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
zavuch27 [327]
3 years ago
5

If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate (in cm/min) at which the diameter d

ecreases when the diameter is 9 cm. (Round your answer to three decimal places.)
Mathematics
1 answer:
grin007 [14]3 years ago
7 0

Answer:

The diameter decreases at a rate of 0.053 cm/min.

Step-by-step explanation:

Surface area of an snowball

The surface area of an snowball has the following equation:

S_{a} = \pi d^2

In which d is the diameter.

Implicit differentiation:

To solve this question, we differentiate the equation for the surface area implictly, in function of t. So

\frac{dS_{a}}{dt} = 2d\pi\frac{dd}{dt}

Surface area decreases at a rate of 3 cm2/min

This means that \frac{dS_{a}}{dt} = -3

Tind the rate (in cm/min) at which the diameter decreases when the diameter is 9 cm.

This is \frac{dd}{dt} when d = 9. So

\frac{dS_{a}}{dt} = 2d\pi\frac{dd}{dt}

-3 = 2*9\pi\frac{dd}{dt}

\frac{dd}{dt} = -\frac{3}{18\pi}

\frac{dd}{dt} = -0.053

The diameter decreases at a rate of 0.053 cm/min.

You might be interested in
Please answer this correctly
Katarina [22]

Answer:

SA = 1,176 ft².

Step-by-step explanation:

To find the surface area of the triangular prism, we can solve for the rectangular base, both triangular faces, and lateral sides separately.

For the rectangular base: (Use formula l×w)

20 × 18 = 360 ft²

For the triangular faces: (Use formula 1/2(b·h)

1/2(18 × 12) = 108 ft²

Since there are two faces, we need to double the amount.

108 × 2 = 216 ft².

Finally, solve for the lateral sides:

20 × 15 = 300 ft².

There are two sides, so:

300 × 2 = 600 ft².

Add up all of these areas:

600 + 216 + 360 = 1,176 ft²

5 0
3 years ago
Given the equation y = 4 + 2x find the values for y given the value x
Leviafan [203]

Answer:

If x = 3 then y = 10

If x = -3 then y = -2

If x = 4 then y = 12

If x = -2 then y = 0

4 0
3 years ago
Classify the number -84.
Drupady [299]
-84 is a real number, a rational number, and an integer
5 0
3 years ago
A water sprinkler sends water out in a circular pattern. How large is the watered area if the radius of the watering pattern is
Serhud [2]

Answer:

706.5 ft^2

Step-by-step explanation:

area = radius^2 (Pi)

15^2(3.14) = 706.5

5 0
3 years ago
Read 2 more answers
Find the image of the given point
lbvjy [14]

Answer:

P' = (2, -2)

Step-by-step explanation:

You have the x-value and the y-value of the pre-image, so all you have to do is plug that into the translation statement (x + 9 , y - 3).

Since x = -7 and y = 1 that would be (-7 + 9, 1 - 3), or (2, -2).

8 0
3 years ago
Other questions:
  • In the late nineteenth century, the scientist Marie Curie performed experiments that led to the discovery of radioactive substan
    13·1 answer
  • Interest If Bob has $1500 in the bank and pays a 5% intrest for 2 years how much money will he have left?
    13·1 answer
  • Which statement is a correct interpretation of the vertical line test?
    14·2 answers
  • Using the Law of Sine or Cosine, solve for the unknown variable (round to the
    5·1 answer
  • Convert 12 ounces to pounds use the conversion rate 16 ounces = 1 pound
    12·2 answers
  • < 5 and <7 are vertical angles.
    15·1 answer
  • In an arithmetic-sudoku, the values 1,2,3,4 appear exactly once in each row and each column. Which value belongs in the grey squ
    9·1 answer
  • What is 36 x 36<br>A. 1296<br>B. 1256<br>C. 1298<br>D. 1301​
    11·2 answers
  • In the following figure the value of x is
    15·2 answers
  • The area of a tennis court is 312 yd^2 How many ft^2 is that? *
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!