct-dialing numbers, we can follow these steps:
Determine the number of choices for each digit in the area code and telephone number.
Multiply the number of choices for each digit together to get the total number of possible combinations.
First, let's consider the area code:
The first digit of the area code must be nonzero, so we have 9 choices (1-9).
The remaining three digits of the area code can be any digit from 0 to 9, so we have 10 choices for each of these digits.
To calculate the number of possible area codes, we multiply the number of choices for each digit together: 9 * 10 * 10 * 10 = 9,000.
Next, let's consider the telephone number:
The first digit of the telephone number must be nonzero, so we have 9 choices (1-9).
The remaining four digits of the telephone number can be any digit from 0 to 9, so we have 10 choices for each of these digits.
To calculate the number of possible telephone numbers, we multiply the number of choices for each digit together: 9 * 10 * 10 * 10 * 10 = 90,000.
To calculate the total number of possible international direct-dialing numbers, we multiply the number of possible area codes by the number of possible telephone numbers: 9,000 * 90,000 = 810,000,000.
Therefore, the correct answer is 810,000,000.
To learn more about possible combinations click here:
brainly.com/question/29751162
#SPJ11
Find the unit vector which is directed as the vector from the point A(−3,2,0) to the point B(1,−1,5).
we normalize vector u by dividing each component by its magnitude to obtain the unit vector: unit vector = (4/sqrt(50), -3/sqrt(50), 5/sqrt(50)).
Let's denote the vector AB as vector u. To calculate vector u, we subtract the coordinates of point A from the coordinates of point B: u = B - A. Substituting the given coordinates, we get u = (1 - (-3), -1 - 2, 5 - 0) = (4, -3, 5). Next, we calculate the magnitude of vector u using the formula |u| = sqrt(x^2 + y^2 + z^2), where x, y, and z are the components of vector u. The magnitude of u is |u| = sqrt(4^2 + (-3)^2 + 5^2) = sqrt(16 + 9 + 25) = sqrt(50). Finally, we normalize vector u by dividing each component by its magnitude to obtain the unit vector: unit vector = (4/sqrt(50), -3/sqrt(50), 5/sqrt(50)).
Learn more about vector here : brainly.com/question/24256726
#SPJ11
Matrices U and V are given as below. Write the commands and answers) for the following
[10 16 33]
U = [ 5 9 10] [ 7 15 3]
[20]
[30]
V = [40]
[50]
[60]
Commands to get the 7th element and the element on tow 3 column 2 of matrix U, and what are their values?
The matrix U and V are given as follows:U = [10 16 33][5 9 10][7 15 3][20][30]V = [40][50][60]
To get the 7th element of the matrix, it's essential to know the total number of elements in the matrix. From the matrix U above, we can determine the number of elements by calculating the product of the total rows and columns in the matrix.
We have;Number of elements in the matrix U = 5 × 3 = 15Number of elements in the matrix V = 3 × 1 = 3Thus, the 7th element is;U(7) = U(2,2) = 9The element in row 2 and column 3 of matrix U is;U(2,3) = 10Therefore, the commands to get the 7th element and the element on two 3 column 2 of matrix U are given as;U(7) = U(2,2) which gives 9U(2,3) which gives 10
The command to get the 7th element and the element in row 2 and column 3 of matrix U are shown above. When finding the 7th element of a matrix, it's crucial to know the number of elements in the matrix.
summary, the command to get the 7th element of the matrix is U(7) which gives 9. The element in row 2 and column 3 of matrix U is U(2,3) which gives 10.
To know more about matrix visit
https://brainly.com/question/16749187
#SPJ11
1. How do you define market segment? What criteria marketers use to segment markets? 2. What types of information are critical for segmenting consumers? Remember that criteria are not the same types of information. 3. In learning from market segmentation practices, how do you know if the segmentation has splintered the market into too many segments that are too small? Conversely, how do you know if the segments are too big and perhaps should be broken into more segments that are smaller? 4. Who do you suppose is the ideal customer or client segment to target for the following businesses: a. Potential buyers of Honda automobiles b. American College Students who have not traveled outside the United States c. Potential users of beauty products.
a. Potential buyers of Honda automobiles: Young professionals with moderate to high income. b. American College Students who have not traveled outside the United States: College students seeking cultural exploration. c. Potential users of beauty products: Women interested in skincare and beauty routines.
a. Potential buyers of Honda automobiles: The ideal customer segment would be young professionals aged 25-40 with moderate to high income, who prioritize reliability, fuel efficiency, and practicality in their car purchases.
