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2 years ago

What is the rate of change of the volume of the cylinder at that instance (in cubic kilometers per second)?

Mathematics

1 answer:

Kay [80]2 years ago

3 0

Answer:

hello your question is incomplete attached below is the complete question

answer : -2400 π

Step-by-step explanation:

dr/dt = -12 km/s

h = 2.5 km

r = 40 km at some instant

hence the rate of change of Volume of cylinder at that instance

= dv / dt = $d(\pi r^h ) / dt$

= $\pi h\frac{d(r^2)}{dt}$ = $-\pi h *2r *dr/dt$

hence ; dv / dt = -2400 π

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Step-by-step explanation:

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2 years ago

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1 The perimeter of a square is 40 yards. What is its area?

Makovka662 [10]

Answer:

100 yds^2

Step-by-step explanation:

To find the area of a square, we need to know the length of one side of the square. Since the perimeter is 4 times the length of one side, or 4s, and since 4s = 40 yds, s must be 10 yds.

Then the area of the square is (10 yds)^2 = 100 yds^2.

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2 years ago

Find the volume of an oblique cone.

AURORKA [14]

V = (1/3) π r² t

= (1/3) π (10 cm)². 16 cm

= (1/3) π (100 cm²). 16 cm

= (1/3) π (1600 cm³)

= (1600π)÷3 cm³ (B)

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2 years ago

A standard piece of paper is 0.05 mm thick. Let's imagine taking a piece of paper and folding the paper in half multiple times.

tatyana61 [14]

Answer:

(a) $g(n)=0.05\cdot 2^n$

(b) $g^{-1}(n)=\log_{2}20g(n)$

Step-by-step explanation:

Part A

The paper's thickness = 0.05mm

When the paper is folded, its width doubles (increases by 100%).

The thickness of the paper grows exponentially and can be modeled by the function:

$g(n)=0.05(1+100\%)^n\\\\g(n)=0.05\cdot 2^n$

Part B

$g(n)=0.05\cdot 2^n\\2^n=\dfrac{g(n)}{0.05}\\ 2^n=20g(n)\\$Changing to logarithm form, we have:\\\log_{2}20g(n)=n\\$Therefore:\\g^{-1}(n)=\log_{2}20g(n)$

Part C

If the thickness of the paper, g(n)=384,472,300,000 mm

Then:

$g^{-1}(n)=\log_{2}20g(n)\\g^{-1}(n)=\log_{2}20\times 384,472,300,000\\=\dfrac{\log 20\times 384,472,300,000}{\log 2} \\g^{-1}(n)=42.8 \approx 43\\n=43$

You must fold the paper 43 times to make the folded paper have a thickness that is the same as the distance from the earth to the moon.

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2 years ago

Hector invests $20,000 at age 21. He hopes the investment will be worth $200,000 when he turns 40. If the interest compounds con

KiRa [710]

Answer:

12.12%

Step-by-step explanation:

We have that the formula is given by:

A = p * e ^ (r * t)

From here, we know that A = 200000; p = 20000 and the time we can calculate 40 - 21 = 19

if we replace we have:

200000 = 20000 * e ^ (19 * r)

we must calculate r:

e ^ (19 * r) = 200000/20000

e ^ (19 * r) = 10

19 * r = ln 10

r = ln 10/19

r = 0.1212

In other words, the rate of growth is 12.12%

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2 years ago

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