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3 years ago

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Please need help on this question 20 points

1 answer:

notsponge [240]3 years ago

3 0

Answer:C

Step-by-step explanation:

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Volumes of the solids with disk or shell method?

lina2011 [118]

The answer to the questions of volumes are given as follows

a) $v=128 \pi$

b) $v=\frac{128}{3} \pi$

c) $v=\frac{1024}{5} \pi$

d) $V=\frac{13568}{15} \pi$

Generally, the questions are mathematically solved below

$y=\sqrt{x}, y=4, x=0$

a) x-axis

if $y=4, x=16, x=0$

Using disk method

$} v=\pi \int_{0}^{16}(\sqrt{x})^{2} d x \\$

$v=\pi\left(\frac{x^{2}}{2}\right)_{0}^{16} \\$

$v=\frac{\pi}{2} \times 16 \times 16 \\$

$v=128 \pi$

b) line y=4

if x=0, y=0 ;

$y=\sqrt{x} \Rightarrow x=y^{2}$

Using shell method

$v = \int_{0}^{4} 2 \pi(4-y) \cdot y^{2} d y \\$

$v=2 \pi \int_{0}^{4}\left(4 y^{2}-y^{3}\right) d y$

$v=2 \pi\left[\frac{4 y^{3}}{3}-\frac{y^{4}}{4}\right]_{0}^{4} \\$

$v=\frac{2 \pi}{12}[1024-768] \\$

$v=\frac{512 \pi}{12} \\$

$v=\frac{128}{3} \pi$

c) y-axis

0 ≤ y ≤ 4

x=y^2

Using disk method

volume

$v=\pi \int_{0}^{4} y^{4} d y$$

$v=\pi\left(\frac{y 5}{5}\right)_{0}^{4} \\$

$v=\frac{1024}{5} \pi$

d) line x=-1

y=√x, y=4, x=0

0 ≤ x ≤ 6

Using shell method

volume is

$V=\int_{0}^{16} 2 \pi(1+x) \sqrt{x} d x$$

$V=2 \pi\int_{0}^{16}(x^{1 / 2}+x^{3 / 2}\right) )d x\right. \\$

$V=2 \pi\left[\frac{x^{3 / 2}}{3 / 2}+\frac{x^{5 / 2}}{5 / 2}\right]_{0}^{16} \\$

$V=2 \pi\left[2 / 3 \cdot\left(4^{2}\right)^{3 / 2}+2 / 5\left(4^{2}\right)^{5 / 2}\right] \\$

$V=4 \pi / 3 \cdot 4^{3}+4 \pi / 5 \cdot 4^{5} \\$

$V=4 \pi\left(\frac{1}{3}+\frac{4^{2}}{5}\right)$

$V=\frac{256}{15}(5+48) \pi \\$

$V=\frac{256 \times 53}{15} \pi \\$

$V=\frac{13568}{15} \pi$

Read more about volumes

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8 0

2 years ago

an average sized dog weighs about A. 15 grams B. 50 grams C. 5,000 grams D. 15,00 grams I don't know the answer, please help

Fed [463]

The answer to your question is C

6 0

3 years ago

Read 2 more answers

HELP ME PLS & FAST!!

lukranit [14]

There are 6 outcomes for the cube and 4 for the spinner. So you can multiply 6 and 4. That gives you 24. The answer is C. 24. Hope this helps!

8 0

3 years ago

What is the solution to the system of equations

Scrat [10]

C (3,1)

There is the answer and also a check to make sure hope this helps

6 0

3 years ago

Match each complex number with its equivalent expression i^157 i^315 i^102 i^76

ryzh [129]

Answers:

$i^{157} = i\\\\i^{315} = -i\\\\i^{102} = -1\\\\i^{76} = 1\\\\$

=====================================================

Explanation:

By definition, $i = \sqrt{-1}$

Squaring both sides gets us $i^2 = -1$

Then multiply both sides by i to get $i^3 = -i$

Repeat the last step and you should get $i^4 = -i^2 = -(-1) = 1$

---------------

Notice we have this pattern going on:

$i^0 = 1\\\\i^1 = i\\\\i^2 = -1\\\\i^3 = -i\\\\i^4 = 1\\\\$

Once we reach i^4, we start the process over again.

It repeats every 4 terms.

This means we'll divide the exponent over 4 and look at the remainder. We ignore the quotient completely.

157/4 = 39 remainder 1

That remainder 1 is the exponent of the simplified term

$i^{157} = i^1 = i$

---------------

Similarly,

315/4 = 78 remainder 3

So $i^{315} = i^3 = -i$

---------------

102/4 = 25 remainder 2

$i^{102} = i^2 = -1$

----------------

76/4 = 19 remainder 0

$i^{76} = i^0 = 1$

8 0

2 years ago