Match each inequality to the correct graph.

Suppose the radius of the sphere is increasing at a constant rate of 0.3 centimeters per second. At the moment when the radius i

elixir [45]

<h2>At the moment when the radius is 24 centimeters, the volume is increasing at a rate of 2171.47 cm³/min.</h2>

Step-by-step explanation:

We have equation for volume of a sphere

$V=\frac{4}{3}\pi r^3$

where r is the radius

Differentiating with respect to time,

$\frac{dV}{dt}=\frac{d}{dt}\left (\frac{4}{3}\pi r^3 \right )\\\\\frac{dV}{dt}=\frac{4}{3}\pi \times 3r^2\times \frac{dr}{dt}\\\\\frac{dV}{dt}=4\pi r^2\times \frac{dr}{dt}$

Given that

Radius, r = 24 cm

$\frac{dr}{dt}=0.3cm/s$

Substituting

$\frac{dV}{dt}=4\pi r^2\times \frac{dr}{dt}\\\\\frac{dV}{dt}=4\pi \times 24^2\times 0.3\\\\\frac{dV}{dt}=2171.47cm^3/min$

At the moment when the radius is 24 centimeters, the volume is increasing at a rate of 2171.47 cm³/min.

4 0

3 years ago

How long must a ladder be to reach the top of a 12-foot wall if the bottom of the ladder is placed 3 feet from the base of the w

laila [671]

Answer:Q: What is the unknown information that could be found using the Pythagorean theorem?

A: The hypotenuse, or the length of the ladder.

Q: what is the approximate length of the ladder needed, rounding to the nearest hundredth?

A: 12.37 ft.

5 0

3 years ago

Read 2 more answers

Describe how to construct a sequence of nested intervals that have precisely the number √2 in common. There are many possible wa

iris [78.8K]

Answer:

See answer below

Step-by-step explanation:

Define the intervals:

$I_n:=(\sqrt{2}-\frac{1}{n},\sqrt{2}+1/n)$ for n≥1.

The intervals are nested, in the sense that $I_1\supset I_2\supset I_3 \supset \cdots$ To see this, use the fact that for all n≥1, -1/n≤-1/(n+1) and 1/n≥1/(n+1) (intuitively, the intervals are "shrinking" in size, and are centered around √2).

The only point common to all intervals is √2, in the sense that $\bigcap_{n\geq 1}I_n=\{2\}$

The idea for this construction is to center the intervals around √2 and shrink their size with the summand 1/n. As n goes to infinity, 1/n tends to zero and the intervals became closer and closer to √2, but they NEVER degenerate to the point √2, in contrast to their intersection.

7 0

4 years ago

Please help! Pls and thank you!

mars1129 [50]

Answer:

${4}^{11} \div {4}^{5 } = {4}^{11 - 5} = {4}^{6}$

Step-by-step explanation:

please mark me as brainlest

7 0

2 years ago

David uses 2/3 cup of milk to bake a batch of muffins. He wants to make 12 batches of muffins for a fundraiser. How much milk do

kipiarov [429]

Answer: 8

Step-by-step explanation:

12*2/3=8

7 0

3 years ago