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
The data in the table represents the volume of helium, in cubic feet, inside a balloon relative to the elapsed time in minutes.
Mila [183]

The volume of helium inside the balloon decreased at a rate of 0.1 cubic feet per minute. The linear equation that represents the given data is y = -0.1x + 6 and its slope m = -0.1.

<h3>What is the equation of a line passing through two points?</h3>

The equation of the line passing through the points (x1, y1) and (x2, y2) is

(y - y1) = m(x - x1).

Where m is the slope of the line and is calculated by

m = (y2 - y1)/(x2 - x1)

<h3>Calculation:</h3>

The given data in the table represents the volume of helium (cu ft), inside a balloon relative to the elapsed time in minutes.

x: 5, 10, 15, 20, 25, 30, 35, 40

y: 5.5, 5, 4.5, 4, 3.5, 3, 2.5, 2

From this table, consider two points (5, 5.5) and (10, 5)

So, the equation of the line is

y- y1 = m(x - x1)

Where slope m = (y2 - y1)/(x2 - x1)

⇒ m = (5 - 5.5)/(10 - 5)

⇒ m = -0.5/5

∴ m = -0.1

Thus, the equation is

y - 5.5 = -0.1(x - 5)

⇒ y - 5.5 = -0.1x + 0.5

⇒ y = -0.1x + 0.5 + 5.5

⇒ y = -0.1x + 6.0

∴ y = -0.1x + 6

Since the slope of the line is negative, the volume of the helium inside the balloon decreased at a rate of 0.1 cubic ft per minute.

So, option 2 is correct.

Learn more about the slope of a line here:

brainly.com/question/3493733

#SPJ1

3 0
1 year ago
Kylie has only quarters and nickels in a jar the total value in the jar is $2 if there are a total of 20 coins how many of each
alexdok [17]

Answer: 7quarters and 3 nickels

Step-by-step explanation:

7=$1.75 3=.15

6 0
3 years ago
A bag contains 2 blue marbles, 3 green marbles, 1 white marble and 4 red marbles.
Dima020 [189]

Answer:

2/5

Step-by-step explanation:

add all marbles together: 10 marbles

since only 4 are red, the fraction would be 4/10

4/10 can be simplified to 2/5

3 0
2 years ago
Read 2 more answers
Combine like terms: x +x - x + y + y + y - z + z - z
Tomtit [17]
X  + x - x is   x
y + y + y is   3y
-z + z - z is   -z
x + 3y 
5 0
3 years ago
Which solid has five faces, four lateral faces, one base, five vertices, and eight edges?
Tanzania [10]
The solid that has five faces , four lateral faces, one base, five vertices, and eight edges would be :
Square pyramid

Hope this helps
6 0
3 years ago
Other questions:
  • Is y=3x linear or nonlinear
    9·1 answer
  • NEED HELP FAST!<br> --100 points--<br> (if accurate)<br> What is the value of x?
    11·1 answer
  • If a meteor hits the Earth and forms a crater that measures 10 miles in diameter, what is the area of the crater formed?
    6·1 answer
  • 3 Identify, if the question is
    6·1 answer
  • Find the sum using the number line.10+( -5​) Move the point on the number line as needed to choose the correct value for the sum
    14·1 answer
  • Answer the following monomial of division (-2x^2y^5)^3 (5x^4)/10x^7y^13
    12·2 answers
  • A shipment to a warehouse consists of 4,500 MP3 players. The manager chooses a random sample of 50 MP3 players and finds 4 that
    12·1 answer
  • Find the perimeter FOR BRAINLIEST
    10·1 answer
  • Solve the inequality for x= 1 + 2x &gt; -23
    10·1 answer
  • What is the relationship between the amplitude of light of light waves and brightness
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!