if a = 2 and b = 7 then b^a =

The volume of the cylinder inside the given sphere is 8 cubic units.

To determine the volume of the cylinder inside the given sphere, we need to find the limits of integration and set up the integral.

Let's analyze the equations:

Cylinder equation:[tex]r^2 + y^2 = 4[/tex]

Sphere equation: [tex]r^2 + y^2 + 2^2 = 16[/tex]

From the equations, we can see that the cylinder is centered at the origin (0, 0) with a radius of 2 and an infinite height along the y-axis. The sphere is centered at the origin as well, with a radius of 4.

To find the limits of integration, we need to determine where the cylinder intersects the sphere. By substituting the cylinder equation into the sphere equation, we can solve for the values of r and y:

[tex](2^2) + y^2 + 2^2 = 16\\4 + y^2 + 4 = 16\\y^2 = 8[/tex]

y = ±√8

We can see that the cylinder intersects the sphere at y = √8 and y = -√8. Since the cylinder has infinite height, the limits of integration for y will be from -√8 to √8.

Now we can set up the integral to calculate the volume of the cylinder:

V = ∫∫∫ dV

  = [tex]\int_0^ 2 \int_{\sqrt -8} ^ {\sqrt 8}\int _{\sqrt-(16 - r^2 - y^2)} ^{\sqrt (16 - r^2 - y^2)} dz dy dr[/tex]

Since the integrand is equal to 1, we can simplify the integral to:

V = [tex]\int_0 ^ 2 \int _{-\sqrt8} ^ {\sqrt8} 2\sqrt{(16 - r^2 - y^2)}[/tex] dy dr

Evaluating this integral will give us the volume of the cylinder inside the sphere.

To evaluate the integral and calculate the volume, we can integrate the given expression with respect to y first and then with respect to r.

[tex]\int_0 ^ 2 \int _{-\sqrt8} ^ {\sqrt8} 2\sqrt{(16 - r^2 - y^2)}[/tex]

Let's begin by integrating with respect to y:

[tex]\int_{-\sqrt8} ^ {\sqrt8} 2\sqrt(16 - r^2 - y^2) dy[/tex]

We can simplify the integrand using the trigonometric substitution y = √8sinθ:

dy = √8cosθ dθ

y = √8sinθ

Replacing y and dy in the integral:

[tex]\int _{-\pi /2} ^{\pi/2} 2\sqrt(16 - r^2 - (\sqrt 8sin\theta)^2) \sqrt 8cos\theta d\theta[/tex]

= 16[tex]\int _{-\pi /2} ^ {\pi /2} \sqrt(1 - (r/4)^2 - sin^2\theta)[/tex]cosθ dθ

To simplify the integral further, we can use the trigonometric identity [tex]sin^2\theta + cos^2\theta = 1:[/tex]

16[tex]\int _{-\pi /2} ^ {\pi /2} \sqrt(1 - (r/4)^2 - sin^2\theta)[/tex]cosθ dθ

= 16 [tex]\int _{-\pi /2} ^ {\pi /2} \sqrt(r^2/16)[1 - cos^2\theta][/tex]cosθ dθ

= 4r[tex]\int _{-\pi/2} ^ {\pi/2}[/tex] sinθ cosθ dθ

= 4r [tex][ -cos^2\theta/2[/tex] ]| [-π/2 to π/2 ]

= 4r [ [tex]-cos^2(\pi/2)/2 + cos^2(-\pi/2)/2[/tex] ]

= 4r [ -1/2 + 1/2 ]

= 4r

Now, we can integrate with respect to r:

[tex]\int_0 ^ 2[/tex] 4r dr

= 2[tex]r^2[/tex]| [0 to 2]

= 2[tex](2^2 - 0^2)[/tex]

= 2(4)

= 8

Therefore, the volume of the cylinder is 8 cubic units.

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Answer:

1 : 30

Step-by-step explanation:

300mm:9m​

We need to change the meters to mm

1 meter is 1000 mm

so 9 m is 9000 mm

300mm:9000mm

Divide both sides by 300

​300mm/300 : 9000/300

1 : 30

Answer:

One solution

I actually do not think you're going to give me brainliest

Answer:

Option D: P + 42 = 91

Step-by-step explanation:

Plates collected in February = 42

Total Plates collected = 91

Plates in February + Plates in March = total plates

42 + P = 91 or

P + 42 = 91

The test statistic value can be calculated using the formula (sample mean - population mean) / (sample standard deviation / sqrt(sample size)).

To calculate the test statistic value, we use the formula (sample mean - population mean) / (sample standard deviation / sqrt(sample size)). In this case, the sample mean is 122, the population mean is 130, the sample standard deviation is 20, and the sample size is 20.

