Answer:
100 times
Step-by-step explanation:
It is predicted that a 1 or a 6 will be rolled 50 times in 150 rolls of a standard number cube.
A standard number cube has six faces, each numbered from 1 to 6.
The probability of rolling a 1 or a 6 on any given roll is,
P = 2/6
P = 1/3
Since, there are two favorable outcomes out of six possible outcomes.
Hence, To predict how many times a 1 or a 6 will be rolled in 150 rolls, we can use the formula:
Number of times = Probability x Total number of rolls
So, the number of times a 1 or a 6 is expected to be rolled in 150 rolls is:
Number of times = (1/3) x 150 = 50
Therefore, it is predicted that a 1 or a 6 will be rolled approximately 50 times in 150 rolls of a standard number cube.
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Need help please and thank you!
The value of angle 1 , angle 2 and angle 3 are 60°, 30° and 60° respectively
What is a regular polygon?A polygon is called regular if it has equal sides and angles. Thus, a regular triangle is an equilateral triangle, and a regular quadrilateral is a square.
An hexagon is a six sided polygon. This means that;
The sum of angle in an hexagon = (6-2)180 = 180× 4 = 720
Therefore each angle in the hexagon = 720/6 = 120°
The angles are equally bisected
therefore, angle 3 = 120/2 = 60°
angle 1 = 180-(60+60)
= 180-120 = 60°
angle 2 = 180-(90+60)
= 180-150
= 30°
therefore the value of angle 1 , angle 2 and angle 3 are 60°, 30° and 60° respectively
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2,900 dollars is placed in an account with an annual interest rate of 9%. how much will be in the account after 13 years to the nearest cent .
Answer:$8,890.83
Step-by-step explanation:
At a certain farm, there are horses, goats, and sheep. The ratio of the number of horses to the number of goats is 4 to 3. The ratio of the number of horses to the number of sheep is 3 to 2. If there are 24 sheep at the farm, how many goats are at the farm? A 18 B 24 C 27 D 36 E 48
Answer: C 27
Step-by-step explanation:
there would be 24 sheep, which means there is 36 horses.
if ratio from horses to goats is 4-3
then there is only 27 goats.
Juro circles of radii 5cm and 3cm intersect at two points and the distance between their centres is 4cm. Find the length of the common chord
By using Pythagorean theorem, the length of the common chord is approximately 4.58 cm.
What is the Pythagorean theorem?
The Pythagorean theorem is a fundamental result in Euclidean geometry that describes the relationship between the three sides of a right-angled triangle.
In equation form, this can be written as:
[tex]c^2 = a^2 + b^2[/tex]
where c is the length of the hypotenuse, and a and b are the lengths of the other two sides (also known as the legs) of the right-angled triangle.
Let O1 and O2 be the centers of the circles with radii 5cm and 3cm, respectively, and let A and B be the points of intersection of the circles.
Let O1 and O2 be the centers of the circles with radii 5 cm and 3 cm, respectively, and let A and B be the points of intersection of the circles. Then, by the Pythagorean theorem, we have:
[tex]$$\begin{aligned} AB^2 &= AO_1^2 - BO_1^2 \ &= (5^2 - 2^2) , \text{cm}^2 \ &= 21 , \text{cm}^2 \end{aligned}$$[/tex]
Therefore, the length of the common chord AB is:
[tex]$$AB = \sqrt{21} \approx 4.58 , \text{cm}$$[/tex]
Thus, the length of the common chord is approximately 4.58 cm.
