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2 years ago

The volume of a cylinder is 540 pi ft^3 the height is 15 ft. what is the diameter

Mathematics

2 answers:

tankabanditka [31]2 years ago

8 0

Answer:

b. 12

Step-by-step explanation:

The volume of a cylinder is

$\pi {r}^{2} h$

Let us compose an equality and solve for the radius.

540pi = pi × r^2 × 15.

Divide both sides of the equation by 15pi.

r^2 = 36

r = +/- 6.

Length cannot be negative, so r = 6.

diameter = 2 × r. In this case,

d = 2 × 6 = 12.

The diameter is 12 ft.

jek_recluse [69]2 years ago

6 0

Answer:

Step-by-step explanation:

Volume of cylinder is pi*r^2*h (this is equal to 540pi in this case)

So we have 540pi=pi*r^2*h

this means that 540=r^2*h (I just divided both sides by pi since both sides were being multiplied by pi)

The height,h, is 15 so plug in 540=r^2*15

Divide both sides by 15 giving 540/15=r^2

So r^2=36

So r=6

The diameter,d, is twice the radius, r.

So d=2(6)=12

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3 years ago

The sum of two numbers is 6, their difference is 4, find the two numbers. What is their product?

Firlakuza [10]

Answer:

The two numbers are 5 and 1. Their product is 5

Step-by-step explanation:

x + y = 6 (*)

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Let (*) + (**)

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<=> 2x = 10 <=> x = 5

Substitute x= 5

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3 years ago

Luci Lulu opened a cookie store in the mall. She found that the relationship between the price of a cookie, p, and the number of

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Answer:

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The price Luci Lulu should sell the cookies to make the maximum revenue is $1.

Step-by-step explanation:

From the question, we have:

x = −2000p + 4000 ..................... (1)

Where;

x = number of cookies sold

p = price of a cookie, p, and the

Revenue function (R) can therefore be obtained as follows:

R = px ……………………….. (2)

If we substitute equation (1) into (2), we will have:

R = p(−2000p + 4000)

R = −2000p^2 + 4000p ……………… (3)

Differentiating equation (3) with respect to p and set it equal to zero, we have:

−4000p + 4000 = 0

Solving for p, we have:

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p = 4000 / 4000

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Therefore, this implies the price Luci Lulu should sell the cookies to make the maximum revenue is $1.

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2 years ago

In right ABC, AN is the altitude to the hypotenuse. FindBN, AN, and AC,if AB =2 5 in, and NC= 1 in.

Rama09 [41]

From the statement of the problem, we have:

• a right triangle △ABC,

• the altitude to the hypotenuse is denoted AN,

• AB = 2√5 in,

• NC = 1 in.

Using the data above, we draw the following diagram:

We must compute BN, AN and AC.

To solve this problem, we will use Pitagoras Theorem, which states that:

$h^2=a^2+b^2\text{.}$

Where h is the hypotenuse, a and b the sides of a right triangle.

(I) From the picture, we see that we have two sub right triangles:

1) △ANC with sides:

• h = AC,

• a = ,NC = 1,,

• b = NA.

2) △ANB with sides:

• h = ,AB = 2√5,,

• a = BN,

• b = NA,

Replacing the data of the triangles in Pitagoras, Theorem, we get the following equations:

$\begin{cases}AC^2=1^2+NA^2, \\ (2\sqrt[]{5})^2=BN^2+NA^2\text{.}\end{cases}\Rightarrow\begin{cases}NA^2=AC^2-1, \\ NA^2=20-BN^2\text{.}\end{cases}$

Equalling the last two equations, we have:

$\begin{gathered} AC^2-1=20-BN^2.^{} \\ AC^2=21-BN^2\text{.} \end{gathered}$

(II) To find the values of AC and BN we need another equation. We find that equation applying the Pigatoras Theorem to the sides of the bigger right triangle:

3) △ABC has sides:

• h = BC = ,BN + 1,,

• a = AC,

• b = ,AB = 2√5,,

Replacing these data in Pitagoras Theorem, we have:

$\begin{gathered} \mleft(BN+1\mright)^2=(2\sqrt[]{5})^2+AC^2 \\ (BN+1)^2=20+AC^2, \\ AC^2=(BN+1)^2-20. \end{gathered}$

Equalling the last equation to the one from (I), we have:

$\begin{gathered} 21-BN^2=(BN+1)^2-20, \\ 21-BN^2=BN^2+2BN+1-20 \\ 2BN^2+2BN-40=0, \\ BN^2+BN-20=0. \end{gathered}$

(III) Solving for BN the last quadratic equation, we get two values:

$\begin{gathered} BN=4, \\ BN=-5. \end{gathered}$

Because BN is a length, we must discard the negative value. So we have:

$BN=4.$

Replacing this value in the equation for AC, we get:

$\begin{gathered} AC^2=21-4^2, \\ AC^2=5, \\ AC=\sqrt[]{5}. \end{gathered}$

Finally, replacing the value of AC in the equation of NA, we get:

$\begin{gathered} NA^2=(\sqrt[]{5})^2-1, \\ NA^2=5-1, \\ NA=\sqrt[]{4}, \\ AN=NA=2. \end{gathered}$

Answers

The lengths of the sides are:

• BN = 4 in,

• AN = 2 in,

• AC = √5 in.

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