Sam's Grades

Karo-lina-s [1.5K]

Answer:

radius: 1.84 in
height: 3.68 in

Step-by-step explanation:

After you've worked a couple of "optimum cylinder" problems, you find that the cylinder with the least surface area for a given volume has a height that is equal to its diameter. So, the volume equation becomes ...

V = πr²·h = 2πr³ = 39 in³

Then the radius is ...

r = ∛(39/(2π)) in ≈ 1.83779 in ≈ 1.84 in

h = 2r = 3.67557 in ≈ 3.68 in

_____

The total surface area of a cylinder is ...

S = 2πr² + 2πrh

For a given volume, V, this becomes ...

S = 2π(r² +r·(V/(πr²))) = 2πr² +2V/r

The derivative of this with respect to r is ...

S' = 4πr -2V/r²

Setting this to zero and multiplying by r²/2 gives ...

0 = 2πr³ -V

r = ∛(V/(2π)) . . . . . . . . looks a lot like the expression above for r

__

If we substitute the equation for V into the equation just above this last one, we have ...

0 = 2πr³ - πr²·h

Dividing by πr² gives ...

0 = 2r - h

h = 2r . . . . . generic solution for cylinder optimization problems

3 0

3 years ago

What is prime factorization?

Mila [183]

The process of finding which prime numbers you need to multiply together to get a certain number. ex: 21=7x3 20=2x2x5

4 0

3 years ago

Read 2 more answers

Please help I need it

ivolga24 [154]

Answer:

<h2>Yes. It's a right triangle.</h2>

Step-by-step explanation:

If a ≤ b < c are the length of the sides of a right triangle, then

a² + b² = c².

We have:

a =30 ft, b = 40 ft and c = 50 ft.

Check the equality:

L = 30² + 40² = 900 + 1600 = 2500

R = 50² = 2500

L = R

5 0

3 years ago

Can y’all help me *********

melisa1 [442]

Answer:

33. The sheep pen is 16 square yards

Step-by-step explanation:

You can divide the rhombus inside into two triangles. Each triangle has a base of 4 yards and height 4 yards.

Area of triangle: A = 0.5*b*h = 0.5(4)(4) = 8

Since there are 2, then 2*8 = 16 square yards.

7 0

3 years ago

In 2018, the population will grow over 700,000.The population of a city in 2010 was 450,000 and was growing at a rate of 5% per

Firlakuza [10]

Answer:

The year is 2020.

Step-by-step explanation:

Let the number of years passed since 2010 to reach population more than 7000000 be 'x'.

Given:

Initial population is, $P_0=450,000$

Growth rate is, $r=5\%=0.05$

Final population is, $P=700,000$

A population growth is an exponential growth and is modeled by the following function:

$P=P_0(1+r)^x$

Taking log on both sides, we get:

$\log(P)=\log(P_0(1+r)^x)\\\log P=\log P_0+x\log (1+r)\\x\log (1+r)=\log P-\log P_0\\x\log(1+r)=\log(\frac{P}{P_0})\\x=\frac{\log(\frac{P}{P_0})}{\log(1+r)}$

Plug in all the given values and solve for 'x'.

$x=\frac{\log(\frac{700,000}{450,000})}{\log(1+0.05)}\\x=\frac{0.192}{0.021}=9.13\approx 10$

So, for $x > 9.13$ , the population is over 700,000. Therefore, from the tenth year after 2010, the population will be over 700,000.

Therefore, the tenth year after 2010 is 2020.

8 0

3 years ago