Test Statistic Value = (122 - 130) / (20 / sqrt(20))

                     = (-8) / (20 / 4.47)

                     = -8 / 4.47

                     ≈ -1.79

Therefore, the test statistic value is approximately -1.79.

The test statistic value (t) measures the difference between the sample mean and the assumed population mean in terms of the standard error. It helps us determine the likelihood of obtaining such a sample mean if the population mean is indeed equal to the assumed value.

In this case, the test statistic value is -1.79, indicating that the sample mean is 1.79 standard errors below the assumed population mean of 130. The negative sign indicates that the sample mean is lower than the assumed value.

To determine the significance of this difference, we would compare the test statistic to critical values from the t-distribution or calculate the p-value associated with the observed test statistic. This would allow us to make conclusions about the statistical significance of the difference between the sample mean and the assumed population mean.

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Answer:

I have

Step-by-step explanation:

Step-by-step explanation:

[tex]57.6 - 41.9 = 5.7[/tex]

To find the volume and total area of the right circular cone, we will use the formulas below. Volume of the right circular cone: $$V = \frac{1}{3}πr^2h$$

Total surface area of the right circular cone:$$A = πr^2 + πrl$$, Where r is the radius, l is the slant height and h is the height of the cone.π (pi) is a mathematical constant that is approximately equal to 3.14159 and is used to calculate the circumference and area of a circle. The radius of the right circular cone is 3.5 cm and its height is 7 cm. To calculate the slant height, we will use the Pythagorean theorem which states that the square of the hypotenuse (l) is equal to the sum of the squares of the other two sides:$$l^2 = r^2 + h^2$$$$l = \sqrt{r^2 + h^2} = \sqrt{3.5^2 + 7^2} \approx 7.98\ cm$$

Volume of the right circular cone:$$V = \frac{1}{3}πr^2h = \frac{1}{3}π(3.5)^2(7) \approx 89.75\ cm^3$$. Total surface area of the right circular cone:$$A = πr^2 + πrl = π(3.5)^2 + π(3.5)(7.98) \approx 91.86\ cm^2$$. Hence, the volume of the right circular cone is approximately 89.75 cm³ and the total surface area is approximately 91.86 cm².

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Answer:17

Step-by-step Experlation: The volume is 108 cm. 3,2,15.a square prism with a base edge of 9.5 inches and a height of 17 ... amount for a landowner

hello i know its wrong but lol. i tried to help.

Part A:

Six Tents Holds 42 People

Nine Tents Holds 63 People

10 Tents Holds 70 People

Part B:

Number of tents|||Number of people

1                          |||7

6                         |||42

9                         |||63

10                        |||70

Part C:

Tents=x

1x=7 people

Answer: $17.55

Step-by-step explanation:

36 x 0.65 = $23.40 total for all cookies

($23.40/1) x (3/4) = (70.2/4)

70.2 divided by 4 = $17.55

or

$23.40 x .75 = $17.55

Answer:

2.5 liters of gas is used with per liter of oil

Step-by-step explanation:

Max is missing oil and gas for his moped.

Amount of gas used = 3.75 liters

Amount of oil required = 1.5 liters

Ratio in which gas and oil are mixed = [tex]\frac{3.75}{1.5}[/tex]

                                                             = [tex]\frac{2.5}{1}[/tex]

That means if he uses 1 liter of oil then the gas required for the mixture = 2.5 liters

Therefore, 2.5 liters of gas is used per liter of oil.

Answer:

x = 1

Step-by-step explanation:

5x^5 + 5 = 10

Start the solution by subtracting 5 from both sides:

5x^5 = 5

Dividing both sides by 5 yields x^5 = 1.

Taking the 5th root of both sides, we get x = 1

Answer: Singing

Mode: The value that appears the most in a list

Also by the way, the frequency table is most likely just a table of every single value and how many times they appear in the list. Its super easy all you have to do is count them

The y-intercept is n intercept is a point on the y-axis, through which the slope of the line passes and the y-intercept of the given equation is 38,000.

In Maths, an intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept.

The given equation is y=700x+38,000 to predict his annual salary, y, after x years.

In the given equation, y-intercept is 38,000.

Therefore, the y-intercept is n intercept is a point on the y-axis, through which the slope of the line passes and the y-intercept of the given equation is 38,000.

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Answer:

h(x)=6^x/3 is what I got hope I could help

Answer:

however it works for you along as you get the right answer

Step-by-step explanation:

Answer:

Yeah you will most likely get the same answer

Step-by-step explanation:

as long as you don't mix up (for this example of course) the service call fee (which is the constant) and the fee for each hour of labor (the coefficient of the variable), you are good

The contour integral of the function f(z) over the contour C is zero because the function f(z) is analytic inside and on the contour C.

