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
larisa86 [58]
3 years ago
10

Helium is pumped into a spherical balloon at a rate of 3 cubic feet per second. How fast is the radius increasing after 2 minute

s? Note: The volume of a sphere is given by V=43πr3V=43πr3. Rate of change of radius (in feet per second) =
Mathematics
1 answer:
Arisa [49]3 years ago
8 0

Answer:

The rate of change of radius is 0.0530 ft/sec.

Step-by-step explanation:

Given : Helium is pumped into a spherical balloon at a rate of 3 cubic feet per second.

To find : How fast is the radius increasing after 2 minutes?

Solution :

The volume of the sphere is V=\frac{4}{3}\pi r^3

Differentiating w.r.t. r,

\frac{dV}{dr}=4\pi r^2

We have given, Helium is pumped into a spherical balloon at a rate of 3 cubic feet per second.

i.e. \frac{dV}{dt}=3

Integrate w.r.t. t,

V=3t+C

Assuming V=0 when  t=0 then C=0

So, \frac{4}{3}\pi r^3=3t

r^3=\frac{t}{4\pi}

r=\sqrt[3]{\frac{t}{4\pi}}

Now, we apply chain rule

i.e.  \frac{dV}{dt}=\frac{dV}{dr}\cdot \frac{dr}{dt}

3=4\pi(\frac{t}{4\pi})^{\frac{2}{3}}\cdot \frac{dr}{dt}

The radius increasing after 2 minutes i.e. at t=2\times 60=120

3=4\pi(\frac{120}{4\pi})^{\frac{2}{3}})\cdot \frac{dr}{dt}

3=56.56\cdot \frac{dr}{dt}

\frac{dr}{dt}=\frac{3}{56.56}

\frac{dr}{dt}=0.0530

Therefore, the rate of change of radius is 0.0530 ft/sec.

You might be interested in
Find the Area. Simplify your answer.​
Vaselesa [24]

Answer:

Area = 9x^2 square units

Step-by-step explanation:

<u>Key skills needed: Area of a parallelogram</u>

1) This shape is a parallelogram, and the way to find the area of a parallelogram is:

                                A = bh

A = area

b = base (the side at the bottom

h = the height ( the length that runs from one side to another and makes a right angle)

2) The base (b) would be 3x. The height (h) would also be 3x

3) This means A = 3x(3x)

3 times 3 is 9 --> and x times x is x^2

Therefore the area is --> 9x^2

<em>Hope you understood and have a nice day!! :D</em>

5 0
3 years ago
Find the difference (4ab-9a-8)-(7ab-1)
OLga [1]
(4ab - 9a - 8) - (7ab - 1)
distribute (multiply) the negative through the parenthesis
<span>(4ab - 9a - 8) - 7ab + 1
No need for other parenthesis because nothing in front or to combine inside. </span>
<span>4ab - 9a - 8 - 7ab + 1 </span>
Combine like terms
- 3ab - 9a - 7


7 0
3 years ago
Help please!
Alina [70]

Step-by-step explanation:

Given

f(x) = 8x - 9

Then

For a.

f(3y - 1 ) = 8(3y - 1 ) - 9

= 24y - 8 - 9

= 24y - 17

Now for b.

f(x) = - 23

or, 8x - 9 = - 23

8x = - 23 + 9

8x = - 14

x = - 14 / 8

x = - 7 / 4

Hope it will help :)

7 0
2 years ago
What is the value of a° in the figure shown below?
VMariaS [17]
The answer would be 18 because if you put 3a+6a+a=180 (the degrees of a triangle) and solve it a becomes 18
3 0
3 years ago
If two sweaters and four shirts cost $150, and four sweaters and three shirts cost $200, find the price of each shirt and each s
STALIN [3.7K]

Answer:

shirt = $20

sweater = $35

Step-by-step explanation:

This question would be solved using simultaneous equation

Let the price of sweater be represented by a

Let the price of shirt be represented by b

The following equations can be derived from the question

2a + 4b = 150   equation 1

4a + 3b = 200   equation 2

Multiply equation 1 by 2

4a + 8b = 300    equation 3

Subtract equation 2 from 3

5b = 100

divide both sides of the equation by 5

b = 20

substitute for b in equation 1

2a + 4(20) = 150

2a + 80 = 150

collect like terms

2a = 150 - 80

2a = 70

divide both sides by 2

a = 35

Price of sweater = $35

Price of shirt = $20

4 0
2 years ago
Read 2 more answers
Other questions:
  • Rewrite each of the following linear equation in equivalent y=mx+b
    13·1 answer
  • If 4 times a number is 48, what is the number?
    9·2 answers
  • Need help with this question please​
    7·2 answers
  • Solve the equation x^3 + 2x^2 - 11x -12 = 0
    5·1 answer
  • Can you help me plz <br> and thank you
    8·1 answer
  • How does the stimulus check impact society please help me please i really need help please
    10·1 answer
  • T=2p squared make p the subject
    6·1 answer
  • Dan borrowed $745 for new coffee table. He will make 10 monthly payments of $85 to repay the loan how much will he pay in intere
    14·1 answer
  • Whats is the ratio of blue paint to yellow paint
    11·2 answers
  • 6.39x10^23kg in standard form
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!