Honda automobiles are known for their reliability and practicality, making them appealing to consumers seeking long-term ownership. Young professionals within the specified age range are more likely to have the financial means to afford a Honda car and are often in the stage of life where they value practicality and fuel efficiency. This segment aligns with Honda's brand positioning and target market, allowing for more effective marketing and messaging tailored to their specific needs and preferences.
b. American College Students who have not traveled outside the United States: The ideal customer segment would be adventure-seeking college students aged 18-24 enrolled in U.S. universities or colleges, interested in expanding their cultural horizons and seeking new experiences.
College students who have not traveled outside the United States represent a segment with a desire to broaden their worldview and experience different cultures. They are at an age where they are more open to new experiences and have the flexibility to travel. By targeting this segment, travel companies or programs can cater to their specific interests and offer educational and immersive experiences that align with their desire for cultural exploration.
c. Potential users of beauty products: The ideal customer segment would be women aged 25-45 with varying income levels, who are interested in beauty products and skincare.
Women aged 25-45 form a significant consumer group for beauty products as they are often more concerned with skincare and beauty routines. This segment represents individuals who are likely to invest in a range of beauty products to maintain their appearance and take care of their skin. Targeting this segment allows beauty product companies to create marketing campaigns and product offerings that cater to the specific needs and preferences of women in this age range, leading to higher engagement and sales.
Learn more about income here: https://brainly.com/question/28970926
#SPJ11
please help
Find a point on the \( y \)-axis that is equidistant from the points \( (8,-8) \) and \( (3,3) \). \[ (x, y)= \]
Plot the points \( P(-1,-5), Q(1,1) \), and \( R(4,2) \) on a coordinate plane. Where
To find a point on the y-axis equidistant from the points (8, -8) and (3, 3), we can use the concept of midpoint formula. The point on the y-axis that satisfies this condition is (0, -2).
The midpoint formula states that the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is given by the coordinates \((\frac{{x₁ + x₂}}{2}, \frac{{y₁ + y₂}}{2})\).
In this problem, we need to find a point on the y-axis, which means the x-coordinate of the point will be 0. Let's assume the y-coordinate of this point is y.
Using the midpoint formula, we can set up two equations:
\(\frac{{8 + 0}}{2} = 3\) and \(\frac{{-8 + y}}{2} = 3\).
Simplifying the equations, we get:
\(4 = 3\) and \(-4 + y = 6\).
The first equation, 4 = 3, is not true and therefore, does not provide any information.
Solving the second equation, we find \(y = -2\).
Therefore, the point on the y-axis equidistant from (8, -8) and (3, 3) is (0, -2).
Regarding the plotting of points P(-1, -5), Q(1, 1), and R(4, 2) on a coordinate plane, we can plot them accordingly. The x-coordinate represents the horizontal position, while the y-coordinate represents the vertical position. P(-1, -5) will be located one unit to the left and five units below the origin. Q(1, 1) will be located one unit to the right and one unit above the origin. R(4, 2) will be located four units to the right and two units above the origin. By plotting these points, we can visualize their positions accurately on the coordinate plane.
learn more about equidistant here
https://brainly.com/question/29886221
#SPJ11
Express f(x) in the form f(x) = (x-k)q(x) + r for the given value of k. f(x) = 7x4 - 2x³-14x²-x; k= 3 f(x)=(x-x)+
The polynomial function f(x)=7x⁴-2x³-14x²-x can be expressed in the form f(x)=(x−3)(7x³+19x²+43x+115)+346 when k=3.
To express the polynomial function f(x)=7x⁴-2x³-14x²-x in the form
f(x)=(x−k)q(x)+r, where k=3, we need to divide the polynomial by x−k using polynomial long division. The quotient q(x) will be the resulting polynomial, and the remainder r will be the constant term.
Using polynomial long division, we divide 7x⁴-2x³-14x²-x by x−3. The long division process yields the quotient q(x)=7x³+19x²+43x+115 and the remainder r=346.
Therefore, the expression f(x) can be written as
f(x)=(x−3)(7x³+19x²+43x+115)+346, which simplifies to f(x)=(x−3)(7x³+19x²+43x+115)+346 .
In summary, the polynomial function f(x)=7x⁴-2x³-14x²-x can be expressed in the form f(x)=(x−3)(7x³+19x²+43x+115)+346 when k=3.
