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
Juliette [100K]
3 years ago
7

Use the definition of the derivative to differentiate v=4/2 pie r^3

Mathematics
1 answer:
nata0808 [166]3 years ago
3 0

I suspect 4/2 should actually be 4/3, since 4/2 = 2, while 4/3 would make V the volume of a sphere with radius r. But I'll stick with what's given:

\displaystyle \frac{dV}{dr} = \lim_{h\to0} \frac{2\pi(r+h)^3-2\pi r^3}{h}

\displaystyle \frac{dV}{dr} = 2\pi \lim_{h\to0} \frac{(r^3+3r^2h+3rh^2+h^3)- r^3}{h}

\displaystyle \frac{dV}{dr} = 2\pi \lim_{h\to0} \frac{3r^2h+3rh^2+h^3}{h}

\displaystyle \frac{dV}{dr} = 2\pi \lim_{h\to0} (3r^2+3rh+h^2)

\displaystyle \frac{dV}{dr} = 2\pi \cdot 3r^2 = \boxed{6\pi r^2}

In Mathematica, you can check this result via

D[4/2*Pi*r^3, r]

You might be interested in
A. 1189<br> B. 28<br> C. 784<br> D. 891<br> E. 1059
ch4aika [34]

Answer:

Its E c;

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
The question is<br> Simplify the Expression. I don't know what they mean<br> 14 - 16 / 8 + 32 x 5
xeze [42]
\sf 14 -  \frac{16}{8} + (32) (5) \\  \\ 14 - 2 + (32)(5)  \\  \\  12 + (32) (5) \\  \\ 12 + 160  \\  \\ 172.

Using PEMDAS is the best.
7 0
3 years ago
Read 2 more answers
Solve the following proportion problem for x: 14/3x=20/x-5
Butoxors [25]

14        20

----  =  -----  cross multiply

3x       x-5


14(x-5) = 3x (20)

14x - 70 = 60x

-14x          -14x

-70 = 36x

/36    /36

-70/36  = x

or

-35/18 = x

5 0
4 years ago
Read 2 more answers
Multiply the two mixed numbers 4 1/2 x 3 2/3 simplify your answer and write it as a mixed number
konstantin123 [22]

Answer: 16 1/2

Step-by-step explanation:

It's easiest to multiply improper fractions and then to convert them back into mixed numbers, so 4 1/2 would become 9/2 and 3 2/3 would become 11/3. \frac{9}{2} *\frac{11}{3}= 99/6. Now just simplify to 33/2 and then convert back into a mixed number.  16 1/2

8 0
3 years ago
Simplify <br> x^2/3 / x^-4/3
Helga [31]
I think it would be too confusing to type but it would look like this

3 0
3 years ago
Other questions:
  • 9/10-?=1/5 please help
    15·2 answers
  • Diana brought 8 3/5 yards of blue velvet material for a dress and coat. She used 3 4/5 yards on the coat. How much is left for t
    11·1 answer
  • Which expression represents “seventeen more than one-fourth y”
    12·2 answers
  • What is the surface area of the sphere shown below with a radius of 6?
    14·1 answer
  • Jon invests $4,100 into an account that pays 5 percent simple interest each year. What is the total balance in the account after
    11·2 answers
  • Mr. Jenkins won $500 in a raffle. He split
    9·2 answers
  • Cora's kitten weighs 1,200 grams. If he weighed 550 grams at the last visit to the veterinarian's office, what is the percent in
    6·2 answers
  • This is unit rates please help me <img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Bg%7D%7B30%20seconds%7D%20%3D%20%20%5Cfrac%7B20%
    8·2 answers
  • What is the ratio of a nickel to one dollar, reduces to simplest form?
    9·2 answers
  • A dinner plate is in the shape of an isosceles right triangle. The leg length is 13 inches. What is the length of the hypotenuse
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!