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
If a plate is moving 3.3 cm/yr, what distance [in kilometers (km)] will the plate move in 1 million years?
sasho [114]

\huge{\textbf{\textsf{{\color{pink}{An}}{\red{sw}}{\orange{er}} {\color{yellow}{:}}}}}

<h2>33 km</h2>

3.3cm = 0.000033km (divide by 100,000.

So, 0.000033km/yr.

0.000033 × 1,000,000

=33km

  • Thanks
  • Hope it helps

3 0
3 years ago
Write a life situation for the inequality x&lt;2
iVinArrow [24]

Answer:

see below (I hope this helps!)

Step-by-step explanation:

A real-life situation for this inequality could be "Tom runs a lemonade stand. His profit is x. If Tom knows that his profit is less than 2 dollars, what inequality represents this situation?"

3 0
3 years ago
Write the coordinate rule to describe The translasion​
sergejj [24]

Answer:

The coordinates are:

A ( 4,7 )

B ( 8,10 )

c ( 7,7 )

Step-by-step explanation:

You could take the original coordinates and add the x value with 3 and y value with 6. Like for example...

The original coordinates of C is ( 4,1 ). Hence you could add the x value with 3 and y value with 6. 4 + 3 and 1 + 6 giving you the coordinates after translation = ( 7,7 )

6 0
3 years ago
Simplify 17+(-4)-(-16)-2
ankoles [38]

Answer:

17 - 4 + 16 - 2

13 + 14

27

Hope it helps!! Good luck on your assignment!! :)

Step-by-step explanation:

You have been given the equation: 17+(-4)-(-16)-2. Remember we can always use tricks to find the equation. Plus times Minus is Minus. Minus times Minus is plus. And Plus times Plus is Minus. I would appreciate if you mark me as brainliest!! :)

7 0
3 years ago
Read 2 more answers
Prove that it is impossible to dissect a cube into finitely many cubes, no two of which are the same size.
solniwko [45]

explanation:

The sides of a cube are squares, and they are covered by the respective sides of the cubes covering that side of the big cube. If we can show that a sqaure cannot be descomposed in squares of different sides, then we are done.

We cover the bottom side of that square with the bottom side of smaller squares. Above each square there is at least one square. Those squares have different heights, and they can have more or less (but not equal) height than the square they have below.

There is one square, lets call it A, that has minimum height among the squares that cover the bottom line, a bigger sqaure cannot fit above A because it would overlap with A's neighbours, so the selected square, lets call it B, should have less height than A itself.

There should be a 'hole' between B and at least one of A's neighbours, this hole is a rectangle with height equal to B's height. Since we cant use squares of similar sizes, we need at least 2 squares covering the 'hole', or a big sqaure that will form another hole above B, making this problem inifnite. If we use 2 or more squares, those sqaures height's combined should be at least equal than the height of B. Lets call C the small square that is next to B and above A in the 'hole'. C has even less height than B (otherwise, C would form the 'hole' above B as we described before). There are 2 possibilities:

  • C has similar size than the difference between A and B
  • C has smaller size than the difference between A and B

If the second case would be true, next to C and above A there should be another 'hole', making this problem infinite. Assuming the first case is true, then C would fit perfectly above A and between B and A's neighborhood.  Leaving a small rectangle above it that was part of the original hole.

That small rectangle has base length similar than the sides of C, so it cant be covered by a single square. The small sqaure you would use to cover that rectangle that is above to C and next to B, lets call it D, would leave another 'hole' above C and between D and A's neighborhood.

As you can see, this problem recursively forces you to use smaller and smaller squares, to a never end. You cant cover a sqaure with a finite number of squares and, as a result, you cant cover a cube with finite cubes.

3 0
3 years ago
Other questions:
  • HELP I WILL GIVE BRAINLIEST THANKYOU PLEASE YOU DONT HAVE TO ANSEER ALL
    8·2 answers
  • David made a table to relate two customary units. Label the columns of the table
    11·2 answers
  • Explain 2 other ways other than rotating 180 degrees counterclockwise or clockwise, that would allow the point to find it’s way
    12·1 answer
  • Help with 5 and 6 please !! (13 points!!)
    11·2 answers
  • Two lines extend from point S to create a right angle. The vertical line extends from point S through point R. The horizontal li
    5·1 answer
  • Three times a number increased by ten is equal to twenty less than six times the number. Find the number
    7·1 answer
  • Which is the least time 9.675,9.7,9.75
    11·1 answer
  • Consider the following functions f(x)=2^x/2 <br><br><br>G(x)= square root of x-3
    10·2 answers
  • Hi can anyone tell me the answer
    13·1 answer
  • Can I get steps on how to solve this?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!