Answer: c = 10, d = 7
Step-by-step explanation:
To solve this system using the linear combination method, we want to eliminate one of the variables, either c or d, by adding or subtracting the two equations. One way to do this is to add the two equations together, which will cancel out the d terms:
(c + d) + (c - d) = 17 + 3
2c = 20
c = 10
Now we can substitute this value of c into either equation to solve for d:
c - d = 3
10 - d = 3
d = 7
Therefore, the solution to the system is:
c = 10, d = 7.
Answer:
c=10 and d=7
Step-by-step explanation:
Use linear combination to solve the following system of equations.
Linear combination is synonymous with the method of elimination. The goal of elimination is to "eliminate" one of the variables so that we may solve for the other.
[tex]\left\{\begin{array}{ccc}c+d=17\\c-d=3\end{array}\right[/tex]
Notice how the "d" term has opposite signs in the system. We can add these two equations together to "eliminate" d.
[tex](c+d=17)+(c-d=3)=\boxed{2c=20}\\\\\therefore \boxed{\boxed{c=10}}[/tex]
We now know what "c" equals, plug this value into either of the equations and solve for "d."
[tex]c=10\\\\\Longrightarrow 10+d=17\\\\\therefore \boxed{\boxed{d=7}}[/tex]
Thus, the system is solved. c=10 and d=7.
Amelia rented a DVD and it was due to be returned on 26 November.
She actually returned it to the shop on 12 December.
The rental shop applies a fine for 9p for everyday the DVD is over due
Work out the total fine paid by Amelia
Give your answer in £
Amelia paid a total fine of £1.44 for returning the DVD 16 days overdue.
To calculate the total fine paid by Amelia, we need to determine the number of days the DVD was overdue and then multiply that by the fine rate.
The rental period for the DVD is from 26 November to 12 December. To find the number of days overdue, we subtract the due date from the actual return date:
12 December - 26 November = 16 days
Since the fine rate is 9p per day, we multiply the number of days overdue by the fine rate:
16 days × £0.09/day = £1.44
Therefore, Amelia paid a total fine of £1.44 for returning the DVD 16 days overdue.
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fill in the blanks. (enter the range in interval notation.) function alternative notation domain range y
The range of this function can be represented using the interval [-1,1]. However, if we have a function h(x) = x^3, we know that the output values can take on any real number, so the range of this function can be represented using the interval (-∞, ∞).
Interval notation is a shorthand way of representing a range of numbers using brackets and parentheses. For example, the interval [0,1] represents all real numbers between 0 and 1, including 0 and 1 themselves. The interval (0,1) represents all real numbers between 0 and 1, excluding 0 and 1 themselves.
To represent the domain of a function using interval notation, we consider the set of all input values for which the function is defined. For example, if we have a function f(x) = x^2, we know that this function is defined for all real numbers. Therefore, the domain of this function can be represented using the interval (-∞, ∞).
To represent the range of a function using interval notation, we consider the set of all output values that the function can take. This can be a bit trickier, as some functions may take on a continuous range of values, while others may only take on a finite set of values. For example, if we have a function g(x) = sin(x), we know that the output values will always be between -1 and 1. Therefore, the range of this function can be represented using the interval [-1,1]. However, if we have a function h(x) = x^3, we know that the output values can take on any real number, so the range of this function can be represented using the interval (-∞,∞).
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Complete Question:
Fill in the blanks. (Enter the range in interval notation.) Function Alternative Notation Domain Range y = y = cos-1 x -1 < x< 1
prove that h is a subgroup of s5. how many elements are in h? is your argument valid when 5 is replaced by any ? how many elements are in h when 5 is replaced by any ?
There are (n-1)! ways to permute n-1 elements.
What is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.
In order to prove that a subset H of a group G is a subgroup of G, we need to show that H satisfies the three conditions of a subgroup:
Closure: for any a, b in H, the product ab is also in H.
Identity: H contains the identity element of G.
Inverses: for any a in H, the inverse of a in G is also in H.
Let H be the subset of S5 consisting of all permutations that fix the element 1. In other words, H consists of all permutations that map 1 to 1. We will show that H is a subgroup of S5.
