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
vagabundo [1.1K]
2 years ago
5

A rectangular box has a square base with an edge length of x cm and a height of h cm. The volume of the box is given by V = x2h

cm3. Find the rate at which the volume of the box is changing when the edge length of the base is 4 cm, the edge length of the base is increasing at a rate of 2 cm/min, the height of the box is 15 cm, and the height is decreasing at a rate of 3 cm/min.
Mathematics
1 answer:
Tanya [424]2 years ago
8 0

Answer:

  192 cm^3/min

Step-by-step explanation:

Differentiating the volume expression, we get ...

  dV/dt = 2xh(dx/dt) +x^2(dh/dt)

We are given that ...

  x = 4 cm, dx/dt = 2 cm/min, h = 15 cm, dh/dt = -3 cm/min

Putting these values into the formula for volume rate of change, we get ...

  dV/dt = 2(4 cm)(15 cm)(2 cm/min) +(4 cm)^2(-3 cm/min)

  = 240 cm^3/min -48 cm^3/min

  dV/dt = 192 cm^3/min

You might be interested in
M³×n=189 Find m and n
Flura [38]

Answer:

m=3, n = 7

Step-by-step explanation:

Assuming m and n are integers, the following are the possible values of m and n

Let m = 1, then m³ = 1 and n= 189

If m = 2 we get 8n = 189 and 189/8 is not an integer so m ≠ 2

If m = 3, we get 27n = 189 and n = 189/27 = 7

Any higher integer values of m will not result in n being an integer and I am assuming m > 1 so the correct answer is m=3, n = 7

3 0
1 year ago
An area rug has an area of 48 square feet.Two similar rugs have areas of 108 square feet and 192 square feet. In each rug, the l
Svetllana [295]
For area A, the width will be √(3A/4), so for the three rugs, the widths are 6 ft, 9 ft, 12 ft. Corresponding lengths are 4/3 times that, so are 8 ft, 12 ft, 16 ft.

The rug dimensions are
.. 6 ft x 8 ft
.. 9 ft x 12 ft
.. 12 ft x 16 ft

Pick the one(s) that are on your list.
4 0
2 years ago
In the graphic below,
sukhopar [10]

The external angle is suplementary to the internal angle close to it. We also know that the sum of all the internal angles of the triangle are equal to 180 degrees, this means that the angle "a" is suplementary to the sum of the angles "b" and "c". Through this logic, we can conclude that since:

\begin{gathered} \angle d=180-\angle a \\ \angle b+\angle c=180-\angle a \end{gathered}

Then we can conclude that:

\angle d=\angle b+\angle c

Therefore the statement is true, the exterior angle is equal to the sum of its remote interior angles.

Let's use an example:

On this example, the external angle is 120 degrees, therefore the sum of the remote interior angles must also be equal to that. Let's try:

x=75+45=120

The sum of the remote interior angles is equal to the external angle.

6 0
11 months ago
VERY IMPORTANT... write the equation of the line that has a y intercept of (0.4) and a slope of -3/2​
shutvik [7]

Answer:

y = -3/2 x + 4

Step-by-step explanation:

y-4 = -3/2 ( x-0)

y = -3/2 x + 4

7 0
3 years ago
3-(-6/7)(3/8) what will it equal?
kompoz [17]
This is equals 3 and 18/56 which reduces to 3 and 9/28 all you have to do is plug it the calculator like it is shown and then you will get this answer
4 0
3 years ago
Other questions:
  • Six less than twice a number is -22
    5·1 answer
  • What is the equation of a line that is parallel to −3x+4y=4 and passes through the point (4, 0) ?
    11·1 answer
  • Help!!! One no choices math question! What is the perimeter of the figure shown on the coordinate plane?
    12·1 answer
  • Suppose that the functions f and g are defined for all real numbers x as follows.
    9·1 answer
  • What is the measure of the circumference of D
    5·2 answers
  • A pet shop has 96 pounds of dog food. It packages the food in 48-ounce bags. How many bags will the pet shop need to package all
    9·2 answers
  • There are some goats, cows, and sheep on a farm. 2/5 of the animals were goats. There are 3 times as many sheep as cows. If ther
    6·1 answer
  • How can transformations show that two images are congruent?
    6·1 answer
  • Which of these lines have a scale factor of 2?
    8·2 answers
  • Bridget has captured many purple-footed bog frogs. She weighs each one
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!