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
katrin2010 [14]
3 years ago
12

The surface area of a melting snowball decreases at a rate of3.8cm2/min. Find the rate at which its diameter decreases when the

diameter is13cm. (Round your answer to three decimal places if required)
Mathematics
1 answer:
Scorpion4ik [409]3 years ago
7 0

Answer:

Step-by-step explanation:

This is a pretty basic related rates problem. I'm going to go through this just like I do in class when I'm teaching it to my students.

We see we have a snowball, which is a sphere. We are talking about the surface area of this sphere which has a formula of

S=4\pi r^2

In the problem we are given diameter, not radius. What we know about the relationship between a radius and a diameter is that

d = 2r so

\frac{d}{2}=r Now we can have the equation in terms of diameter instead of radius. Rewriting:

S=4\pi(\frac{d}{2})^2 which simplifies to

S=4\pi(\frac{d^2}{4}) and a bit more to

S=\pi d^2 (the 4's cancel out by division). Now that is a simple equation for which we have to find the derivative with respect to time.

\frac{dS}{dt}=\pi*2d\frac{dD}{dt} Now let's look at the problem and see what we are given as far as information.

The rate at which the surface area changes is -3.8, and we are looking for \frac{dD}{dt}, the rate at which the diameter is changing, when the diameter is 13. Filling in:

-3.8=\pi(2)(13)\frac{dD}{dt} and solving for the rate at which the diameter is changing:

-\frac{3.8}{26\pi}=\frac{dD}{dt} and divide to get

\frac{dD}{dt}=-.459\frac{cm}{min} Obviously, the negative means that the diameter is decreasing.

You might be interested in
A new car is purchased for \$18,000$18,000 and over time its value depreciates by one half every 3.5 years. How long, to the nea
Taya2010 [7]

Answer:

15.1

Step-by-step explanation:

5 0
2 years ago
What would you earn in total commissions on the following sales of $5100 $4876 $5215 $6225 and $5235 if you if you earn a commis
lisov135 [29]

Answer:

$5100 would be $76.50

$4876 would be $73.14

$5215 would be $78.23

$6225 would be $93.38

$5235 would be $78.53

Step-by-step explanation:

To find commissions take your sale price and multiply it by your percentage and divide by 100

5 0
3 years ago
Help!! Which number is NOT in scientific notation?
ki77a [65]

D is not in correct scientific notation. To be correct, the answer would be 5.0 x 10^2

If this helped you, please list me as brainliest!

4 0
3 years ago
URGENT again having difficulty, please answer as soon as possible would be appreciate it :)
aliina [53]
1. X=-2 x=1 x=5/2
2. X=0 x=-1/5 x=4/3 x=1
3.x>-2
4.X>_8
6 0
2 years ago
Solve for y: 2(3y + 5) = 3 (5y +1/3).
kaheart [24]

Answer:

2(3y + 5) = 3 (5y +1/3)

6y+10=15y+1

9=9y

y=1

4 0
2 years ago
Read 2 more answers
Other questions:
  • Jerry went for an 18 mile bike ride, he completed 2/9 of his trip. How many more miles of the trip does jerry have to complete
    15·1 answer
  • How do you find measure a and c
    7·2 answers
  • An inlet pipe can fill a swimming pool in 9 hours and an outlet pipe can empty the pool in 12 hours. Through an error, both pipe
    14·1 answer
  • C) The determinant of 2 x 2 matrix A is 3. If you switch the rows and multiply the first row by 6 and the second row by 2, expla
    13·1 answer
  • Can you use the ASA Postulate or the AAS Theorem to prove the triangles congruent? (1)
    8·1 answer
  • What’s the value of x?
    5·2 answers
  • Clothing dan has 4 pairs of white​ socks 5 pairs of black​ socks, and several pairs of blue socks. has 12 pairs of socks altoget
    12·1 answer
  • 2x + 4y = 22<br> What is the answer?
    11·2 answers
  • There are 3 fourths as many cows as pigs on an animal farm. If there are 35 pigs and cows on the farm, how many of them are pigs
    6·1 answer
  • Please answer this question​
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!