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HELP ASAP i give you brainleast
graphing quadratic functions
Some of the features of the quadratic function y = 2(x - 2)² + 3 are
Vertex = (2, 3)a = 2. Others are added belowCompleting the features of the quadratic functionsThe vertex form of a quadratic equation is
y = a(x - h)² + k
Where
Vertex = (h, k)Leading coefficient = aAxis of symmetry: x = hRange: y ≥ k if a > 0, otherwise y ≤ kIncreasing on: (h, ∝) if a > 0, otherwise (-∝, h)Decreasing on: (-∝, h) if a > 0, otherwise (h, ∝)Using the above features, we have the following key features
Quadratic function 1
y = 2(x - 2)² + 3
Vertex = (2, 3)a = 2Axis of symmetry: x = 2Domain = (-∝, ∝)Range: y ≥ 2 Increasing on: (2, ∝)Decreasing on: (-∝, 2)Quadratic function 2
y = 3(x + 2)² - 2
Vertex = (-2, -2)a = 3Axis of symmetry: x = -2Domain = (-∝, ∝)Range: y ≥ -2 Increasing on: (-2, ∝)Decreasing on: (-∝, -2)Read more about quadratic functions at
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Divide. Express your answer in simplest form.
2 1/2 ÷ 2 1/6
Answer:
15/13 OR 1.154
Step-by-step explanation:
2 1/2=5/2
2 1/6=13/6
5/2 / 13/6
=5/2 x 6/13
=30/26
=15/13
=1.15384615385
≈ 1.154
Sanskar invested 20% of money h le received every month's his total investment is ₹ 18000 per month find his total money gain per month
By technicality, he earns 18000*5 which equals 90000, however after his investments, it is 72000.
PLEASE SHOW WORK!!!!!!!!!
In response to the given question, we can state that Rounding this to the Pythagorean theorem nearest inch gives an answer of [tex]$\boxed{\textbf{(D) }45}$[/tex]
what is Pythagorean theorem?The Pythagorean Theorem is the foundational Euclidean geometry relationship among a right triangle's three sides. The area of a cube with the velocity vector side is the sum of something like the areas of squares that have the other two sides, according to this rule. The rectangle that spans the slope of a triangular shape across the sharp angle equals the total of the rectangles that span its sides, as defined by the Pythagorean Theorem. In general algebraic notation, it is written as a2 + b2 = c2.
The height of each triangle can be found using the Pythagorean theorem:
[tex]$15^2 - \left(\frac{20}{2}\right)^2 = 225 - 100 = 125$, so the height of each triangle is $\sqrt{125} = 5\sqrt{5}$.[/tex]
The overall height of the kite is the sum of the heights of the two triangles, which [tex]is $2 \cdot 5\sqrt{5} = 10\sqrt{5}$.[/tex]
Rounding this to the nearest inch gives an answer of [tex]$\boxed{\textbf{(D) }45}$[/tex]
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A softball coach has ordered softballs for two different leagues. The Junior League uses an 11-inch softball priced at $2.50 each. The Senior League uses a 12-inch softball priced at $3.50 each. The softball coach ordered a total of 120 softballs for $350.
How many of each size softball did the softball coach order?
11-inch softballs:
12-inch softballs:
The number of 11-inch softballs ordered is 70 and the number of 12-inch softballs ordered is 50
How many of each size of softball was ordered?a + b = 120 equation 1
2.50a + 3.50b = 350 equation 2
Where:
a = number of 11-inch softballs ordered b = number of 12-inch softballs orderedThe elimination method would be used to determine the number of each size of softball ordered.
Multiply equation 1 by 2.5
2.5a + 2.5b = 300 equation 3
Subtract equation 3 from equation 2
b = 50
Substitute for b in equation 1
a + 50 = 120
a = 120 - 50
a = 70
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A company claims their batteries will last an average of 100 days with a standard deviation of 15 days. If 20 of these batteries are selected what is the probability that the average life of the selected batteries is between 95 and 105?
The probability that the average life of the selected batteries is between 95 and 105 is 0.9292.
