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]
3 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]3 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
Use a calculator to find the approximate value of arccos(0.77).
Amiraneli [1.4K]
39.65 is the approximate value of arccos0.77
7 0
3 years ago
Read 2 more answers
Which expressions are equivalent??
Brilliant_brown [7]

<u>Given</u>:

The given expression is 2\left(\frac{3}{4} x+7\right)-3\left(\frac{1}{2} x-5\right)

We need to determine the equivalent expression.

<u>Option A:</u> -1

Solving the expression, we get;

\frac{3}{2} x+14-\frac{3}{2} x+15

Simplifying, we get;

14+15=29

Thus, the expression 2\left(\frac{3}{4} x+7\right)-3\left(\frac{1}{2} x-5\right) is not equivalent to -1.

Hence, Option A is not the correct answer.

<u>Option B</u>: 29

Solving the expression, we get;

\frac{3}{2} x+14-\frac{3}{2} x+15

Simplifying, we get;

14+15=29

Thus, the expression 2\left(\frac{3}{4} x+7\right)-3\left(\frac{1}{2} x-5\right) is equivalent to 29.

Hence, Option B is the correct answer.

<u>Option C</u>: 2\left(\frac{3}{4} x+7\right)+(-3)\left[\frac{1}{2} x+(-5)\right]

Let us rewrite the given expression.

2\left(\frac{3}{4} x+7\right)+(-3)\left[\frac{1}{2} x+(-5)\right]

Thus, the expression 2\left(\frac{3}{4} x+7\right)-3\left(\frac{1}{2} x-5\right) is equivalent to 2\left(\frac{3}{4} x+7\right)+(-3)\left[\frac{1}{2} x+(-5)\right]

Thus, Option C is the correct answer.

<u>Option D</u>: 2\left(\frac{3}{4} x\right)+2(7)+3\left(\frac{1}{2} x\right)+3(-5)

Rewriting the expression, we get;

2\left(\frac{3}{4} x+7\right)+(-3)\left[\frac{1}{2} x+(-5)\right]

Hence, the expression 2\left(\frac{3}{4} x+7\right)-3\left(\frac{1}{2} x-5\right) is equivalent not to 2\left(\frac{3}{4} x\right)+2(7)+3\left(\frac{1}{2} x\right)+3(-5)

Thus, Option D is not the correct answer.

<u>Option E:</u> 2\left(\frac{3}{4} x\right)+2(7)+(-3)\left(\frac{1}{2} x\right)+(-3)(-5)

Multiplying the terms within the bracket, we get;

2\left(\frac{3}{4} x\right)+2(7)+(-3)\left(\frac{1}{2} x\right)+(-3)(-5)

Hence, the expression 2\left(\frac{3}{4} x+7\right)-3\left(\frac{1}{2} x-5\right) is equivalent to 2\left(\frac{3}{4} x\right)+2(7)+(-3)\left(\frac{1}{2} x\right)+(-3)(-5)

Thus, Option E is the correct answer.

4 0
2 years ago
Igneous rock that cools slowly will have what type of mineral grains??
daser333 [38]
I think it would have crystal formations if I remember correctly.
7 0
3 years ago
Principal = $8100; rate = 17%; time = 7 years What is the amount of interest earned?
miskamm [114]
<span>it must be nnnnnnnnnnnnnnnnnnnnnnnnn
4.37%

</span>
4 0
2 years ago
The entire group beging studied and from which sample are taken is called the​
navik [9.2K]

Answer:

individual is the correct answer

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • An initial population of 7 chipmunks increases by 6% each year. If the function f(x) = abx models this situation, which function
    10·2 answers
  • If x+y=10 and x-y=6 , what is the value of x³-y³​
    11·1 answer
  • Help I need this is easy for most people
    11·1 answer
  • What is 225/23*488-236b=4428
    14·2 answers
  • ABCD is a parallelogram.<br><br> If AB =4.7 cm and BD =10.6cm, what is CD?
    10·1 answer
  • Find the sum of (1-1/n) + (1-2/n) + (1 - 3/n)....upto n terms
    9·1 answer
  • What is the answer?​
    6·1 answer
  • Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.
    13·2 answers
  • On the number line, is -3 8/9 or -3.89 farther from 0? Explain.<br><br> plz help :)
    13·1 answer
  • The temperature outside changed from 82°F to 46°F over a period of six days. If the temperature changed by the same amount
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!