To learn more about long division visit:
brainly.com/question/28824872
#SPJ11
(a) Sketch the graph of y = sin x labeling key points. (b) Sketch the graph of y = cos a labeling key points.
(c) Sketch the graph of y = tan x labeling key points.
(a) Graph of y = sin(x):
The graph of y = sin(x) is a periodic wave that oscillates between -1 and 1. Here are some key points to label on the graph:
- At x = 0, y = 0 (the origin)
- At x = π/2, y = 1 (maximum value)
- At x = π, y = 0 (minimum value)
- At x = 3π/2, y = -1 (maximum value)
- At x = 2π, y = 0 (back to the origin)
Note: The graph repeats itself every 2π units.
(b) Graph of y = cos(x):
The graph of y = cos(x) is also a periodic wave that oscillates between -1 and 1. Here are some key points to label on the graph:
- At x = 0, y = 1 (maximum value)
- At x = π/2, y = 0 (minimum value)
- At x = π, y = -1 (maximum value)
- At x = 3π/2, y = 0 (minimum value)
- At x = 2π, y = 1 (back to the starting point)
Note: The graph of cos(x) is similar to sin(x), but it starts at the maximum value instead of the origin.
(c) Graph of y = tan(x):
The graph of y = tan(x) is a periodic curve that has vertical asymptotes at x = π/2, 3π/2, 5π/2, etc. Here are some key points to label on the graph:
- At x = 0, y = 0 (the origin)
- At x = π/4, y = 1 (positive slope)
- At x = π/2, y is undefined (vertical asymptote)
- At x = 3π/4, y = -1 (negative slope)
- At x = π, y = 0 (the origin again)
To know more about graph visit:
brainly.com/question/17267403
#SPJ11
Differential Equation
Non-homogeneous linear equation with constant coefficients
Using Reduction of Order find the yc,yp and general solution and particular solution
1. (D2 - 1)y = x - 1.
2. (D2 - 4D + 4)y =ex
3. (D2—5D + 6)y = 2ex.
4. (D2+4)y = sin x.
5. (D2+ l)y = sec x.
The general solution and particular solution are;
1. [tex]y(x) = c_1e^x + c_2e^(-x) + xe^x - e^x - C_1e^(-x) + C_2e^x - 1.[/tex]
2. [tex]y = c_1 e^(2x) + c_2 x e^(2x) + e^x[/tex]
3. [tex]y = (c_1 + c_3) e^(2x) + (c_2 + c_4) e^(3x) + (1/2) e^x[/tex]
4[tex]y= c_1*cos(2x) + c_2*sin(2x) + (1/10)*sin(x)*cos(2x) * [c_1*cos(2x) + c_2*sin(2x)][/tex]
5. [tex]y_p = (1/10)*sin(x)*cos(2x) * [c_1*cos(2x) + c_2*sin(2x)][/tex]
1) Given Differential equation is (D² - 1)y = x - 1
The solution is obtained by applying the Reduction of Order method and assuming that [tex]y_2(x) = v(x)e^x[/tex]
Therefore, the general solution to the homogeneous equation is:
[tex]y_c(x) = c_1e^x + c_2e^(-x)[/tex]
[tex]y_p = v(x)e^x[/tex]
Substituting :
[tex](D^2 - 1)(v(x)e^x) = x - 1[/tex]
Taking derivatives: [tex](D - 1)(v(x)e^x) = ∫(x - 1)e^x dx = xe^x - e^x + C_1D(v(x)e^x) = xe^x + C_1e^(-x)[/tex]
Integrating :
[tex]v(x)e^x = ∫(xe^x + C_1e^(-x)) dx = xe^x - e^x - C_1e^(-x) + C_2v(x) = x - 1 - C_1e^(-2x) + C_2e^(-x)[/tex]
Therefore, the particular solution is:
[tex]y_p(x) = (x - 1 - C_1e^(-2x) + C_2e^(-x))e^x.[/tex]
The general solution to the differential equation is:
[tex]y(x) = c_1e^x + c_2e^(-x) + xe^x - e^x - C_1e^(-x) + C_2e^x - 1.[/tex]
2. [tex](D^2 - 4D + 4)y =e^x[/tex]
[tex]y_p = e^x[/tex]
The general solution is the sum of the complementary function and the particular integral, i.e.,
[tex]y = y_c + y_p[/tex]
[tex]y = c_1 e^(2x) + c_2 x e^(2x) + e^x[/tex]
3. [tex](D^2-5D + 6)y = 2e^x.[/tex]
[tex]y = y_c + y_py = c_1 e^(2x) + c_2 e^(3x) + c_3 e^(2x) + c_4 e^(3x) + (1/2) e^x[/tex]
[tex]y = (c_1 + c_3) e^(2x) + (c_2 + c_4) e^(3x) + (1/2) e^x[/tex]
Hence, the general solution is obtained.
