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3 years ago

Find the volume of the sphere. Round your answer to the nearest tenth if necessary.

Mathematics

1 answer:

Lady bird [3.3K]3 years ago

4 0

Answer:

below

Step-by-step explanation:

v =4/3πr³

v= 4/3* 3.142*8³

v= 2144.94 ft

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20 POINTS

TiliK225 [7]

Answer:

Step-by-step explanation:

There are 6 different shapes

You want the outcome to be a Nonagon

You put the outcome as a ratio 1/6

1/6=0.1666667

0.1666667*100=16.6667%

Chance of pulling out a nonagon

3 0

3 years ago

An auto insurance company has 10,000 policyholders. Each policy is defined as: young or old male or female; and married or singl

Blababa [14]

Answer:

880

Step-by-step explanation:

This problem a bit annoying, but let's classify the numbers and see where we can get from there:

Total = 10,000

Young = 3,000

Old = 7,000 (not young defined as 10,000 - 3,000)

Male = 4,600

Female = 5,400

Married = 7,000

Single = 3,000

Young Males = 1,320

Young Females = 3,000 (young) - 1,320 = 1,680

Married Males = 3,010

Married Females = 7,000 - 3,010 = 2,990

Young Married = 1,400

Young Married Males = 600

Young Married Females = 1,400 - 600 = 800

Young Female Single = ?

Young Female = 1,680 from above. But not all of them are single.

Young Married Females = 800 from above

Young Female Single = Young Female - Young Married Females = 1,680 - 800 = 880

6 0

3 years ago

Evaluate the integral, show all steps please!

Aloiza [94]

Answer:

$\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x=\dfrac{x}{9\sqrt{9-x^2}} +\text{C}$

Step-by-step explanation:

Fundamental Theorem of Calculus

$\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))$

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given indefinite integral:

$\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x$

Rewrite 9 as 3² and rewrite the 3/2 exponent as square root to the power of 3:

$\implies \displaystyle \int \dfrac{1}{\left(\sqrt{3^2-x^2}\right)^3}\:\:\text{d}x$

Integration by substitution

$\boxed{\textsf{For }\sqrt{a^2-x^2} \textsf{ use the substitution }x=a \sin \theta}$

$\textsf{Let }x=3 \sin \theta$

$\begin{aligned}\implies \sqrt{3^2-x^2} & =\sqrt{3^2-(3 \sin \theta)^2}\\ & = \sqrt{9-9 \sin^2 \theta}\\ & = \sqrt{9(1-\sin^2 \theta)}\\ & = \sqrt{9 \cos^2 \theta}\\ & = 3 \cos \theta\end{aligned}$

Find the derivative of x and rewrite it so that dx is on its own:

$\implies \dfrac{\text{d}x}{\text{d}\theta}=3 \cos \theta$

$\implies \text{d}x=3 \cos \theta\:\:\text{d}\theta$

Substitute everything into the original integral:

$\begin{aligned}\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x & = \int \dfrac{1}{\left(\sqrt{3^2-x^2}\right)^3}\:\:\text{d}x\\\\& = \int \dfrac{1}{\left(3 \cos \theta\right)^3}\:\:3 \cos \theta\:\:\text{d}\theta \\\\ & = \int \dfrac{1}{\left(3 \cos \theta\right)^2}\:\:\text{d}\theta \\\\ & = \int \dfrac{1}{9 \cos^2 \theta} \:\: \text{d}\theta\end{aligned}$

Take out the constant:

$\implies \displaystyle \dfrac{1}{9} \int \dfrac{1}{\cos^2 \theta}\:\:\text{d}\theta$

$\textsf{Use the trigonometric identity}: \quad\sec^2 \theta=\dfrac{1}{\cos^2 \theta}$

$\implies \displaystyle \dfrac{1}{9} \int \sec^2 \theta\:\:\text{d}\theta$

$\boxed{\begin{minipage}{5 cm}\underline{Integrating $\sec^2 kx$}\\\\$\displaystyle \int \sec^2 kx\:\text{d}x=\dfrac{1}{k} \tan kx\:\:(+\text{C})$\end{minipage}}$