The company claims their batteries will last an average of 100 days with a standard deviation of 15 days. If 20 of these batteries are selected, the probability that the average life of the selected batteries is between 95 and 105 can be determined by the central limit theorem. In statistics, the central limit theorem (CLT) states that as the sample size increases, the distribution of the sample means approaches a normal distribution, irrespective of the population's underlying distribution. Therefore, the distribution of the sample means is a normal distribution with a mean equal to the population mean and standard deviation equal to population standard deviation divided by the square root of the sample size. Hence, the probability that the average life of the selected batteries is between 95 and 105 is the probability that the sample mean lies between 95 and 105.Using the z-score formula, z = (x - μ) / (σ / sqrt(n)), the z-scores can be calculated as follows:z1 = (95 - 100) / (15 / sqrt(20)) = -1.79z2 = (105 - 100) / (15 / sqrt(20)) = 1.79From the standard normal distribution table, the probability of z-score between -1.79 and 1.79 is 0.9292.Therefore, the probability that the average life of the selected batteries is between 95 and 105 is 0.9292.
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A school is building a rectangular stage for its chorus. The stage must have a width of feet. The area of the stage must be at least square feet. (The stage must hold all the singers. ) Write an inequality that describes the possible lengths (in feet) of the stage. Use for the length of the rectangular stage
The possible lengths of the stage (in feet) can be described by the inequality:
L ≥ A/10
where A is the minimum required area of the stage and L is the length of the stage.
Let's denote the length of the rectangular stage as 'L' in feet.
The area of a rectangle is given by the formula A = L × W, where A is the area, L is the length, and W is the width.
We are given that the width of the stage is 'W' feet and the area of the stage must be at least 'A' square feet. So we can write the inequality:
A ≤ L × W
Substituting the given values, we get:
A ≤ L × 10
Dividing both sides by 10, we get:
A/10 ≤ L
Therefore, the possible lengths of the stage (in feet) can be described by the inequality:
L ≥ A/10
where A is the minimum required area of the stage and L is the length of the stage.
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Select the correct answer.
A sport statistician gathered data on the number of points scored in each game by high school basketball players across the country. She found
a population mean of 20. 15 and a standard deviation of 3. 7. Each sample size was 20 players. By the central limit theorem, which interval do
68% of the sample means fall within?
A. 19. 32 and 20. 98
B. 17. 67 and 22. 63
C. 19. 96 and 20. 34
D. 18. 50 and 21. 81
68% of the sample means fall within 19.32 and 20.98.
By the central limit theorem, we know that the distribution of sample means will approach a normal distribution with a mean equal to the population mean (20.15) and a standard deviation equal to the population standard deviation divided by the square root of the sample size (3.7 / sqrt(20) ≈ 0.828).
To find the interval within which 68% of the sample means fall, we need to find the z-scores corresponding to the 16th and 84th percentiles of the normal distribution (which is the range that encompasses 68% of the data in a normal distribution).
Using a z-table or a calculator, we can find that the z-score for the 16th percentile is approximately -1.0 and the z-score for the 84th percentile is approximately 1.0.
Therefore, the interval within which 68% of the sample means fall is:
20.15 - 1.0(0.828) = 19.32
to
20.15 + 1.0(0.828) = 20.98
So the answer is option A: 19.32 and 20.98.
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The polynomial of degree 4, P ( x ) , has a root of multiplicity 2 at x = 1 and roots of multiplicity 1 at x = 0 and x = − 3 . It goes through the point ( 5, and 128 ).
Find a formula for P ( x ).
P ( x ) =
The polynomials P(x) can be formulized as P(x) = (1/5)(x-1)²(x)(x+3).
The given problem states that a degree 4 polynomial, P(x), has the following properties:
Multiplicity of 2 at x = 1Multiplicity of 1 at x = 0Multiplicity of 1 at x = -3The polynomial goes through the point (5,128)The degree of the polynomial is 4, so the polynomial can be written as;
P(x) = a(x-1)²(x-0)(x+3)
To find the value of 'a', substitute the given point (5,128) into the equation, P(x);
P(5) = a(5-1)²(5-0)(5+3) = 128
P(5) = a(4)²(5)(8) = 128
Simplifying, we get;
128 = 640a,
a = 1/5
Thus, the formula for P(x) is; P(x) = (1/5)(x-1)²(x)(x+3)
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The following are NOT examples of using the "Distributive Property"
Example 1:4(x-2)=4•x-4•2
Example 2:4•26
4•(20+6)=4•20+4•6
A:True
B:False
False, Example 1:4(x-2)=4•x-4•2 and Example 2:4•26 and Example 3: 4•(20+6)=4•20+4•6 are NOT examples of using the "Distributive Property".
