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2 years ago

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A sphere and a cylinder have the same radius and height. The volume of the cylinder is 27 pi feet cubed. A sphere with height h

and radius r. A cylinder with height h and radius r. Which equation gives the volume of the sphere?

1 answer:

Tems11 [23]2 years ago

8 0

Answer:

Two- thirds (27)

Step-by-step explanation:

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Which of the following expressions is equivalent to a3 + b3?

lubasha [3.4K]

ANSWER
${a}^{3} + {b}^{3} = (a + b)( {a}^{2 } - ab + {b}^{2} )$

EXPLANATION

To find the expression that is equivalent to
${a}^{3} + {b}^{3}$
we must first expand
${(a + b)}^{3}$
Then we rearrange to find the required expression.

So let's get started.

${(a + b)}^{3} = (a + b) {(a + b)}^{2}$

We expand the parenthesis on the right hand side to get,

${(a + b)}^{3} = (a + b) ( {a}^{2} + 2ab + {b}^{2} )$

We expand again to obtain,

${(a + b)}^{3} = {a}^{3} + 3 {a}^{2}b + 3a {b}^{2} + {b}^{3}$

Let us group the cubed terms on the right hand side to get,

${(a + b)}^{3} = {a}^{3} + {b}^{3} + 3 {a}^{2}b + 3a {b}^{2}$

${(a + b)}^{3} = {a}^{3} + {b}^{3} + 3ab (a+ b)$

We make the cubed terms the subject,

${(a + b)}^{3} - 3ab (a+ b) = {a}^{3} + {b}^{3}$

We factor to get,

$(a + b)({(a + b)}^{2} - 3ab ) = {a}^{3} + {b}^{3}$

We expand the bracket on the left hand side to get,

$(a + b)( {a}^{2} + 2ab + {b}^{2} - 3ab ) = {a}^{3} + {b}^{3}$

We finally simplify to get,

$(a + b)( {a}^{2} - ab + {b}^{2} ) = {a}^{3} + {b}^{3}$

5 0

3 years ago

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What’s the answer to this

madam [21]

B is the correct answer I think

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3 years ago

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Nattalie picked 135 berries in 15 minutes at this rate how long will it take her to pick 486 berries

forsale [732]

Well, If she takes 15 minutes to pick 135 berries, 30 minutes total would be 270 berries, so if you take another 15 minutes picking berries it would be a total of 405 berries but you still need 81 more. so if she can pick 405 in 45 minutes, it would be around a hour and something.

Hope I helped or at least made you think about it

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3 years ago

It is known that 60% of customers will need additional maintenance on their vehicle when coming in for an oil change. A random s

inn [45]

Answer:

the probability that more than 70% of customers in the sample will need additional maintenance is 0.0371

Step-by-step explanation:

From the information given:

we are to determine the probability that more than 70% of customers in the sample will need additional maintenance

In order to achieve that, let X be the random variable that follows a binomial distribution.

Then X $\sim$ Bin(48, 0.6)

However 70% of 48 samples is

= 0.7 × 48 = 33.6 $\simeq$ 34

Therefore, the required probability is:

= P(X> 34)

$= \sum \limits ^{48}_{x=34} (^{48}_{x}) (0.6)^x(1 - 0.6)^{48-x}$

$= \dfrac{48!}{34!(48-34)!} (0.6)^{34} (0.4)^{48-34}$

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= 0.03709524328

$\simeq$ 0.0371

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The sphere's radius is half the radius of the hemisphere. How does the volume of this hemisphere compare with the volume of the

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Answer: D It is greater than the volume of the sphere

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