Physics, 20.07.2019 04:30 kelseychristian24

The radius of a circle is increasing at a constant rate of 0.2 meters per second. what is the rate increase in the area of the circle at the instant when the circumference of the circle is 20π meters? v

Answers: 1

Show answers

Answers

The rate of increase in the area of the circle at the instant when the circumference of the circle is 20π m is 12.56 $\rm m^2/sec$ .

Given :

Radius of a circle is increasing at a constant rate of 0.2 m/sec.

Circumference of the circle at an instant is $20 \pi$ m.

Solution :

We know that area of the circle is,

$\rm A = \pi\times r^2$ --- (1)

Now differentiate equation (1) with respect to time t,

$\rm \dfrac{dA}{dt}=2\pi r \dfrac{dr}{dt}$

Given that

$\rm \dfrac{dr}{dt}=0.2\;m/sec$

so,

$\rm \dfrac{dA}{dt}= 0.4\times \pi\times r$ ------ (2)

We also know that circumference of the circle is,

$\rm C=2 \pi r$ --- (3)

At $\rm C = 20 \pi$ from equation (3) we get,

$2\pi r = 20 \pi$

$\rm r =10\;m$

Now put the value r in equation (2) we get

$\rm \dfrac{dA}{dt}=0.4\times \pi \times 10$

$\rm \dfrac{dA}{dt} = 12.56\;m^2/sec$

The rate of increase in the area of the circle at the instant when the circumference of the circle is 20π m is 12.56 $\rm m^2/sec$ .

For more information, refer the link given below

link

Answer from: lizzyhearts

This question involves the concepts of circumference, area, and derivative.

The rate of increase in area is "12.57 m²/s".

The area of a circle is given as:

$A = \pi r^2$

Taking the derivative with respect to time (t) on both sides, we get:

$\frac{dA}{dt}= \pi\frac{d(r^2)}{dt}\\\\\frac{dA}{dt}= 2\pi r\frac{dr}{dt}\\$

where,

$\frac{dA}{dt}$ = rate of change in area = ?

$2\pi r$ = Circumference of the circle = 20π m

$\frac{dr}{dt}$ = rate of increase in radius = 0.2 m/s

Therefore,

$\frac{dA}{dt}=(20\pi\ m)(0.2\ m/s)\\\\\frac{dA}{dt}=12.57\ m^2/s$

Learn more about the area of the circle here:

link

The attached picture shows the area of circle.

The radius of a circle is increasing at a constant rate of 0.2 meters per second. what is the rate i

Answer from: Quest

1.the balanced chemical equation is as below

cu + 2 ag(no)₃ → cu(no₃)₂ +2 ag

2.the much silver produced is 50.9 g

step 1: find the moles of cu

moles = mass÷ molar mass

from periodic table the molar mass of cu = 63.5 g/mol

moles is therefore = 15.00 g÷ 63.5 g/mol = 0.236 moles

step 2: use the mole ratio to determine the moles of ag

from equation above cu: ag is 1: 2

therefore the moles of ag =0.236 moles x 2/1 =0.472 moles

step 3: find the mass of ag

mass = moles x molar mass

from periodic table the molar mass of ag =107.87 g/mol

mass = 0.472 moles x 107.87 g/mol = 50.9 g

3. the much silver collected worth is 1.797 oz

convert 50.9 g to oz

that is 1 gram = 0.0353 oz

50.9 grams =? oz

by cross multiplication

={(50.9 grams x 0.0353 oz) / 1 gram} =1.797 oz

Answer from: Quest

Independent variable is something that is changed in a experiment.

Another question on Physics

Physics, 22.06.2019 02:30

The boy of mass 30 kg is at r1= 2 meters from the fulcrum. of the girl is 45 kg, at what r2 must she sit so that they are balanced ?

Answers: 3

Answer

Physics, 22.06.2019 03:00

Isla’s change in velocity is 30 m/s, and hazel has the same change in velocity. which best explains why they would have different accelerations? isla had negative acceleration, and hazel had positive. isla had a different time than hazel. isla had positive acceleration, and hazel had negative. isla went a farther distance than hazel.

Answers: 1

Answer

Physics, 22.06.2019 11:30

Which of the following is the phase that results when the moon is on the opposite side of the earth from the sun? a. quarter moon b. crescent moon c. new moon d. full moon

Answers: 1

Answer

Physics, 22.06.2019 14:40

You throw a small rock straight up from the edge of a highway bridge that crosses a river. the rock passes you on its way down, 7.00 s after it was thrown. what is the speed of the rock just before it reaches the water 28.0 m below the point where the rock left your hand? ignore air resistance.

Answers: 2

Answer

You know the right answer?

The radius of a circle is increasing at a constant rate of 0.2 meters per second. what is the rate i...

Questions