Closure: Let a and b be two permutations in H. Then a(1) = 1 and b(1) = 1. Therefore, (ab)(1) = a(b(1)) = a(1) = 1. Hence, ab fixes 1 and is in H.
Identity: The identity permutation e always fixes 1. Therefore, e is in H.
Inverses: Let a be a permutation in H. We need to show that [tex]a^-1[/tex] is also in H. Since a fixes 1, we know that [tex]a^{-1}[/tex] also fixes 1. Moreover, since a is a bijection, we know that [tex]a^{-1}[/tex] is also a bijection. Therefore, [tex]a^{-1}[/tex] is a permutation of S5 that fixes 1, and hence, [tex]a^{-1}[/tex] is in H.
Since H satisfies the three conditions of a subgroup, we can conclude that H is a subgroup of S5.
How many elements are in H? We can count the number of elements in H by counting the number of ways we can permute the remaining four elements. There are 4! = 24 ways to permute four elements. Therefore, there are 24 elements in H.
Is this argument valid when 5 is replaced by any n? Yes, the argument is valid for any n. We can define H as the set of permutations in Sn that fix the element 1. The same three conditions hold, and we can conclude that H is a subgroup of Sn.
How many elements are in H when 5 is replaced by any n?
There are (n-1)! elements in H. We can count the number of elements in H by counting the number of ways we can permute the remaining n-1 elements. There are (n-1)! ways to permute n-1 elements. Therefore, there are (n-1)! elements in H.
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help im on a test and i need to get it right
The owner of the bookstore sells the used books for $6 each. J.
The price of a used book in the bookstore we need to calculate how much the owner is selling the books for.
The owner of the bookstore buys the used books from customers for $1.50 each.
The owner resells the used books for we need to multiply the cost price by 400%:
$1.50 x 400% = $1.50 x 4
= $6
The markup percentage for the used books is very high.
The owner is reselling the used books for four times the amount he paid for them.
This is a common practice in the used book industry as it allows the owner to make a profit on the books they sell.
It is important for customers to be aware of the markup and shop around for the best prices.
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What is the circumference of the circle? Use 3.14 for π.
circle with a segment drawn from the center of the circle to a point on the circle labeled 5 inches
31.40 inches
78.50 inches
15.70 inches
246.49 inches
Answer:
31.40 inches
Step-by-step explanation:
The circle has a radius of 5 inches (as the radius is drawn from the center to the point labeled 5 inches).
Pi (π) = 3.14
Circumference = 2 * pi * Radius
Substitute the radius of 5 inches: Circumference = 2 * 3.14 * 5
= 31.40 inches
So the circumference of the full circle is 31.40 inches.
The other options do not match the given radius of 5 inches and the formula for circumference.
Hence, the correct option is:
31.40 inches
For each pair of data sets, which is likely to have the greater standard deviation?
ages of thirty college students
ages of thirty high school students
Need help ASAP, will mark brainliest look at picture.
Answer:
24
Step-by-step explanation:
posabaly 24 cause 8 times three is 24 and with these it's length times width
Complete the 2 column proof below the reasons are already given so only the mathematical statement needs to be completed
Here is the completed two-column proof:
Given: ZA and B are complementary angles. ZB and ZC are complementary angles.
Reasons Statements
Given ZA + B = 90° and ZB + ZC = 90°
Definition of complementary angles |
ZA = 90° - B and ZB = 90° - ZC
Substitution property of equality |
90° - B = 90° - ZC
Subtraction property of equality |
ZA = ZC
Angles that have equal measure are congruent |
ZAZC
What are complementary angles?Complementary angles are a pair of angles that add up to 90 degrees. In other words, when you have two complementary angles, the sum of their measures is always 90 degrees. Each angle in a pair of complementary angles is said to be the complement of the other angle.
For example, if you have one angle that measures 30 degrees, its complement would measure 60 degrees, because 30 + 60 = 90. Similarly, if you have an angle measuring 45 degrees, its complement would be 45 degrees as well, because 45 + 45 = 90.