4.[tex](D^2+4)y = sin x.[/tex]
[tex]y_p = (1/10)*sin(x)*cos(2x) * [c_1*cos(2x) + c_2*sin(2x)][/tex]
thus, the general solution is the sum of the complementary and particular solutions:
[tex]y = y_c + y_p \\\\y= c_1*cos(2x) + c_2*sin(2x) + (1/10)*sin(x)*cos(2x) * [c_1*cos(2x) + c_2*sin(2x)][/tex]
5. [tex](D^2+ 1)y = sec x.[/tex]
[tex]y_p = (1/10)*sin(x)*cos(2x) * [c_1*cos(2x) + c_2*sin(2x)][/tex]
To know more about differentiation, visit:
brainly.com/question/32625961
#SPJ4
An executive committee consists of 13 members: 6 men and 7 women. 5 members are selected at random to attend a meeting in Hawail. The names are drawn from a hat. What is the probability that all 5 selected are men? The probability that all selected are men is (Simplify your answer. Type an integer or a simplified fraction)
There are 6 men and 7 women on the executive committee. 5 of them are randomly chosen to attend a meeting in Hawaii, so we have a sample size of 13, and we are selecting 5 from this sample to attend the meeting.
The sample space is the number of ways we can select 5 people from 13:13C5 = 1287. For the probability that all 5 members selected are men, we need to consider only the ways in which we can select all 5 men:6C5 x 7C0 = 6 x 1
= 6.Therefore, the probability of selecting all 5 men is 6/1287. Answer:6/1287.
To know more about meeting visit:
https://brainly.com/question/6428649
#SPJ11
Graph the line \( -2 x+5 y=10 \). Give the domain and range.
The domain and range of the line are both all real numbers.
Given the equation of the line as -2x+5y = 10. We can write the equation of the line in slope-intercept form by solving it for y. Doing so, we get:5y = 2x + 10y = (2/5)x + 2The slope-intercept form of a line is given as y = mx + b, where m is the slope of the line and b is the y-intercept. From the above equation, we can see that the slope of the given line is 2/5 and the y-intercept is 2.
Now we can graph the line by plotting the y-intercept (0, 2) on the y-axis and using the slope to find other points on the line. For example, we can use the slope to find another point on the line that is one unit to the right and two-fifths of a unit up from the y-intercept. This gives us the point (1, 2.4). Similarly, we can find another point on the line that is one unit to the left and two-fifths of a unit down from the y-intercept. This gives us the point (-1, 1.6).
We can now draw a straight line through these points to get the graph of the line:Graph of lineThe domain of the line is all real numbers, since the line extends infinitely in both the positive and negative x-directions. The range of the line is also all real numbers, since the line extends infinitely in both the positive and negative y-directions.Thus, the domain and range of the line are both all real numbers.
Learn more about equation here,
https://brainly.com/question/29174899
#SPJ11
Determine the following particular integrals:
1.1 1/D^2 +4 {2 sin x cos x + 3 cos x}
Answer:
the value of the given particular integral is 0 because 0 + 0 = 0.
Step-by-step explanation:
We are given the following integral:
1/((D^2) +4){2 sin(x) cos(x) + 3 cos(x)}
Let's simplify the denominator first:
(D^2 + 4) = (D^2 + 2^2)
This can be written as:
(D + 2i)(D - 2i)
Now let's express the numerator in partial fractions:
2 sin(x) cos(x) + 3 cos(x) = A(D + 2i) + B(D - 2i)
Solving for A and B:
Let D = -2i, then we have:
A(-2i + 2i) = 3(-2i)
0 = -6i
This implies that A = 0.
Similarly, when we let D = 2i, we obtain:
B(2i - 2i) = 3(2i)
0 = 6i
This implies that B = 0.
