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
QveST [7]
2 years ago
6

A spherical balloon is inflated so that its volume is increasing at the rate of 3 ft3/min. How fast is the diameter of the ballo

on increasing when the radius is 1 ft
Mathematics
1 answer:
beks73 [17]2 years ago
3 0

When an spherical balloon volume is increasing at the rate of 3ft^3/min then the diameter of the balloon is increasing \frac{3}{2\pi }ft /min

How can we find the rate of change of balloon's diameter ?

The volume of a spherical balloon is v=\frac{4}{3} \pi r^3

In form of diameter we can write as

v=\frac{4}{3} \pi (\frac{D}{2} )^3\\=\frac{1}{6} \pi D^3

Now we will differentiate both sides wrt to t we get

\frac{dv}{dt} =\frac{1}{6} \pi 3D^2 \frac{dD}{dt} \\\frac{dD}{dt} =\frac{2}{\pi D^2} \frac{dv}{dt} \\\\when r=1\\D=2ft

Given in the question \frac{dv}{dt} =3ft^3/min

thus when we substitute the values we get

\frac{dD}{dt} =\frac{2}{\pi *2^2} (3)\\\frac{dD}{dt}=\frac{3}{2\pi }  ft/min

Learn more about the differentiation here:

brainly.com/question/28046488

#SPJ4

You might be interested in
Calculate the circumference and area of this circle. 4cm radius​
Alja [10]

Answer:

the circumference is 25.133 and the area is 50.265

5 0
3 years ago
Read 2 more answers
Simplify (6ab3c)(-abc2).
sp2606 [1]
Sorry, I know it's a little late.The answer is -6a^2 b^4 c^3
4 0
3 years ago
Who else likes my fursona? Give me your honest opinion 1-10<br><br><br><br> (3+(5-1+2)=n)
dmitriy555 [2]

Answer:

its really cool

Step-by-step explanation:

BRAINLIEST PLEASEEE

4 0
3 years ago
Read 2 more answers
Solve for x -x=-5<br> How do you solve for x?<br> can it remain negative ?
Svet_ta [14]
<span>Solve for x
-x=-5

multiply both sides by (-1)
</span>-x (-1) =-5 (-1)
simplify
x = 5

answer is 5 (positive 5)
4 0
3 years ago
Read 2 more answers
Expand <br>Your answer should be a polynomial in standard form. <br><br>(×-9) (×-9)= ​
Rama09 [41]

Answer:

X^2-18x+81

OR

(X-9)^2

Step-by-step explanation:

X(x-9)-9(x-9)=

x^2-9x-9x+81

X^2-18x+81

7 0
3 years ago
Read 2 more answers
Other questions:
  • How much is 10% to the power of 2?
    11·2 answers
  • A 100 foot ladder is leaning against a tree so that the top of the ladder is 96 feet above the ground. How far is the base of th
    10·2 answers
  • 67 times a number minus 58 is equal to 36 less than the number
    11·1 answer
  • (15,-9) is dilated by a scale factor of 3 what is its new location
    13·1 answer
  • The midpoint of CD is M(7,5). One endpoint is C(6, 8). Find the coordinates of the other
    14·1 answer
  • What is 4(x-7)=2(x+3)?
    7·2 answers
  • Solve for each variable X and Y.
    5·1 answer
  • K(x) = X +-6<br> k(3) =
    10·2 answers
  • - 0.2 ( 25x + 5 ) - 5 = 4
    10·2 answers
  • Use Venn diagram of prime factors to show the heck and Lcm of 15 and 22
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!