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
yan [13]
3 years ago
14

Assume that the radius rr of a sphere is expanding at a rate of 19 in./min.19 in./min. The volume of a sphere is V=43πr3V=43πr3.

Determine the rate at which the volume is changing with respect to time when t=5 min.t=5 min. assuming that r=4r=4 at t=0t=0. The volume is changing at a rate of
Mathematics
1 answer:
djverab [1.8K]3 years ago
7 0

Answer:

744876\pi in^3/min.

Step-by-step explanation:

We are given that

\frac{dr}{dt}=19 in/min

Volume of sphere=\frac{4}{3}\pi r^3

r=4 at t=0

dr=19 dt

Integrating on both sides then  we get

r=19 t+C

Substitute r=4 and t=0

4=C

r=19t+4

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

\frac{dV}{dt}=4\pi (19t+4)^2(19)

Substitute t=5

\frac{dV}{dt}=4\pi (19(5)+4)^2(19)

\frac{dV}{dt}=4 \pi (99)^2 (19)=744876\pi in^3/min

Hence, the volume is changing at the rate of 744876\pi in^3/min.

You might be interested in
Assume that the function call operator() is overloaded for data type String in the usual sense of selecting a substring from a l
krek1111 [17]

Answer:

"EF"

Step-by-step explanation:

Given

String1 = "ABCDEFGHI"

Substring : String1(4,2)

To solve this, one must understand the following

1. The function call operator () is used to overload objects of class type.

2. A copy constructor must receive its argument by reference to prevent an otherwise infinite recursion.

3. overload ( ), doesn't mean that one is not creating a new way to call a function; instead, it is a way to create an operator function that can be passed an arbitrary number of parameters

Having pointed out this,

The string to overload goes thus

String1 = "ABCDEFGHI"

The parameters goes thus

String1(4,2)

To represent this properly, we have

("ABCDEFGHI",4,2)

Which means to return 2 strings starting from the 4th index character.

It should be noted that index starts at 0.

So, the character at the 4th index is "E"

Then, we count 2 characters starting from E (i.e. E, inclusive)

This gives

"EF"

So, the returned string is "EF"

6 0
3 years ago
X+7= what commutative property
Ugo [173]
The commutative pooperty of x + 7 is equal to 7 + x.
8 0
3 years ago
A right rectangle prism has a length of 5 cm, a width of 4 cm, and a height of of 3 cm. The dimensions of the prism are doubled.
MaRussiya [10]
As the volume of cuboid is given by,
l×b×h
as the dimensions are doubled,
l2×b2×h2
5×2×4×2×3×2
= 480 cm^3
6 0
3 years ago
Read 2 more answers
Rate my looks from 1/10 and pls dont judge me i woke up early and got no sleep last night plss
storchak [24]

Answer:

10 million out of 10

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Pls help me I don’t understand this
I am Lyosha [343]
You didn’t put a question
3 0
3 years ago
Read 2 more answers
Other questions:
  • Side of square is 5.3cm long, whats the area :D
    15·1 answer
  • Can someone help meh with this simply question? The info is in the picture.
    9·2 answers
  • Find the product of 20*9*5
    5·2 answers
  • Im desperate xD
    15·2 answers
  • Angle θ is in standard position. if sin(θ) = − 1/3, and π < θ < 3π/2 , find cos(θ).
    15·2 answers
  • Anyone know the answers??
    13·1 answer
  • There are 36 female teachers and 12 male teachers at Rachel's high school. What is the ratio of
    14·1 answer
  • Write in slope-intercept form the equation of the line that contains the points (-3,7) and (2, -3). * Your answer​
    14·1 answer
  • ) Buyers are charged a shipping fee of $4.75 for each scarf order.
    12·2 answers
  • !!
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!