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find the indefinite integral. (use c for the constant of integration.) tan3 x sec6 x dx
The indefinite integral of tan^3(x) sec^6(x) dx is (1/5)sec^5(x) + (1/3)sec^3(x) + C, where C is the constant of integration.
To solve this integral, we can use the substitution u = sec(x) and du = sec(x)tan(x) dx.
Then, we can rewrite the integral as ∫tan^3(x) sec^6(x) dx = ∫tan^2(x) sec^5(x) sec(x) tan(x) dx = ∫(sec^2(x) - 1)sec^5(x) du.
Simplifying and integrating, we get (1/5)sec^5(x) - (1/3)sec^3(x) + C.
Therefore, The indefinite integral of tan^3(x) sec^6(x) dx is (1/5)sec^5(x) + (1/3)sec^3(x) + C, where C is the constant of integration.
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Jim has $84,410 in a savings account that earns 15% interest per year. How much will he have in 4 years?
We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
where:
A = final amount
P = principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case, we have:
P = $84,410
r = 15% = 0.15
n = 1 (compounded annually)
t = 4
Substituting these values into the formula, we get:
A = $84,410(1 + 0.15/1)^(1*4)
= $84,410(1.15)^4
= $148,982.74
Therefore, Jim will have $148,982.74 in 4 years.
suppose x and y have joint probability mass function (pmf) p(x = x, y = y) = x y 54 , x = 1, 2, 3, y = 1, 2, 3,
The given joint probability mass function defines the probabilities of the discrete random variables x and y taking on values 1, 2, or 3.
The probability p(x = x, y = y) is equal to xy/54 for all (x, y) in the set {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)}. To find the marginal probability mass functions for x and y, we sum the joint probabilities over all possible values of the other variable. That is,
p(x = x) = ∑ p(x = x, y = y) = ∑ xy/54, y=1 to 3
= (x/54)∑y=1 to 3 y
= (x/54)(1+2+3)
= (x/54)(6)
= x/9
Similarly, we have
p(y = y) = ∑ p(x = x, y = y) = ∑ xy/54, x=1 to 3
= (y/54)∑x=1 to 3 x
= (y/54)(1+2+3)
= (y/54)(6)
= y/9
Hence, the marginal probability mass functions for x and y are given by p(x) = x/9 and p(y) = y/9, respectively.
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HELPPPPP PLLLLSSSS WITH THISSSS
The answer for the question is D. That is the Pythagorean Theoram
John is saving money for a new phone which will cost $950. He already saved $150 and plans to save an additional $15 each week. Write an equation to find the number of weeks, x, that Joseph must save in order to afford the phone.
Answer: 15x + 150 = 950
Step-by-step explanation:
Let x equal the number of weeks.
He saves $15 per week, so 15 times the number of weeks, 15x.
He has already saved $150, so the money saved up over the weeks gets added to 150, 15x + 150.
all of the money he saves up has to equal 950, so 15x + 150 = 950.
I hope this helps!
Answer:
15x + 150 = 950
Step-by-step explanation:
I did dont paper I dont knwo how to upload it
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The tiles shown are placed in a bag. You randomly select one of the tiles, return it to the bag, and then randomly select another tile. What is the probability that the first number plus the second number is less than zero?
The numbers:
-4
-2
-1
2
I will give 30 points!
At a local high school, 95 students have permission to park on campus. Each month, the student council holds a "golden ticket & parking lottery. " The three lucky winners are given reserved parking spots next to the main entrance. Last month, the winning tickets were drawn by a student council member who is in Mr. Wilder's statistics class. When all three golden tickets went to & members of that class, some people thought the lottery had been rigged. There are 30 students in the statistics class, all of whom É are eligible to park on campus
The probability of all three golden tickets going to members of the statistics class by chance is low, leading to suspicion that the lottery was rigged.
The probability of one student from the statistics class winning a golden ticket is 30/95. The probability of a second student from the same class winning is 29/94, since one student has already won and there are now 29 eligible students in the class. The probability of a third student from the same class winning is 28/93, given that two students from the class have already won. Therefore, the probability of all three golden tickets going to members of the statistics class is (30/95) × (29/94) × (28/93) ≈ 0.00018, which is a very low probability. This supports the suspicion that the lottery may have been rigged. However, it is important to note that this is only a probability, and further investigation would be necessary to determine if the lottery was actually rigged or if this was just a rare occurrence.
