Answer this Idk what tor do

Hello , how to do 6(iii)?

Doss [256]

Answer:

$\displaystyle \frac{dS}{dt}=\frac{3}{50r}$

Step-by-step explanation:

Water is being pumped into an inflated rubber sphere at a constant rate of 0.03 cubic meters per second.

So, dV/dt = 0.03.

We want to show that dS/dt is directly proportional to 1/r.

In other words, we want to establish the relationship that dS/dt = k(1/r), where k is some constant.

First, the volume of a sphere V is given by:

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

Therefore:

$\displaystyle \frac{dV}{dt}=4\pi r^2\frac{dr}{dt}$

Next, the surface area of a sphere S is given by:

$\displaystyle S=4\pi r^2$

Therefore:

$\displaystyle \frac{dS}{dt}=8\pi r\frac{dr}{dt}$

We can divide both sides by 2:

$\displaystyle \frac{1}{2}\frac{dS}{dt}=4\pi r\frac{dr}{dt}$

We can substitute this into dV/dt. Rewriting:

$\displaystyle \frac{dV}{dt}=r\Big(4\pi r\frac{dr}{dt}\Big)$

So:

$\displaystyle \frac{dV}{dt}=\frac{1}{2}r\frac{dS}{dt}$

Since dV/dt = 0.03 or 3/100:

$\displaystyle \frac{3}{100}=\frac{1}{2}r\frac{dS}{dt}$

Therefore:

$\displaystyle \frac{dS}{dt}=\frac{3}{50r}=\frac{3}{50}\Big(\frac{1}{r}\Big)$

Where k = 3/50.

And we have shown that dS/dt is directly proportional to 1/r.

4 0

3 years ago

Can somebody help me with this pleas.

Yuki888 [10]

Answer:

what do you need help with <33

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

Need help! Nd please write down steps. Thank u

erma4kov [3.2K]

Answer:

what the question I font see it

3 0

3 years ago

Read 2 more answers

A pound of weed and feed covers 200 square feet how many pounds are needed to fertilize a lawn measuring 70 feet by 50 feet

nika2105 [10]

You would have to find out how many square feet the lawn is first:
70 x 50 = 3500 square feet
You are told that one pound = 200 square feet so use this to calculate how many pound you’ll need for 3500 square feet.
3500 square feet divided by 200 square feet = 17.5 pounds
Answer: 17.5 pounds

5 0

2 years ago

A sociologist recorded the estimated life expectancies of women born in Center City. Use the data from women born in 1970 and 20

Veronika [31]

$Y=0.213x-352$ will represent this linear model shown in the data table.

<h3>What will be the linear model for the given data?</h3>

Put the values of the x in the all given equations and then check the value of y if the value of y matches the given values in the option

So if we put the value x=1980 in the $Y=0.213x-352$ then

$Y=0.213(1980)-352$

$Y=69.74$

These values are closest to 70.1 whereas other options do not satisfy the condition.

Thus $Y=0.213x-352$ will represent this linear model shown in the data table.

To know more about Statistics follow

brainly.com/question/21508412

3 0

1 year ago