The Distributive Property is a fundamental property of algebra that is used to simplify expressions involving multiplication and addition. It states that the product of a number and the sum or difference of two or more numbers is equal to the sum or difference of the products of that number and each of the numbers in the sum or difference.
Example 1 uses the Distributive Property correctly, showing how 4 multiplied by the difference of x and 2 is equal to the difference of 4 times x and 4 times 2.Example 2 is not an example of using the Distributive Property because it is just a multiplication of two numbers, which does not involve addition or subtraction.Example 3 uses the Distributive Property correctly, showing how 4 multiplied by the sum of 20 and 6 is equal to the sum of 4 times 20 and 4 times 6.Learn more about the Distributive Property at
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-5(x-2)+4x=x(3-x)-4(x-2)+xx+2
Answer: x = (-1 + sqrt(85)) / 6, or x = (-1 - sqrt(85)) / 6
Step-by-step explanation:
Let's simplify and solve the equation step by step:
Distribute the -5 and -4 on the left side and combine like terms:
-5x + 10 + 4x = 3x^2 - x - 4x + 8 + x + 2
Simplifying the left side and combining like terms on the right side, we get:
-x + 10 = 3x^2 + 3
Subtract 10 from both sides to isolate the variable on one side:
-x = 3x^2 - 7
Add x to both sides to get the quadratic equation in standard form:
3x^2 + x - 7 = 0
Use the quadratic formula to solve for x:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 3, b = 1, and c = -7. Substituting these values, we get:
x = (-1 ± sqrt(1^2 - 4(3)(-7))) / 2(3)
Simplifying under the square root, we get:
x = (-1 ± sqrt(85)) / 6
Therefore, the solutions to the equation are:
x = (-1 + sqrt(85)) / 6, or x = (-1 - sqrt(85)) / 6
These are approximate values since sqrt(85) is irrational.
I need to pass this math question pls help
The length x of the similar triangle is 17.3 units.
How to find the sides of similar triangle?Similar triangles are the triangles that have corresponding sides in ratio to each other and corresponding angles congruent to each other.
Therefore, the triangles are similar to each other. Let's use the similarity to find the side length x.
Therefore,
10 / x = x / 30
cross multiply
30 × 10 = x²
x² = 300
square root both sides of the equation
x = √300
x = 17.3205080757
x = 17.3 units
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A tire has a radius of 20 inches. What is the Circumference of the tire?
C=πd
Answer:
125.6637061
Step-by-step explanation:
Answer:
40π inches, or approximately 125.66 inches
Step-by-step explanation:
The formula to find the circumference of a circle is C = 2πr, where r is the radius of the circle and π is a mathematical constant approximately equal to 3.14.
In this case, the radius of the tire is 20 inches. So, the circumference of the tire is:
C = 2πr
C = 2π(20)
C = 40π
Therefore, the circumference of the tire is 40π inches, or approximately 125.66 inches if you round to two decimal places.
Identify the error in the student solution shown below. Find the correct answer. 2ln(x) = ln(3x) - [ln(9) - 2ln(3)] ln(x^2) = ln(3x) -0 in(x^2) = in(3x/0); division by 0, undifined
The correct answer is x = 9.
How do you compute a logarithm?Making use of the logarithm table, Compute the characteristic that the provided integer's whole number component dictates. Using the significant digits of the given number, find the mantissa. Add a decimal point after combining the characteristic and mantissa.
The student's solution has a division by zero error. The wrong step is when ln(x2) = ln(3x) - 0. It would have been better to first simplify the addition of ln(9) - 2ln(3) as follows:
The formula is ln(9) - 2ln(3) = ln(9) - ln(32) = ln(9/32) = ln(1/3).
