If A is the area of a circle with radiusr and the circle expands as time passes, find dA/dt in terms of dr/dt.
So I have, A= π r2
dA/dt = 2π r (dr/dt)

Answers

Answer 1

Answer:

[tex]\frac{dA}{dt} = 2\pi r(\frac{dr}{dt})[/tex]

Step-by-step explanation:

Your solution is correct (See explanation):

Area (A) of a circle is

[tex]A = \pi r^2[/tex]

Where

[tex]r = radius[/tex]

Differentiate both sides with respect to t

[tex]\frac{dA}{dt} = 2\pi r(\frac{dr}{dt})[/tex]

This is so because, we have to differentiate A on the left hand side and r on the right hand side because [tex]2\pi[/tex] is a constant

Hence, your solution is correct and and

[tex]\frac{dA}{dt} = 2\pi r(\frac{dr}{dt})[/tex]


Related Questions

A barrel contained 70 gallons of water. Water leaked out of the barrel at a rate of 5 gallons every 3 days.


At this rate, how many days did it take for all 70 gallons of water to leak out of the barrel?

Answers

Answer:

42 days

Step-by-step explanation:

Given

[tex]Gallons = 70[/tex]

Leakage = 5 gallons in 3 days

Required

Determine the number of days it finish leaking out

The scenario can be represented as:

5 gallons = 3 days

and

70 gallons = x

Where x represents the number of days to leak out 70 gallons

Cross Multiply:

[tex]5 * x = 3 * 70[/tex]

[tex]5 x = 210[/tex]

Divide both sides by 5

[tex]x = \frac{210}{5}[/tex]

[tex]x = 42[/tex]

Hence, it'll take 42 days

Two-thirds of the sum of three times a number and six is ten what is the number ?

Answers

Answer:

X=3

Step-by-step explanation:

2/3*(3x+6)=10

2x+4=10

X=6/2

x=3

Solve (x-5)^2- 45 = 0, where x is a real number

Answers

Answer:

Step-by-step explanation: the answer is x= 3[tex]\sqrt{5}[/tex] +5, -3 [tex]\sqrt{5}[/tex] +5

Find the lengths of HJ

Answers

Answer:

What's HJ? Never heard of it

51. التي سجل 16 لاعبا للاشتراك في دروس التنس. ويخطط المدرب لاستخدام 50 كرة تنس لكل لاعب وامتلاك
200 إضافية كك عدد كرات التنس اللازمة للدروس

Answers

Answer:

no islamic state propaganda in my country

Step-by-step explanation:

his that
The Prime Minister enforced
stated no one
could be out in public after 9:00 p.m.

Answers

yes is because of riots?

ayo who is wiining the election now?

Answers

Answer:

Joe Biden

Step-by-step explanation:

Solve for x by answering the number below/

Answers

X = 5.

2(5)+8=4(5)-2
18=18

Answer:

The value of x is 5.

Step-by-step explanation:

In a square, all sides are equal so you can compare the expressions to solve x :

[tex]4x - 2 = 2x + 8[/tex]

[tex]4x - 2x = 8 + 2[/tex]

[tex]2x = 10[/tex]

[tex]x = 5[/tex]

I just need help filling in the rest of this table. I've done some, but I've been stuck for a while now. Huge thanks to anyone who can help!

Answers

Answer:

i think 20 is above 12 and 17 under 30 and 36 is on top of 20 the rule is .50(x) +2

Answer:

Step-by-step explanation:

c = 0.5t + 2

12 = 0.5t + 2 ⇒ 0.5t = 10 ⇒ t = 20

c = 0.5(30)  + 2 ⇒ c = 17

20 = 0.5t + 2 ⇒ 0.5t = 18 ⇒ t = 36

PLEAS4EE!!
180°- 125° 15'=

Answers

Answer:

180.25°

Step-by-step explanation:

AND DANG U SO CUTE!!!!

this as a decimali if you respond for first you will have
the brainlest answer​

Answers

Answer:

8.525

Step-by-step explanation:

please help. i give brainliest ti correct answer

Answers

Here’s the answer luv. It’s D. 9

12 out of 15 students play in the school band. In a class of 45 students, how many do NOT play in the band? HELP!

Answers

Answer:

9 students

Step-by-step explanation:

because 15x 3 = 45 so 12x3= 36 so 45-36= 9 Can i be branliest

CAN YOU HELP ME WITH MY TESTT PLEASEE!!

Answers

Answer:

$0.44 per lb.

Step-by-step explanation:

Divide the total cost of the dog food ($10.56) by the 24 pounds to get cost per pound.

$10.56 ÷ 24 = $0.44 per lb.

Answer:

0.44 per pound

Step-by-step explanation:

10.56 divided by 24

PLSSS HELP ME! WILL GIVE BRAINLIEST WHEN I CAN

Answers

Answer:

first one: 5/8

second one; 1/2

third one 2/7

fourth one 3/14

fifth one 1/11

I hope this is good enough:

0.06/ 0.5334 Find the quotient

Answers

Answer:

the answer is 0.11248593

Step-by-step explanation:

Explain radical form. Discuss why it is more accurate than decimal approximation.