In this case, the function f(z) = (8² - 16)5 = 64 × 5 = 320 is a constant function. Constant functions are always analytic within their domain. Therefore, f(z) is analytic within the region enclosed by the contour C.

According to Cauchy's Integral Formula, the contour integral of a function over a closed contour C is given by:

∮C f(z) dz = 2πi × sum of the residues of f(z) at its isolated singularities within C.

Since f(z) is a constant function, it does not have any singularities. Therefore, all the residues of f(z) are zero.

Hence, the contour integral of f(z) over the contour C is zero:

∮C f(z) dz = 0.

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Answer:

5. 18 that is what i think the answers are

6. 13.75

5 2 11 8 35 32

Based on the given data, the hypothesis test results show that there is not enough evidence to conclude that women chat on their phones more than men at the 5% significance level.

For the hypothesis test comparing the chat times of male and female students, we can use a two-sample t-test since we have two independent samples with unequal variances. The null hypothesis (H0) assumes that there is no difference in chat times between men and women, while the alternative hypothesis (Ha) suggests that women chat more than men.

Calculating the test statistic and degrees of freedom using the provided sample data and formulas, we find that the test statistic is approximately 1.03. Comparing this with the critical value at a 5% significance level (t-critical value), we find that it does not fall in the rejection region.

Therefore, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that women chat on their phones more than men at the 5% significance level.

For the second scenario comparing energy expenditure using conventional and perforated shovels, we would need more information, such as the sample sizes, means, and standard deviations, to perform the relevant hypothesis test. The provided data alone does not allow us to conduct the hypothesis test.

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Answer:

V = 339.12

Step-by-step explanation:

Volume of a cone:

V = πr²(h/3)

Given:

r = 6

h = 9

Work:

V = πr²(h/3)

V = 3.14(6²)(9/3)

V = 3.14(36)(3)

V = 113.04(3)

V = 339.12

Answer:

3(y-9)^2

Step-by-step explanation:

Answer:

See in the picture mark brainliest if correct

Answer:

-1.889 rad

Step-by-step explanation:

180 degrees = [tex]\pi[/tex]

-340 x [tex]\frac{\pi }{180}[/tex]

-340[tex]\pi[/tex]/180

-34[tex]\pi[/tex]/18

-1.889 rad

f: A → B and g: B → A are functions such that f∘g=idB. It is true that g is injective and f is surjective.

Let y1, y2 ∈ B such that g(y1) = g(y2).

We need to show that y1 = y2.

To do this, we use the following facts;

f(g(y1)) = y1 (since f∘g=idB).

f(g(y2)) = y2 (since f∘g=idB).

Now, f(g(y1)) = f(g(y2)).

Since f is a function, g(y1) = g(y2) ⟹ f(g(y1)) = f(g(y2)).

So, we have y1 = y2 as required. Therefore, g is injective.

Let b ∈ B be arbitrary. We need to show that there exists an element a ∈ A such that f(a) = b.

Since f∘g=idB, we know that for any element y ∈ B,f(g(y)) = y.

Now, we can use b ∈ B to obtain the element g(b) ∈ A.

Then, f(g(b)) = b as required. Therefore, f is surjective.

So, the functions f and g satisfy the following properties:

if f: A → B and g: B → A such that f∘g=idB, then g is injective and f is surjective.

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Answer:

16,-8,4,-2,1

-15,-18,-21.6,25.92,-31.104...

625,125,25,5,1

Step-by-step explanation:

Answer: 16, –8, 4, –2, 1. has a common ratio,r = (-1/2)

-15, –18, –21.6, –25.92, –31.104 has a common ratio, r = (1.2)

625, 125, 25, 5, 1 has a common ratio, r= (1/5)

Step-by-step explanation: just took the test

Answer:

A. Jan 1

Dr cash $800,000

Cr Bonds payable $800,000

B. Dr Interest expense $72,000

Cr Interest Payable $72,000

Step-by-step explanation:

Preparation of the entries to record the issuance of the bonds and the first annual interest accrual on December 31

A. Preparation of the entries to record the issuance of the bonds

Jan 1

Dr cash $800,000

Cr Bonds payable $800,000

(Being to record issuance of the bonds)

B. Preparation of the Journal entry to record first annual interest accrual on December 31

Dec 31

Dr Interest expense $72,000

Cr Interest Payable $72,000

($800,000*9%)

(Being to record the first year interest expense accrued)