When we substitute this number into the first equation, we get:
ln(1/3) - ln(3x) = 2ln(x)
ln(3x/1/3) = 2ln(x)
2ln(x) = ln (9x)
If we multiply both sides by their exponential, we get:
E = 2ln(x) + eln (9x)
x^2 = 9x
x^2 - 9x = 0
x(x - 9) = 0
As a result, the solutions are x = 0 and x = 9, but since ln(0) is undefined, we must determine whether x = 0 is a valid solution. So x = 9 is a workable answer.
Hence, the right response is x = 9.
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A dairy farmer milks his two cows every day. He determined the chance that he gets anywhere between 12 and 14 gallons of milk in one day is around 32%. Identify the method of probability the farmer used to reach this conclusion. Select the correct answer below: theoretical relative frequency
The dairy farmer used the relative frequency method of probability to reach his conclusion.
Relative frequency is a method of calculating probability that is based on the observation of how often an event occurs in a sample. The farmer likely observed how often he gets between 12 and 14 gallons of milk in a day and used that data to calculate the probability of it happening.
In contrast, theoretical probability is based on the assumption that all possible outcomes are equally likely. It is calculated by dividing the number of desired outcomes by the total number of possible outcomes.
Therefore, the correct answer is relative frequency.
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What is the measure of T ?
ABCDRSTU
60°
100°
110°
125°
The measure of T in the quadrilateral can be found to be B. 100 degrees.
How to find the angle ?The two quadrilaterals given are trapeziums and they are similar. This means that they have the same angles meausures.
As this is a quadrilateral, the total measure of the interior degrees would be the value of 360 degrees.
The value of T is the only missing angles and so can be found to be:
T = 360 - 125 - 60 - 75
T = 360 - 260
T = 100 degrees
In conclusion, the measure of T is 100 degrees.
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Find the value of h of the parallelogram
The value of h of the parallelogram is = 4.2
What is a parallelogram?A parallelogram is a special kind of quadrilateral made up of parallel lines. A parallelogram can have any angle between its adjacent sides, but for it to be a parallelogram, its opposite sides must also be parallel.
If the opposing sides of a quadrilateral are parallel and congruent, the shape will be a parallelogram. Hence, if both sets of opposite sides are parallel and equal, a quadrilateral is said to be a parallelogram.
A parallelogram's area is determined as follows:
Area = base × height
In the given parallelogram, we can note that the base is 8.4 inches, and the corresponding height is 5 inches.
This means that:
Area of parallelogram = 8.4 × 5 = 42 in²
This same area can be calculated using the other base (6 in) and its corresponding height (h)
This means that:
Area of parallelogram = 10 × h
42 = 10 × h
h = 42/10
h = 4.2 inches.
Hence, value of h in the parallelogram is equals to 4.2.
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Tyee has a points card for a movie theater.
• He receives 45 rewards points just for signing up.
• He earns 11.5 points for each visit to the movie theater.
• He needs at least 160 points for a free movie ticket.
Use the drop-down menu below to write an inequality representing v, the number of
visits he needs to make in order to get a free movie ticket.
Given:
45 rewards points for signing up
11.5 points for each visit
Total Number of Points are:
45 + 11.5 · number of visits he makes
How many visits must Tyler make to earn a free movie ticket?45 + 11.5 · x ≥ 160 points for a free movie ticket
Where, x is how many visits must Tyler make to earn a free movie ticket
11.5 · x ≥ 160 - 45
x ≥ 115 / 11.5
x ≥ 10
Since the number of visits to reach 180 points is 10 then Tyler has to visit the movie theater 10 times or more.
Check our answer:
45 + 11.5 · 10 = 160 will earn him a free movie ticket
Use the normal approximation to the binomial to find the probabilities for the specific values of X. N=50, p=. 8, X=44
The probability of X = 44 is approximately 0.087 using the normal approximation to the binomial.