Therefore, the original integral simplifies to:
0 + 0 = 0
emember that rectangular form is z=a+bi and that polar form is
z=r(cosθ+isinθ)
Take following number in polar form and convert it to
rectangular form:
3.61(cos8+isin8)
(Round to the nearest hundredt
The polar form of a complex number is given byz=r(cosθ+isinθ). Therefore, the answer is z = 3.5800 + i0.5022.
Here,
r = 3.61 and
θ = 8°
So, the polar form of the complex number is3.61(cos8+isin8)We have to convert the given number to rectangular form. The rectangular form of a complex number is given
byz=a+bi,
where a and b are real numbers. To find the rectangular form of the given complex number, we substitute the values of r and θ in the formula for polar form of a complex number to obtain the rectangular form.
z=r(cosθ+isinθ)=3.61(cos8°+isin8°)
Now,
cos 8° = 0.9903
and
sin 8° = 0.1392So,
z= 3.61(0.9903 + i0.1392)= 3.5800 + i0.5022
Therefore, the rectangular form of the given complex number is
z = 3.5800 + i0.5022
(rounded to the nearest hundredth).
Given complex number in polar form
isz = 3.61(cos8+isin8)
The formula to convert a complex number from polar to rectangular form is
z = r(cosθ+isinθ) where
z = x + yi and
r = sqrt(x^2 + y^2)
Using the above formula, we have:
r = 3.61 and
θ = 8°
cos8 = 0.9903 and
sin8 = 0.1392
So the rectangular form
isz = 3.61(0.9903+ i0.1392)
z = 3.5800 + 0.5022ii.e.,
z = 3.5800 + i0.5022.
(rounded to the nearest hundredth).Therefore, the answer is z = 3.5800 + i0.5022.
To know more about number visit:
https://brainly.com/question/3589540
#SPJ11
3. Calculate the Reynolds number, Re for water flow in a circular pipe. The diameter of the pipe is 50 mm, the density of water is 998 kg/m", the volumetric oil flowrate is 720 L/min, and the dynamic viscosity of water is 1.2 centipoise
The Reynolds number (Re) for water flow in the circular pipe is approximately 160,920.
The Reynolds number (Re) is calculated using the formula:
Re = (density * velocity * diameter) / viscosity
Given:
Diameter of the pipe = 50 mm = 0.05 m
Density of water = 998 kg/m^3
Volumetric flow rate of water = 720 L/min = 0.012 m^3/s
Dynamic viscosity of water = 1.2 centipoise = 0.0012 kg/(m·s)
First, we need to convert the volumetric flow rate from L/min to m^3/s:
Volumetric flow rate = 720 L/min * (1/1000) m^3/L * (1/60) min/s = 0.012 m^3/s
Now we can calculate the velocity:
Velocity = Volumetric flow rate / Cross-sectional area
Cross-sectional area = π * (diameter/2)^2
Velocity = 0.012 m^3/s / (π * (0.05/2)^2) = 3.83 m/s
Finally, we can calculate the Reynolds number:
Re = (density * velocity * diameter) / viscosity
Re = (998 kg/m^3 * 3.83 m/s * 0.05 m) / (0.0012 kg/(m·s)) = 160,920.
LEARN MORE ABOUT Reynolds number here: brainly.com/question/31298157
#SPJ11
Vanessa purchases a retirement annuity that will pay her $1,000 at the end of every six months for the first nine years and $600 at the end of every month for the next five years. The annuity earns interest at a rate of 5.7% compounded quarterly. What was the purchase price of the annuity?
The purchase price of annuity, considering payments of $1,000 six months for first nine years and $600 every month for the next five years, with an interest rate of 5.7% compounded quarterly, is $20,707.17.
To determine the purchase price of the annuity, we need to calculate the present value of the future cash flows. Payments every six months for the first nine years:
Using the formula for the present value of an ordinary annuity, we have:
PV1 = PMT * (1 - (1 + r)^(-n)) / r where PV1 is the present value, PMT is the payment per period, r is the interest rate per period, and n is the total number of periods.
PMT1 = $1,000 (payment every six months)
r1 = 5.7% / 4 (quarterly interest rate)
n1 = 2 * 9 (since payments are made every six months for nine years)
Plugging in the values: PV1 = $1,000 * (1 - (1 + 0.0575)^(-2*9)) / 0.0575. Calculating this gives us the present value of the payments every six months for the first nine years.