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Write the equation for the parabola that has its x intercepts at (-2,0) and (-5,0) and its y intercept at (0,-4)
An equation for the parabola that has its x-intercepts at (-2, 0) and (-5, 0) and its y-intercept at (0, -4) is y = -2/5(x² + 7x + 10).
How to determine the factored or vertex form of a quadratic equation?In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:
f(x) = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Based on the information provided about the y-intercept and x-intercepts, we can write the quadratic function and determine the value of "a" as follows:
f(x) = (x + 2)(x + 5)
f(x) = x² + 2x + 5x + 10
f(x) = x² + 7x + 10
f(x) = a(x² + 7x + 10)
-4 = a(x² + 7x + 10)
-4 = a(0² + 7(0) + 10)
-4 = 10a
a = -4/10
a = -2/5
Therefore, the required quadratic function is given by:
y = a(x - h)² + k
y = -2/5(x² + 7x + 10)
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The number of hours of daylight in New York City d days after March 21, 2010 can be modeled by N(a) = 2.925 sin ( 3.65 ) + 12.18 Solve 11.5 = 2.925 sin (27 d) + 12.18 over the interval [0°, 720°). Using the inverse trigonometric functions, find a solution to the given equation that is reasonable in the context of the problem.
The equation is given, N(a) = 2.925 sin ( 3.65 ) + 12.18, which models the number of hours of daylight in New York City d days after March 21, 2010.
To solve the equation 11.5 = 2.925 sin (27 d) + 12.18 over the interval [0°, 720°), we need to isolate the sine function on one side of the equation.
Subtracting 12.18 from both sides, we get:
-0.68 = 2.925 sin (27 d)
Dividing both sides by 2.925, we get:
sin (27 d) = -0.2333
To find d, we need to use the inverse sine function ([tex]sin^{-1}[/tex]) on both sides:
27 d = [tex]sin^{-1}[/tex] (-0.2333)
Using a calculator, we find that [tex]sin^{-1}[/tex] (-0.2333) = -13.5° or -0.235 radians (rounded to three decimal places).
Dividing both sides by 27, we get:
d = -0.0087 radians / 27
d = -0.00032 radians (rounded to five decimal places)
To make sense of this answer in the context of the problem, we need to convert radians to days.
One complete cycle of the sine function occurs over 360 degrees or 2π radians. Therefore, over the interval [0°, 720°), there are two complete cycles or 4π radians.
To find the number of days, we can set up a proportion:
4π radians = 365 days - 80 days (March 21 to June 9)
Solving for one radian, we get:
1 radian = (365 - 80) days / 4π
1 radian ≈ 71.3 days
Substituting this value, we get:
d = -0.00032 radians x 71.3 days/radian
d ≈ -0.023 days
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What is the equation that qualify in this problems?
The solution is the coordinate point (-1, 4)
How to solve the system of equations?Here we need to solve the system of equations in the diagram. Notice that the system is already graphed, the solutions are all the points where the graphs intercept.
Here we can see that there is one interception point so there is only one soluition, which is at the coordinate point (-1, 4), so that is the solution of the system.
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Find the range of values of x for which
[tex]8 + 2x - {x}^{2} \geqslant 0 \\ 5 {x }^{2} - x - 4 > 0[/tex]
Answer:
Step-by-step explanation:
8 + 2x - x^2 >= 0
x^2 - 2x - 8 <= 0
(x - 1)^2 - 9 <= 0
(x - 1)^2 <= 9
x - 1 <= +- 3
-3 <= x - 1 <= 3
-2 <= x <= 4
An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 140 lb and 201 lb. The new population of pilots has normally distributed weights with a mean of 150 lb and a standard deviation of 31. 5 lb. Click here to view page 1 of the standard normal distribution Click here to view page 2 of the standard normal distribution. A. If a pilot is randomly selected, find the probability that his weight is between 140 lb and 201 lb. The probability is approximately (Round to four decimal places as needed. ) b. If 32 different pilots are randomly selected, find the probability that their mean weight is between 140 lb and 201 lb. The probability is approximately. (Round to four decimal places as needed. ) c. When redesigning the ejection seat, which probability is more relevant? O A. Part (b) because the seat performance for a single pilot is more important. O B. Part (b) because the seat performance for a sample of pilots is more important. C. Part (a) because the seat performance for a sample of pilots is more important D. Part (a) because the seat performance for a single pilot is more important. Click to select your answer(s)
a) The probability that x is between 140 and 201, P(140<X<201) is 0.5719.