The normal approximation to the binomial is a technique used to estimate probabilities for large binomial distributions when calculating by hand becomes impractical. In this case, we have N = 50, p = 0.8, and we want to find the probability of X = 44.
To use the normal approximation, we need to first check if the binomial distribution is approximately normal. This can be done by checking if the conditions np >= 10 and n(1-p) >= 10 are met. In our case, np = 50 x 0.8 = 40 and n(1-p) = 50 x 0.2 = 10, so the conditions are met.
Next, we calculate the mean and standard deviation of the normal distribution using the formulas μ = np and σ = sqrt(np(1-p)). In our case, μ = 40 and σ = sqrt(50 x 0.8 x 0.2) ≈ 2.83.
Finally, we use the normal distribution with mean μ and standard deviation σ to find the probability of X = 44. We need to standardize X using the formula Z = (X - μ) / σ, which gives Z = (44 - 40) / 2.83 ≈ 1.41.
Using a standard normal table or calculator, we find that the probability of Z being less than 1.41 is approximately 0.921. This means that the probability of X being less than or equal to 44 is approximately 0.921.
Therefore, the probability of X being exactly 44 is approximately the difference between the probability of X being less than or equal to 44 and the probability of X being less than or equal to 43. Using a continuity correction, we adjust 43.5 to 43, which gives us:
P(X = 44) ≈ P(43.5 < X < 44.5) ≈ P(Z < (44.5 - 40) / 2.83) - P(Z < (43.5 - 40) / 2.83) ≈ 0.087.
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5/12d+1/6d+1/3d+1/12d=6 solve for d
Answer:
take lcm ...i.e.= 12d then solve it ... value of d=1/6....On a spelling test, Lucy got 4 out of 5 correct. If Lucy got 20 questions correct then how many questions did she miss?
if lucky got 20 questions correct then lucky had missed 4 tests.
If Lucy got 4 out of 5 questions correct, then the proportion of questions she got correct is:
4/5 = 0.8
We can use this proportion to find the number of questions she got correct in the larger set of 20 questions:
0.8 x 20 = 16
So, Lucy got 16 questions correct out of 20. To find the number of questions she missed, we can subtract the number she got correct from the total number of questions:
20 - 16 = 4
Therefore, Lucy missed 4 questions on the test.
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9. Assume a density function of a random variable X is f(x)={ 2 π , 0, 0
Mean value of the function = E(X) = ∞/πOption (b) ∞/π is the correct option.
Given a density function of a random variable X as f(x)={ 2 π , 0, 0. The question is to find the mean value of the function.As we know,The mean value of the function = E(X) = ∫xf(x)dx, where x is the random variable and f(x) is the density function,∫ denotes integral from negative infinity to infinityOn substituting the given values,∫xf(x)dx= ∫x (2/π)dx= (2/π) ∫xdx= (2/π)(x^2/2)+C ……(1)Where C is the constant of integration.But given the density function is zero for all negative x values and f(0) = 2/π, so the integral should be calculated from 0 to infinity instead of negative infinity to infinity.On substituting the values,∫0∞ x (2/π)dx= (2/π) ∫0∞xdx= (2/π) (x^2/2) [0,∞]= ∞/πTherefore, mean value of the function = E(X) = ∞/πOption (b) ∞/π is the correct option.
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Pamela is 7 years older than Jiri. The sum of their ages is 71. what is jiris age?
Answer:
jiris age is 32
Step-by-step explanation:
39(palma's age)+32(jiris age)=71
what 1+1+= to what then 2+2
On solving the question we have that If you meant "1+1=2, then what is equation 2+2?" the answer is four.
What is equation?A math equation is a mechanism for connecting two statements and indicating equivalence with the equals sign (=). To explain the connection between the two sentences put on each side of a letter, a statistical method can be employed. The software and the logo are usually interchangeable. 2x - 4 equals 2, for example. An equation is a logical expression that asserts the equality of some mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14.
