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3 years ago

A sphere has a diameter of 10 in. What is the volume of the sphere?

Mathematics

2 answers:

stich3 [128]3 years ago

8 0

Answer:

500/3 pi

Step-by-step explanation:

i took le quiz :)

givi [52]3 years ago

5 0

The volume of sphere is $\frac{500}{3}\pi$ inches cubed.

Step-by-step explanation:

Given,

Diameter of sphere = 10 inches

Radius of sphere = $\frac{Diameter}{2}=\frac{10}{2}$

Radius of sphere = 5 inches

Volume of sphere = $\frac{4}{3}\pi r^3$

V = $\frac{4}{3}\pi (5)^3$

$V = \frac{4}{3}\pi * 125\\\\V = \frac{500}{3}\pi$

The volume of sphere is $\frac{500}{3}\pi$ inches cubed.

Keywords: volume, division

Learn more about division at:

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svlad2 [7]

Answer:

$3174cm^{2}$

Step-by-step explanation:

Each square has an area of $529cm^{2}$

So we multiply that by the number of squares which is 6.

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2 years ago

Consider the following. f(x) = x5 − x3 + 6, −1 ≤ x ≤ 1 (a) Use a graph to find the absolute maximum and minimum values of the fu

kykrilka [37]

ANSWER

See below

EXPLANATION

Part a)

The given function is

$f(x) = {x}^{5} - {x}^{3} + 6$

From the graph, we can observe that, the absolute maximum occurs at (-0.7746,6.1859) and the absolute minimum occurs at (0.7746,5.8141).

b) Using calculus, we find the first derivative of the given function.

$f'(x) = 5 {x}^{4} - 3 {x}^{2}$

At turning point f'(x)=0.

$5 {x}^{4} - 3 {x}^{2} = 0$

This implies that,

${x}^{2} (5 {x}^{2} - 3) = 0$

${x}^{2} = 0 \: or \: 5 {x}^{2} - 3 = 0$

$x = - \frac{ \sqrt{15} }{5} \: or \: x = 0 \: \: or \: x =\frac{ \sqrt{15} }{5}$

We plug this values into the original function to obtain the y-values of the turning points

$( - \frac{ \sqrt{15} }{5} , \frac{1}{125} ( 6 \sqrt{15} +750)) \:and \: (0, - 6) \: and\: ( \frac{ \sqrt{15} }{5} , \frac{1}{125} ( - 6 \sqrt{15} +750))$

We now use the second derivative test to determine the absolute maximum minimum on the interval [-1,1]

$f''(x) = 20 {x}^{3} - 6x$

$f''( - \frac{ \sqrt{15} }{5} ) \: < \: 0$

Hence

$( - \frac{ \sqrt{15} }{5} , \frac{1}{125} ( 6 \sqrt{15} + 750))$

is a maximum point.

$f''( \frac{ \sqrt{15} }{5} ) \: > \: 0$

Hence

$( \frac{ \sqrt{15} }{5} , \frac{1}{125} (- 6 \sqrt{15} + 750))$

is a minimum point.

$f''(0) \: =\: 0$

Hence (0,-6) is a point of inflexion

4 0

3 years ago

You and your friends want to rent a limo on prom night.

ikadub [295]

Hey there!

You would be able to rent the limo for 4 hours plus the booking fee.

75 x 4 = 300

300 + 50 = 350

350 = 350

Hope this helps you! :)

Hugs!
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4 0

3 years ago

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Solve the equation: |2x + 5| = 11.

MrRa [10]

Answer:

x=3 or x= -8

Step-by-step explanation:

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3 years ago

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Suppose that a sample mean is .29 with a lower bound of a confidence interval of .24. What is the upper bound of the confidence

Ganezh [65]

Answer:

The upper bound of the confidence interval is 0.34

Step-by-step explanation:

Here in this question, we want to calculate the upper bound of the confidence interval.

We start by calculating the margin of error.

Mathematically, the margin of error = 0.29 -0.24 = 0.05

So to get the upper bound of the confidence interval, we simply add this margin of error to the mean

That would be 0.05 + 0.29 = 0.34

3 0

3 years ago