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3 years ago

7

The jacks and balls have to be split among 6 people. Use the Distributive Property to pull the number 6 out of the expression yo

u wrote in part a. Write the resulting expression below.

1 answer:

Nat2105 [25]3 years ago

6 0

Answer: (24 + 60) = (6 × 4 + 6 × 10) = 6 × (4 + 10)

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[25 POINTS] A cylinder has a volume of 400π cm3. Find the dimensions that minimize its surface area.

miss Akunina [59]

Answer:

r = 5.848cm, h = 11.696cm

Step-by-step explanation:

Surface area: $SA=2\pi rh+2\pi r^2$

Volume: $V=\pi r^2h$

Therefore, the height of a cylinder given its volume would be $h=\frac{V}{\pi r^2}$ , thus:

$SA=2\pi r(\frac{V}{\pi r^2})+2\pi r^2\\\\SA=\frac{2V}{r}+2\pi r^2\\\\SA=\frac{2(400\pi)}{r}+2\pi r^2\\\\SA=\frac{800\pi}{r}+2\pi r^2$

We now find the derivative of the surface area of the cylinder with respect to its radius and set it equal to 0, solving for the radius:

$\frac{d(SA)}{dr}=-\frac{800\pi}{r^2}+4\pi r$

$0=-\frac{800}{r^2}+4\pi r$

$0=800\pi+4\pi r^3$

$-800\pi=4\pi r^3$

$-200=r^3$

$r\approx5.848$

If $0If [tex]r>5.848$ , then the surface area of the cylinder increases

Therefore, the surface area is minimized when the radius is $r=5.848cm$ , making the minimum height $h=\frac{V}{\pi r^2}=\frac{400\pi}{\pi(5.848)^2}\approx11.696cm$ .

In conclusion, the 2nd option is correct.

3 0

2 years ago

When 31 times a number is increased by 40 the answer is the same as when 200 is decreased by the number

coldgirl [10]

Answer:

Tye answer is 5 becuase 5*31=195 and 200-5=195

7 0

3 years ago

Of the 50 U.S. states, 4 have names that start with the letter W.

IRINA_888 [86]

8% Start with the Letter "W"

4 0

3 years ago

Read 2 more answers

What is the measure in each angle? A? B? C?

andrey2020 [161]

Answer:

∠A = 48°, ∠B = 48°, and ∠C = 84°

Step-by-step explanation:

AB = CB Given

m ∠A = m ∠C If opposite sides are =, then those opposite angles are =

6(x - 3) = 4(x + 1)

6x - 18 = 4x + 4

2x - 18 = 4

2x = 22

x = 11

m ∠A = 6(11 - 3) = 6(8) = 48°

m ∠C = 4(11+ 1) = 4(12) = 48°

The sum of the angles in a triangle = 180°

48° + 48° m ∠B = 180°

96°+ m ∠B = 180°

84° = m ∠B

5 0

2 years ago

Which of the following notes is G?

Marta_Voda [28]

G in bass clef is the answer D!

7 0

2 years ago