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
Triangle LMN with vertices L(-9,-1) M(-3,-4) and N(-5,-8)
pishuonlain [190]

Answer:

Part A: L(-1,9) M(-4,3) N (-8,5)

Step-by-step explanation:

4 0
2 years ago
2.4 + 5.4q – 4.5q + 3.6<br><br> a.6+1.1q<br> b.9.9q+6<br> c.0.9q+6<br> d.9.9q-6
Yuri [45]
You have to add the same kind of terms, in this case the ones that have a variable (5.4q and -4.5q) and the ones that don't (2.4 and 3.6), like this:

(5.4q - 4.5q) + (2.4 + 3.6) = 0.9q + 6

The answer is c. 0.9 +6

8 0
3 years ago
Which of the following statements about rational numbers is not correct? А All whole numbers are also rational numbers. B All ra
iren2701 [21]

Step-by-step explanation:

  1. 1736-8166x71662=8177103 :D
3 0
3 years ago
Help it’s confusing
noname [10]

Answer:

I think is C like I said not quite sure...

8 0
3 years ago
Read 2 more answers
If 20 chickens laid 120<br> eggs. At this rate, how<br> many eggs would 30<br> chicken lay?
svetoff [14.1K]

Answer:

180 eggs is the correct amount.

6 0
3 years ago
Other questions:
  • A sample data set with a mean of 685 and a standard deviation of 39.8 has a bell-shaped distribution. what range of values inclu
    5·1 answer
  • How much is -1/4 of 1 1/3<br><br> a) - 1/3<br> b) 3/16<br> c) 1 1/12<br> d) -5 1/3
    14·2 answers
  • If the APY of a savings account is 3.2%, and if the principal in the savings account was $2400 for an entire year, what will the
    9·2 answers
  • Solve the linear equation, 2x+4=14​
    9·1 answer
  • 4. The scale factor on a house blueprint is 1 inch = 25
    8·1 answer
  • Righty in equation in standard form using integers Y +1 equals 2/3 parentheses X +3 parentheses
    15·1 answer
  • Solve for all values of x by factoring.'<br> x2 + 10x + 21 = 0
    15·2 answers
  • maria draws one marble from a bag containing 5 red, 3 green, and 4 yellow. the probability she draws a yellow marble is____
    7·1 answer
  • What is the numerator of the simplified sum?<br><br> OX+ 3<br> O 3x+6<br> O 4x+6<br> O 4x+2
    14·1 answer
  • Triple u then divide 3 by the result?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!