b) The probability that their mean weight is between 140 lb and 201 lb is 0.9637.
c) Option d is correct because the seat performance for a single pilot is more important as compared to the sample of pilots.
What is the probability?
The probability of an occurrence is a number used in science to describe how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.
Here, we have
Given: An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 140 lb and 201 lb.
a) We will find probability that x is between 140 and 201, P(140<X<201)
Population mean μ = 150
Population standard deviation σ = 31.5
= P(x- μ/σ < z < y- μ/σ)
= P(140 - 150/31.5 < z < 201- 150/31.5)
= P(-0.317469 < z < 1.619047)
= P(z < 1.619047) - P(z <-0.317469)
Now, we find the value of and we get
= 0.9473 - 0.3754
= 0.5719
Hence, the probability that x is between 140 and 201, P(140<X<201) is 0.5719.
b) We will find probability that x is between 140 and 201, P(140<X<201)
Population mean μ = 150
Population standard deviation σ = 31.5
Sample size n = 32
= P(x- μ/σ/√n < z < y- μ/σ/√n)
= P(140 - 150/31.5/√32 < z < 201- 150/31.5/√32)
= P(-1.79582 < z < 9.15871)
=P(z < 9.15871) - P(z<-1.79582)
Now, we find the value of z and we get
= 1 - 0.0363
= 0.9637
Hence, the probability that their mean weight is between 140 lb and 201 lb is 0.9637.
c) Option d is correct because the seat performance for a single pilot is more important as compared to the sample of pilots. This is because there are only two pilots, so seat performance for a single pilot is more important.
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For the following composite function, find an inner function u- g(x) and an outer function y-f (u such that y - f(a&), Then calculate Cx Select the correct choice below and fill in the answer box to complete your choice. dy dd dx du For the following composite function, find an inner function u-g(x) and an outer function y-f u) such that y-f(g x y Then calculate y 7 +9 sinx Select the correct choice below and fill in the answer box to complete your choice dy dy dy Calculate the derivative of the following function y-7(7x3+8) -6 y-7(7x3+8)6 dy dx Calculate the derivative of the following function. y sec(2x -1) dy dx
We need to find an inner function u=g(x) and an outer function y=f(u) such that y=f(g(x)), and then find dy/dx in terms of du/dx.
Let u = g(x) = a + x, where a is a constant. Then y = f(u) = f(a + x).
If y = f(a + x), then we can express y in terms of u as y = f(u) = f(g(x)) = f(a + x).
Using the chain rule, we have:
dy/dx = dy/du * du/dx
We can find dy/du by taking the derivative of f(u) with respect to u:
dy/du = f'(u)
And we can find du/dx by taking the derivative of g(x) with respect to x:
du/dx = 1
Therefore, we have:
dy/dx = dy/du * du/dx = f'(u) * 1
So the correct answer is: dy/du.
For the second question:
We have y = 7(7x^3 + 8)^-6.
Using the power rule and the chain rule, we have:
dy/dx = -6 * 7 * (7x^3 + 8)^-7 * d/dx(7x^3 + 8)
= -294 * (7x^3 + 8)^-7 * 21x^2
So the correct answer is: -294(7x^3 + 8)^-7 * 21x^2.
For the third question:
We have y = sec(2x - 1).
Using the chain rule and the fact that d/dx(sec(x)) = sec(x)tan(x), we have:
dy/dx = d/dx(sec(2x - 1))
= sec(2x - 1)tan(2x - 1) * d/dx(2x - 1)
= sec(2x - 1)tan(2x - 1) * 2
So the correct answer is: 2sec(2x - 1)tan(2x - 1).