Answers

Answer:

3/45-8=12

Step-by-step explanation:

Answer:

It's more accurate because

Step-by-step explanation:

Expressing in the simplest radical form just means simplifying a radical so that there are no more square roots, cube roots, 4th roots, etc left to find. It also means removing any radicals in the denominator of a fraction.

In 1997, the American Diabetes Association (ADA) and the federal government lowered the standard for diagnosing diabetes from a fasting blood glucose level of 140 mg/dL to 126 mg/dL.7. What is the proportion of people who are considered have diabetes and they were not considered have diabetes before 1997

Answers

Answer:

10 percent

Step-by-step explanation:

- Before 1997, people with a minimum FBGL of 140mg/dl were diagnosed as diabetic

- After 1997, people with a minimum FBGL of 126mg/dl were diagnosed as diabetic

- What is the proportion of people who were not considered diabetic before 1997 but are now considered diabetic (after 1997)?

140 - 126 = 14

In percentage, this proportion is = 14/140 × 100

= 10%

Hence, 10% of the people who were not considered diabetic before 1997 are now or will now be considered diabetic.

I’ll give you a brainliest if you have these answers in 3 minutes —Find the slope and the y-intercept from the equation of this line:

Y=2x-3

-3x+2y=6

Answers

Answer:

1. the slope is 2 and the Y intercept is 3

2. the slope is 3 and the Y intercept is 2

Step-by-step explanation:

53. Pem was given a coin on Monday. Then she was given two coins every day for a long time
Which day did she get her 17th coin?
A. Tuesday
B. Wednesday
C. Sunday
D. Monday​

Answers

I think it’s A.) Tuesday

A bag contains 9 red marbles and 7 yellow marbles. You randomly select three marbles from the bag.

What is the probability that all three marbles are red when you replace each marble before selecting the next marble

Answers

Answer:

9 out of 16 chances three red marbles are gonna come out

Margie walked 3.75 miles on Tuesday morning. On Wednesday morning, she walked 1.2 times as far as she did on Tuesday. How far did she walk on Wednesday?

Answers

4.5 ? not entirely sure but seems simple just multiply 3.75 by 1.2

Find f (x )if f apostrophe apostrophe (x )equals x to the power of negative 2 end exponent comma space x greater than 0 comma space f (1 )equals 0 and f (2 )equals 0.

Answers

Step-by-step explanation:

Given [tex]g'(x) = g^{-2}, x> 0\ g(1) = 0 \ and \ g(2) = 0[/tex]

To get g(x), we will have to integrate g'(x)

[tex]g(x) = \int\limits {x^{-2}} \, dx\\ g(x) = \frac{x^{-2+1}}{-2+1} + C\\ g(x) = -x^{-1} + C\\g(x) = -x^{-1} + C\\[/tex]

If g(1) = 0, this means at x = 1, g(x) = 0

0 = -1⁻¹ + C

C= 1

Substitute C = 1 into the function

g(x) = -x⁻¹ + 1

If g(2) = 0, this means at x = 2, g(x) = 0

0 = -2⁻¹ + C

C= 2⁻¹

C =  1/2

Substitute C = 2 into the function

g(x) = -x⁻¹ + 1/2

Leo bought 18 boxes of cereal. This is 25% of the boxes at the store. How many total boxes of cereal were at the store?

Answers

Answer : There were 72 boxes at the store.
72 boxes at the store

What is the solve for r 9 = -3 -Зr?

Answers

Answer:

Hello the answer is - 4

Step-by-step explanation:

[tex]9 = - 3 - 3r \\ 9 + 3 = - 3r \\ - 3r = 12 \\ r = \frac{12}{ - 3} = - 4[/tex]

Answer:

-4

Step-by-step explanation:

-3r-3=9

9+3=-3r

12=-3r

12/-3=-3/-3r

-4=r

Need help on this one also

Answers

Answer:

its always C trush me

Step-by-step explanation:

Answer: a

Step-by-step explanation:

Which expression is equivalent to RootIndex 3 StartRoot 256 x Superscript 10 Baseline y Superscript 7 Baseline EndRoot? 4 x squared y (RootIndex 3 StartRoot x squared y cubed EndRoot) 4 x cubed y squared (RootIndex 3 StartRoot 4 x y EndRoot) 16 x cubed y squared (RootIndex 3 StartRoot x y EndRoot) 16 x Superscript 5 Baseline y cubed (RootIndex 3 StartRoot y EndRoot)

Answers

Answer:

B

Step-by-step explanation:

edg 2021

Answer: b

Step-by-step explanation:

help meee please and thank you

Answers

Answer

1

Step-by-step explanation:

anything times one equals the number multiplied by one

Hope this helps :)

Answer:

2x1=2, -2x1= -2, 2x0.5=1, -2x (-0.5)=1

HOPEFULLY THIS HELPS :3

Find all solutions to the system
5x − 3y = 2,
15x + 6y = 6.

Answers

Answer:

The answer I got was: (0.4,0)


Denominator of the fraction
2/5.

Denominator of the fraction 13/16.

This is a 20 point question must answer both plzzz plus Brainly

Answers

Answer:

Denominator for 2/5 is 5, and denominator for 13/16 is 16.

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