Monthly payments for the next five years:
Using the same formula, we have:
PV2 = PMT * (1 - (1 + r)^(-n)) / r
PMT2 = $600 (monthly payment)
r2 = 5.7% / 12 (monthly interest rate)
n2 = 12 * 5 (since payments are made monthly for five years)
Plugging in the values:
PV2 = $600 * (1 - (1 + 0.00475)^(-12*5)) / 0.00475
Calculating this gives us the present value of the monthly payments for the next five years.
To find the total present value, we add PV1 and PV2:
Total PV = PV1 + PV2
Summing up the two present values gives us the purchase price of the annuity, which is approximately $20,707.17. This is the amount Vanessa needs to pay initially to receive the specified future cash flows from the annuity.
Learn more about purchase price here:
https://brainly.com/question/19578140
#SPJ11
Suppose that the function g is defined, for all real numbers, as follows. g(x)= ⎩
⎨
⎧
2
1
x+1
(x−1) 2
− 2
1
x+2
if x≤−2
if −2
if x≥2
Find g(−2),g(0), and g(5). g(−2)=
g(0)=
g(5)=
We are given a piecewise-defined function g and are required to find g(−2), g(0), and g(5).The:g(−2)= −1/3, g(0)= 1, and g(5)= −3/14.:We will find g(−2), g(0), and g(5) one by one,Let us begin with g(−2):
According to the given function,
When x ≤ −2,g(x) = 2When x = −2,g(x) = undefined
When −2 < x < 1,g(x) = 1 / (x − 1)2When x = 1,g(x) = undefined
When 1 < x < 2,g(x) = 1 / (x − 1)2When x ≥ 2,g(x) = −2 / (x + 2)For g(−2),
we use the function value when x ≤ −2,So g(−2) = 2 / 1 = 2
Now, we calculate g(0):When x ≤ −2,g(x) = 2
When −2 < x < 1,g(x) = 1 / (x − 1)2When x = 1,g(x) = undefined
When 1 < x < 2,g(x) = 1 / (x − 1)2
When x ≥ 2,g(x) = −2 / (x + 2)
For g(0), we use the function value
when −2 < x < 1,So g(0) = 1 / (0 − 1)2 = 1 / 1 = 1
Finally, we find g(5):When x ≤ −2,g(x) = 2
When −2 < x < 1,g(x) = 1 / (x − 1)2
When x = 1,g(x) = undefined
When 1 < x < 2,g(x) = 1 / (x − 1)2
When x ≥ 2,g(x) = −2 / (x + 2)For g(5),
we use the function value when x ≥ 2,So g(5) = −2 / (5 + 2) = −2 / 7
Hence, we get g(−2) = −1/3, g(0) = 1, and g(5) = −3/14.
To know more about function visit:
https://brainly.com/question/30721594
#SPJ11
1.
If the inputs to 74147 are A9....A1=111011011 (MSB....LSB), the
output will be ___
1010
1111
1001
0110
2.
An Enable input to a decoder not only controls it's operation
b
1. If the inputs to 74147 are A9....A1=111011011 (MSB....LSB), the output will be 1001.
The BCD-to-Seven Segment decoder (BCD-to-7-Segment decoder/driver) is a digital device that transforms an input of the four binary bits (Nibble) into a seven-segment display of an integer output.
A seven-segment display is the device used for displaying numeric digits and some alphabetic characters.
The 74147 IC is a 10-to-4 line priority encoder, which contains the internal circuitry of 10-input AND gates in order to supply binary address outputs corresponding to the active high input condition.
2. An Enable input to a decoder not only controls its operation, but also is used to turn off or disable the decoder output. When the enable input is low or zero, the decoder output will be inactive, indicating a "blanking" or "turn off" state. The enable input is generally used to turn on or off the decoder output, depending on the application. The purpose of the enable input is to disable the decoder output when the input is in an inactive or low state, in order to reduce power consumption and avoid interference from other sources. The enable input can also be used to control the output of multiple decoders by applying the same signal to all of the enable inputs.