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Suppose 30 students participate in a math contest. For each student R there exist students S andM (all three are different students) such that the height of student R equals the average height ofall three students. Find the greatest possible number of different values of all 30 student heights.
The greatest possible number of different values of all 30 student heights is 30.
Let the heights of students R, S, and M be r, s, and m, respectively. Then we have:
r = (s + m + r) / 3
2r = s + m
Similarly, we have:
s = (r + m + s) / 3
m = (r + s + m) / 3
Simplifying these two equations gives:
2s = r + m
2m = r + s
Adding all three equations, we get:
3r + 3s + 3m = 2r + 2s + 2m
r + s + m = 0
This means that the sum of all 30 student heights is 0.
Then the smallest possible sum of 30 distinct integers is 1 + 2 + ... + 30 = 465, and the largest possible sum is 465 + 29 + 28 + ... + 1 = 930.
We can then assign each of these 30 heights to a different student, with the additional condition that for each student R, there exist students S and M (all three are different students) such that the height of student R equals the average height of all three students.
Therefore, the greatest possible number of different values of all 30 student heights is 30.
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which graph shows the image of the triangle reflected across the line of reflection shown
The image is reflected completely opposite to the given figure in the graph is having the following points (2,2), (4,4) and (9,0).
The points which are having the given triangle are,
(2, 4)(4, 2)(9, 6)To reflect the given figure completely to the opposite side of the given line, we have to invert the above given points. Simple it is meaning to flip the triangle without disturbing on point.
The points which are having the flipped triangle figure are,
(2,2)(4,4)(9,0)From the above analysis, the flipped triangle which is the triangle reflected across the line is constructed.
The reflected triangle's diagram is attached below,
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The given question is missing graphs, I am attaching them below:
x < 16. Which of the following statements is the best way to describe the value of x? (3 points) a The value of x is less than 16. b The value of x is more than 16. c The value of x is at most 16. d The value of x is at least 16.
Answer: The correct answer is a. The value of x is less than 16.
Step-by-step explanation:
a. The value of x is less than 16.
b The value of x is more than 16.
c The value of x is at most 16.
d The value of x is at least 16.
We will eliminate the choice of b and c because b is the description of x > 16, and c is the description of x ≥ 16.
The correct answer is a. The value of x is less than 16.
d would the description of x ≤ 16, meaning that is at least 16, meaning that x can be 16.
in this problem you will compute the value of ∑=0[infinity](23).
The series ∑=0infinity diverges, meaning it does not have a finite sum. The sequence of series of partial sums increases without bound, meaning it diverges.
The series ∑=0infinity is an infinite sum of the constant value 23. To determine whether this series converges or diverges, we can use the definition of convergence: if the sequence of partial sums converges to a finite value, then the series converges. Otherwise, if the sequence of partial sums diverges or oscillates, then the series diverges.
The sequence of partial sums for this series is:
S1 = 23
S2 = 23 + 23 = 46
S3 = 23 + 23 + 23 = 69
...
As we can see, the sequence of partial sums increases without bound, meaning it diverges. Therefore, the series ∑=0infinity does not have a finite sum and is said to be divergent.
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helpppp show work pls
Step-by-step explanation:
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ANSWER:
18
STEP-BY-STEP:
To find the maximum value of P, we need to evaluate P at each vertex.
P(0,0)=3(0)+2(0)=0+0=0
P(0,22/3)=3(0)+2(22/3)=0+44/3=44/ 3
Now
P(16/5,0)=3(16/5)+2(0)=48/5+0=48/ 5
P(2,6)=3(2)+2(6)=6+12=18
Therefore, the maximum value of P is *18* when x = *2* and y = *6*.