"1+1+" is an incomplete expression since it requires another operand or operator to form a valid mathematical statement.
Assuming you meant "1+1=," the answer is two.
If you meant "1+1=2, then what is 2+2?" the answer is four.
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On solving the question we get 2 + 2 = 4 because it is given 1 + 1 = 2 it means it is basic addition.
What is Addition?In addition we perform mathematical operation in which we add two or more no with other numbers to get the desire or final output. Output can be positive or negative it only based on your input values.
Mathematical operation is defined as sentence in which two or more number perform an operation which finally gave us result.
Mathematical operations are addition, Subtraction , Multiplication , Division, Percentage etc.
"1+1+" is an incomplete expression since it requires another operand or operator to form a valid mathematical statement.
It is given that "1+1=," so the answer was two.
it meant that if "1+1=2, then what is 2+2 =4 .
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Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3
The steps he can use are [tex]x = -\frac{-16 \± \sqrt{16\² - 4 \cdot 8 \cdot 3}}{16}[/tex], (x + 1)² = 5/8 and 8(x² + 2x + 1) = -3 + 8
How to determine the steps he can useFrom the question, we have the following parameters that can be used in our computation:
8x² + 16x + 3 = 0
Assuming he uses the quadratic formula method, which is represented as
[tex]x = -\frac{-b \± \sqrt{b\² - 4ac}}{2a}[/tex]
So, we have
[tex]x = -\frac{-16 \± \sqrt{16\² - 4 \cdot 8 \cdot 3}}{2 \cdot 8}[/tex]
[tex]x = -\frac{-16 \± \sqrt{16\² - 4 \cdot 8 \cdot 3}}{16}[/tex]
If he uses completing the square, then we have
8x² + 16x = -3
So, we have
x² + 2x = -3/8
x² + 2x + 1 = -3/8 + 1
So, we have
(x + 1)² = 5/8
If he factorizes, then the expression is
8(x² + 2x + 1) = -3 + 8
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dA/dr = d(∩r 2 )/dr = 2∩r,
when r=8 dA/dr=?
dA/dt = 0.4 x dA/dt=?
When the circle's radius is 8 cm and it is shrinking at a rate of 0.4 cm per second, the rate that the area is shrinking is -6.4 cm²/s.
How big is the r² area?Circle area formula: r² = r. The radius squared is multiplied to find the circumference of the circle. When a circle's radius is specified, its area is equal to r². When the diameter "d" is known, the circle's surface area is equal to d²/4.
What is the name for pi's half?90 degrees is equal to a quarter turn. A complete turn is 360 degrees, while a half turn is 180. Moreover, the rotation can be expressed in radians or fraction of pi. Under this system, a complete circle turn is equal to 2 radians, a half circle turn is equal to 1, and so on.
Step 1: Variables involved in the question:
The variables involved in the question are:
The radius of the circle r = 8 cm (constant value)
The rate at which the radius is decreasing (dr/dt) = -0.4 cm/s (negative because it's decreasing)
The rate at which the area of the circle is changing dA/dt = ?
Step 2: Chain rule:
We can use the chain rule to link the three rates:
dA/dt = dA/dr x dr/dt
Step 3:
From the given information, we know that (dr/dt) = -0.4 cm/s.
Step 4: Equation for dA/dr
The formula for the area of a circle is A = πr², where r is the radius of the circle. We can differentiate both sides of the equation with respect to r to get the following formula for dA/dr:
dA/dr = 2πr
Step 5:
Substituting the given value of r = 8 cm in the equation for dA/dr, we get:
dA/dr = 2π(8) = 16π cm
Step 6: dA/dt:
Now we can use the chain rule to find dA/dt by substituting the values we have found for dA/dr and dr/dt:
dA/dt = dA/dr x dr/dt
dA/dt = 16π cm x -0.4 cm/s
dA/dt = -6.4π cm²/s
Therefore, the rate at which the area of the circle is decreasing when its radius is 8cm and decreasing at -0.4 cm/s is -6.4π cm²/s.
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