1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nutka1998 [239]
3 years ago
6

When the area in square units of an expanding circle is increasing twice as fast as its radius in linear units

Mathematics
2 answers:
alexira [117]3 years ago
5 0

Answer:

r=1/π

Step-by-step explanation:

Area of the circle is defined as:

Area = πr²

Derivating both sides

\frac{dA}{dr}=2πr

\frac{dA}{dt}  =  \frac{dA}{dr} x \frac{dr}{dt}  =  2πr\frac{dr}{dt}

If area of an expanding circle is increasing twice as fast as its radius in linear units. then we have : \frac{dA}{dt}  =2\frac{dr}{dt}

Therefore,

2πr \frac{dr}{dt}  =  2  \frac{dr}{dt}

r=1/π

Ber [7]3 years ago
4 0

Answer:

r = 1/π

Step-by-step explanation:

Here we have

Area of a circle given as

Area = πr²

Where:

r = Radius of the circle

When the area of the circle is expanding twice as fast s the radius we have

\frac{dA}{dt} =2 \times  \frac{dr}{dt}

However,

\frac{dA}{dt} = \frac{dA}{dr} \times \frac{dr}{dt} and

\frac{dA}{dr} = \frac{d\pi r^2}{dr} = 2\pi r

Therefore, we have

\frac{dA}{dt} =2 \times  \frac{dr}{dt} = 2\pi r \times  \frac{dr}{dt}

Cancelling like terms

1= \pi r

Therefore, r = \frac{1}{\pi }.

You might be interested in
Suden wants to know the theoretical and experimental probability of rolling a number smaller than a 3 on a 6-sided number cube n
MakcuM [25]

Answer:

The theoretical probability of rolling a number smaller than a 3 is __1/3_____because this is what__we expect to happen____ . The experimental probability of rolling a number smaller than a 3 is __1/4____ because this is what___actually happened____

Step-by-step explanation:

The experimental probability is

P (<3) = (  getting a one or 2)/ number of times that he rolled

        He rolled a one or a two 2 times of the 8 times rolled

          = 2/8 = 1/4

Theoretical probability is what we expect  happen

P (<3) = (getting a one or two) / 6

         = 2/6 = 1/3

The theoretical probability of rolling a number smaller than a 3 is __1/3_____because this is what__we expect to happen____ . The experimental probability of rolling a number smaller than a 3 is __1/4____ because this is what___actually happened____

4 0
3 years ago
How many intersecting planes are there in a cube?
GarryVolchara [31]

Answer: a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube is the only regular hexahedron and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices.

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Find the midpoint of the line segment joining the points (10,14) and (-7,7).
LekaFEV [45]

Answer:

(1.5, 10.5)

Step-by-step explanation:

midpoint =  \bigg( \frac{10 + ( - 7)}{2},  \:  \:  \frac{14 + 7}{2}  \bigg) \\  \\  = \bigg( \frac{3}{2}, \:  \:  \frac{21}{2}  \bigg) \\  \\  = = ( 1.5,  \:  \:  10.5 )

3 0
3 years ago
Solve the equation:<br> 12=19-√3x-11
Alekssandra [29.7K]
The answer is x=20. You isolate the square root. Eliminate the radical on the left handside. And then solve it!
4 0
3 years ago
Read 2 more answers
Mhanifa please answer this question about lines
ratelena [41]
I think the answer is TR
3 0
2 years ago
Other questions:
  • A rectangular standing-only section at the venue changes size as t increases in order to manage the flow of people. Let x repres
    13·1 answer
  • The _____ is measure of a country's total economic output
    5·1 answer
  • Squeezy fruit drink is 36% pure orange juice and 64% water, if 1 L of Squeezyfruit drink is mixed with 600 mL of water what is t
    5·1 answer
  • The data shows the number of grams of fat found in 9 different health bars 12, 14, 16, 17.5, 10, 18, 15, 15.5, 19
    12·1 answer
  • Write the following numbers used in these statements in scientific notation. (Note: Some of these numbers have been rounded.)
    7·1 answer
  • Deshaun is selling raffle tickets for every 4 tickets he charge $28
    11·1 answer
  • <img src="https://tex.z-dn.net/?f=%7B%5Corange%7B%5Cbigstar%7D%7D%20%5C%20%7B%5Cunderline%7B%5Cgreen%7B%5Ctextsf%7B%5Ctextbf%7BG
    11·2 answers
  • Which two equations are equivalent to: 3(3x - 2) = 5(2x + 4) 9x - 6 = 10x + 20
    7·1 answer
  • Figure this out for me!! (60 pts)
    8·2 answers
  • 20. GEOMETRY The measures of two sides of a triangle are given. If p isthe perimeter, and p=10x+5y, find the measure of the thir
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!