Answer:
18
Step-by-step explanation:
To find the maximum value of p, substitute the value of x and the value of y of each vertices in the equation and then compare the results
p = 3x + 2y
For (0,0)
p = 3(0) + 2 (0)
For (0,7.3)
p = 3(0) + 2 (7.3) = 0
For (2,6)
p = 3(2) + 2(6) = 18
For (3.2,0)
p = 3(3.2) + 2(0) = 9.6
therefore the maximum value of p = 18
NECO QUESTEN
o solve the quadratic equation
x² + 3x - 28 = 0, Using
factorisation method
2 find the derivative of
2-2ut 4 with
respect to x
find the Compound interest
for 3 years at
4 The Th and 12th terms of
Arithmetic Ropression
are 50 and 65 respectively.
Find the Son of its firs
70 terms.
* 8,000. 00
es AUCnum
an
The first question requires finding the roots of a quadratic equation using factorization, the second question requires finding the derivative of a given function with respect to x, the third question requires calculating compound interest for a given period, and the fourth question requires finding the sum of the first 70 terms of an arithmetic progression.
To solve the quadratic equation x² + 3x - 28 = 0 using factorization, we need to find two numbers whose sum is 3 and whose product is -28. The two numbers are 7 and -4. Therefore, we can write the quadratic equation as (x + 7)(x - 4) = 0, which gives the roots x = -7 and x = 4.
To find the derivative of 2-2ut4 with respect to x, we need to treat t as a constant and apply the power rule of differentiation. The derivative is -8ut3(d/dx)(2-2ux) = -8ut3(-4u) = 32u2t3.
To find the compound interest for 3 years at 8,000.00 with an annual interest rate of 10%, we can use the formula A = P(1 + r/n)nt, where A is the total amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years. In this case, P = 8,000.00, r = 10%, n = 1 (since interest is compounded annually), and t = 3. Plugging in these values, we get A = 8,000.00(1 + 0.10/1)1(3) = 10,480.00. Therefore, the compound interest for 3 years is 2,480.00.
To find the sum of the first 70 terms of an arithmetic progression whose 10th and 12th terms are 50 and 65, respectively, we need to first find the common difference (d) and the first term (a1). Using the formula for the nth term of an arithmetic progression, we can write the equations a10 = a1 + 9d = 50 and a12 = a1 + 11d = 65. Solving these equations simultaneously, we get a1 = 22 and d = 3. Therefore, the sum of the first 70 terms is given by the formula S70 = (n/2)(2a1 + (n-1)d), where n = 70. Plugging in the values, we get S70 = (70/2)(2(22) + (70-1)3) = 3,955.
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6. find the inverse laplace transform of the function i(s) = (β 2
The inverse Laplace transform of the function i(s) = (β^2)/(s^2 + β^2) is given by f(t) = β sin(βt).
The Laplace transform is a mathematical technique used to solve differential equations by transforming them from the time domain to the frequency domain. The inverse Laplace transform is then used to transform the solution back from the frequency domain to the time domain.
In this case, the Laplace transform of the function i(t) is given by I(s) = β^2/(s^2 + β^2). To find the inverse Laplace transform, we use the partial fraction decomposition technique to break down the function into simpler terms.
We can rewrite I(s) as I(s) = β^2/[(s + iβ)(s - iβ)]. Using partial fraction decomposition, we can express I(s) as I(s) = A/(s + iβ) + B/(s - iβ), where A and B are constants to be determined.
Solving for A and B, we get A = B = β/2i. We can now use the inverse Laplace transform table to find the inverse Laplace transform of each term.
The inverse Laplace transform of A/(s + iβ) is β/2 e^(-iβt), and the inverse Laplace transform of B/(s - iβ) is β/2 e^(iβt). Adding these two terms together gives us the final solution of f(t) = β sin(βt).
Learn more about Laplace transform here: brainly.com/question/31041670.
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What is the critical angle between two mystery transparent materials, in degrees? na = 1.65 and nB = 2.12. Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement.
The critical angle between these two materials does not exist.
The critical angle θc is given by the equation sin θc = nB/na, where na and nB are the refractive indices of the two materials. Substituting na = 1.65 and nB = 2.12 into this equation, we get sin θc = 2.12/1.65 = 1.2848. However, since the sine function is only defined between -1 and 1, this means there is no real value of θc that satisfies this equation. Therefore, the critical angle between these two materials does not exist.
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https://brainly.com/question/15009181
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