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
Norma-Jean [14]
3 years ago
6

a spherical balloon is deflated at a rate of 256pi/3 cm^3/sec. at what rate is the radius of the balloon changing when the radiu

s is 8 cm?
Mathematics
1 answer:
Hunter-Best [27]3 years ago
3 0
What you need to look for is \frac { dr }{ dt } when r=8.

Now:

Volume\quad of\quad a\quad sphere:\\ \\ V=\frac { 4 }{ 3 } \pi { r }^{ 3 }

\therefore \quad \frac { dV }{ dr } =\frac { 4 }{ 3 } \pi \cdot 3{ r }^{ 2 }=4\pi { r }^{ 2 }\\ \\ \therefore \quad \frac { dr }{ dV } =\frac { 1 }{ \frac { dV }{ dr }  } =\frac { 1 }{ 4\pi { r }^{ 2 } }

And:\\ \\ \frac { dV }{ dt } =-\frac { 256\pi  }{ 3 } \\ \\ Therefore:\\ \\ \frac { dr }{ dt } =\frac { dr }{ dV } \cdot \frac { dV }{ dt }

\\ \\ =\frac { 1 }{ 4\pi { r }^{ 2 } } \cdot -\frac { 256\pi  }{ 3 } \\ \\ =-\frac { 256 }{ 12 } \cdot \frac { \pi  }{ \pi  } \cdot \frac { 1 }{ { r }^{ 2 } }

\\ \\ =-\frac { 64 }{ 3{ r }^{ 2 } } \\ \\ When\quad r=8,\\ \\ \frac { dr }{ dt } =-\frac { 64 }{ 3\cdot { 8 }^{ 2 } } =-\frac { 1 }{ 3 } \\ \\ Answer:\quad -\frac { 1 }{ 3 } \quad cm/sec
You might be interested in
Solve for x. x + 3 = 10
ICE Princess25 [194]

Answer:x=7

Step-by-step explanation:

X+3=10

-3 -3

X=7

5 0
3 years ago
Read 2 more answers
So that you get points answer this easy question <br> 2 - 1
Nataly [62]

Answer:

1

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Solve for x.38(2x+16)−2=13 Enter your answer in the box.x =
lys-0071 [83]

Given:

\frac{3}{8}(2x+16)-2=13\frac{3}{8}(2x+16)=13+2\frac{3}{8}(2x+16)=15(2x+16)=15\times\frac{8}{3}(2x+16)=402x=40-162x=24x=\frac{24}{2}x=12

5 0
1 year ago
What is 3/5 divided by 1/2 using the keep change flip method
goblinko [34]

Answer:

6/5

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Suppose two different states each pick a two-digit lottery number between 00 and 99 (for a 100 possible numbers).
Neporo4naja [7]
A. 1/10000 because it is a 1/100 chance for each. 
b. 1/100 because there are 10,000 options and 100 of them are the same options. Simplify for the answer. 
6 0
3 years ago
Other questions:
  • Can you guys help me with question​
    9·2 answers
  • Four less than five times a number is equal to 11
    6·2 answers
  • 675,360.41 in expanded notation
    14·2 answers
  • What is 2*2*2*2*2*2 -6*6
    12·2 answers
  • 9 is greater than w, and 5 is less than or equal to w
    13·2 answers
  • Jen has 2 meters of taffy. She wants to give each of her three best friends in equal amount of taffy how many centimeters of taf
    8·1 answer
  • What is a hypotenuse? <br> I took this picture to help you explain it if you can. Thanks!
    7·2 answers
  • Work out the perimeter of this semicircle with radius 3cm. Give your answer in terms of π​
    15·1 answer
  • Please help me figure out the answer to this question and the processes well!
    11·1 answer
  • Divide the number of meters by to find the number of laps
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!