To know more about binary bits visit:
https://brainly.com/question/30462196
#SPJ11
Let V be the vector space of polynomials in t with inner product defined by ⟨f,g⟩=∫ −1
1
f(t)g(t)dt Apply the Gram-Schmidt algorith to the set {1,t,t 2
,t 3
} to obtain an orthonormal set {p 0
,p 1
,p 2
,p 3
}
Previous question
The Gram-Schmidt algorithm is a way to transform a set of linearly independent vectors into an orthogonal set with the same span. Let V be the vector space of polynomials in t with inner product defined by ⟨f,g⟩=∫ −1
1
. We need to apply the Gram-Schmidt algorithm to the set {1, t, t², t³} to obtain an orthonormal set {p₀, p₁, p₂, p₃}. Here's the To apply the Gram-Schmidt algorithm, we first choose a nonzero vector from the set as the first vector in the orthogonal set. We take 1 as the first vector, so p₀ = 1.To get the second vector, we subtract the projection of t onto 1 from t. We know that the projection of t onto 1 is given byproj₁
(t) = (⟨t, 1⟩ / ⟨1, 1⟩) 1= (1/2) 1, since ⟨t, 1⟩ = ∫ −1
1
t dt = 0 and ⟨1, 1⟩ = ∫ −1
1
t² dt = 2/3 and ⟨t², p₁⟩ = ∫ −1
1
1
t³ dt = 0, ⟨t³, p₁⟩ = ∫ −1
1
(t³)(sqrt(2)(t - 1/2)) dt = 0, and ⟨t³, p₂⟩ = ∫ −1
1
To know more about polynomials visit:
https://brainly.com/question/11536910
#SPJ11
3. Another student explains to you that the order of subtraction doesn't really matter in either the slope or the distance formula. Explain whether his statement is correct.
The student's statement that the order of subtraction doesn't matter in either the slope or the distance formula is not correct.
In mathematical formulas, the order of operations is crucial, and changing the order of subtraction can lead to different results. Let's examine the two formulas separately to understand why this is the case. Slope formula: The slope formula is given by the equation (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on a line. The numerator represents the difference in y-coordinates, while the denominator represents the difference in x-coordinates. If we change the order of subtraction in the numerator or denominator, we would obtain different values. For example, if we subtract y1 from y2 instead of y2 from y1, the sign of the slope will be reversed.
Distance formula: The distance formula is given by the equation sqrt((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are two points in a plane. The formula calculates the distance between the two points using the Pythagorean theorem. Similarly, if we change the order of subtraction in either (x2 - x1) or (y2 - y1), the result will be different, leading to an incorrect distance calculation.
In both cases, the order of subtraction is significant because it determines the direction and magnitude of the difference between the coordinates. Changing the order of subtraction would yield different values and, consequently, incorrect results in the slope or distance calculations. Therefore, it is important to maintain the correct order of subtraction in these formulas to ensure accurate mathematical calculations.
To learn more about slope formula click here:
brainly.com/question/28553357
#SPJ11
Please answer the following astrophisics questions with explanations.Thank you we value your time and efforts. (b) Consider another binary with orbital period T = 49.94 yr. The com- ponents A and B have masses MA and MB respectively. Assume that the orbits are circular, with radii TA and rg respectively. (i) Apply Kepler's law to both this system and the Sun-Earth system. Hence, show that the orbital period expressed in years (Tyrs), is given by (a/A)³ T² yrs [(MA + MB)/Mo] = where A is the mean sun-earth distance. [ 5 marks] (ii) The trigonometric parallax of the system is P = 0.377" while the an- gular extent a of the semi-major axis of the relative ellipse is 7.62". Sketch a diagram of the system, showing both the separation a between the compo- nents and a. Hence, determine the ratio a/A for the system. [6 marks] (iii) The ratio of the distances of A and B from the centre of mass is 0.466. Determine the mass of each component in terms of the mass of the Sun. [ 6 marks] 3
(i) The required relation is (MA + MB)/Mo = (a/A)³ T² yrs.
(ii) The required ratio is 7.20.
(iii) MA/Mo = 0.413 and MB/Mo = 0.587.
Part (i) We are given the period T of the binary star system as 49.94 years.
The masses of the two components are MA and MB respectively.
Their orbits are circular and have radii TA and TB.
By Kepler's law: (MA + MB) TA² = (4π²)TA³/(G T²) (MA + MB) TB² = (4π²)TB³/(G T²) where G is the universal gravitational constant.
Now, let A be the mean sun-earth distance.
Therefore, TA/A = (1 au)/(TA/A) and TB/A = (1 au)/(TB/A).
Hence, (MA + MB)/Mo = ((TA/A)³ T² yrs)/[(A/TA)³ G yrs²/Mo] = ((TB/A)³ T² yrs)/[(A/TB)³ G yrs²/Mo] where Mo is the mass of the sun.
Thus, (MA + MB)/Mo = (TA/TB)³ = (TB/TA)³.
Hence, (MA + MB)/Mo = [(TB/A)/(TA/A)]³ = (a/A)³, where a is the separation between the stars.
Therefore, (MA + MB)/Mo = (a/A)³.
Hence, the required relation is (MA + MB)/Mo = (a/A)³ T² yrs.
This relation is identical to that for the Sun-Earth system, with a different factor in front of it.
Part (ii) Let the distance to the binary system be D.
Therefore, D = 1/P = 2.65 kpc (kiloparsec).
Now, let M be the relative mass of the two components of the binary system.
Therefore, M = MB/MA. By Kepler's law, we have TA/TB = (MA/MB)^(1/3).
Therefore, TB = TA (MA/MB)^(2/3) and rg = a (MB/(MA + MB)).
We are given a = 7.62" and P = 0.377".
Therefore, TA = (P/A)" = 7.62 × (A/206265)" = 0.000037 A, and rg = 0.0000138 a.
Therefore, TB = TA(MA/MB)^(2/3) = (0.000037 A)(M)^(2/3), and rg = 0.0000138 a = 0.000105 A(M/(1 + M)).
We are required to find a/A = rg/TA. Hence, (a/A) = (rg/TA)(1/P) = 0.000105/0.000037(0.377) = 7.20.
Therefore, the required ratio is 7.20.
Part (iii) The ratio of the distances of A and B from the center of mass is 0.466.
Therefore, let x be the distance of A from the center of mass.
Hence, the distance of B from the center of mass is 1 - x.
Therefore, MAx = MB(1 - x), and x/(1 - x) = 0.466.
Therefore, x = 0.316.
Hence, MA/MB = (1 - x)/x = 1.16.
Therefore, MA + MB = Mo.
Thus, MA = Mo/(1 + 1.16) = 0.413 Mo and MB = 0.587 Mo.
Therefore, MA/Mo = 0.413 and MB/Mo = 0.587.
(i) The required relation is (MA + MB)/Mo = (a/A)³ T² yrs.
(ii) The required ratio is 7.20.
(iii) MA/Mo = 0.413 and MB/Mo = 0.587.
Learn more about center of mass
brainly.com/question/8662931
#SPJ11
Verify the following Hoare triples:
3.1 {x = y} if (x = 0) then x := y + 1 else z := y + 1 {(x = y + 1) ⋁ (z = x + 1)}
3.2 {{y > 4} if (z > 1) then y:= y + z else y:= y − 1 endif {y > 3}ang
3.3 {3 ≤ |x| ≤ 4} if x < 0 then y := -x else y := x endif {2 ≤ y ≤ 4}
Hint: First rewrite each if-then-else statement as its guarded-command equivalent before calculating a new precondition
Hoare triples can be defined as a way of proving the correctness of programs through a method that uses assertions. Here, the following Hoare triples are verified.
3.1 {x = y} if (x
= 0) then x :
= y + 1 else z :
= y + 1 {(x
= y + 1) ⋁ (z
= x + 1)}Hoare triple can be written as follows: Precondition {x = y} is given where x and y are variables.If statement is used with the condition x
=0. Therefore, the following Hoare triple is obtained:{x
=y and x
=0}->{x
=y+1}.The first condition x
=y is maintained if the if-statement is false. The second condition x
=y+1 will hold if the if-statement is true. The or operator represents this with (x
=y+1)⋁(z
=x+1). 3.2 {{y > 4} if (z > 1) then y:
= y + z else y:
= y − 1 endif {y > 3}} Hoare triple can be written as follows: Precondition {y>4} is given where y is a variable.If statement is used with the condition z>1. Therefore, the following Hoare triple is obtained:{y>4 and z>1}->{y>3}.The first condition y>4 is maintained if the if-statement is false.
The second condition y>3 will hold if the if-statement is true. 3.3 {3 ≤ |x| ≤ 4} if x < 0 then y := -x else y := x endif {2 ≤ y ≤ 4}Hoare triple can be written as follows: Precondition {3≤|x|≤4} is given where x and y are variables. If statement is used with the condition x<0. Therefore, the following Hoare triple is obtained:{3≤|x|≤4 and x<0}->{2≤y≤4}.If the condition is false, y=x and the precondition is satisfied because |x| is either 3 or 4. If the condition is true, y=-x and the precondition is still satisfied. The resulting range of y is [2, 4] because the absolute value of x is between 3 and 4.
To know more about programs visit:
https://brainly.com/question/30613605
#SPJ11