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
Pepsi [2]
3 years ago
7

The radius of the base of a cylinder is decreasing at a rate of 9 millimeters per hour and the height of the cylinder is increas

ing at a rate of 2 millimeters per hour. At a certain instant, the base radius is 8 millimeters and the height is 3 millimeters. What is the rate of change of the surface area of the cylinder at that instant in square millimeters per hour?
a) 310pi
b) 155pi
c) -155pi
d) -310pi
Mathematics
1 answer:
ivann1987 [24]3 years ago
4 0

Answer:

<em>Answer: d) -310pi</em>

Step-by-step explanation:

<u>Instantaneous Rate of Change</u>

Is the change in the rate of change of a function at a particular instant. It's the same as the derivative value at a specific point.

The surface area of a cylinder of radius r and height h is:

A=2\pi r^2+2\pi r h

We need to calculate the rate of change of the surface area of the cylinder at a specific moment where:

The radius is r=8 mm

The height is h=3 mm

The radius changes at r'=-9 mm/hr

The height changes at h'=+2 mm/hr

Find the derivative of A with respect to time:

A'=2\pi (r^2)'+2\pi (r h)'

A'=2\pi 2rr'+2\pi (r' h+rh')

Substituting the values:

A'=2\pi 2(8)(-9)+2\pi ((-9) (3)+(8)(2))

Calculating:

A'=-288\pi +2\pi (-27+16)

A'=-288\pi +2\pi (-11)

A'=-288\pi -22\pi

A'=-310\pi

Answer: d) -310pi

You might be interested in
Please help me with this thank you
Varvara68 [4.7K]
Too much sand.

Volume is the amount of space something takes up. The formula for volume is v=length x width x height.

The volume of the sandbox is 36 ft^3, because 5x6x1.2 = 36. This means the box takes up 36 cubic feet of space.

If the customer bought 40 cubic feet of sand, than they bought to much because 40 > 36. The amount of sand she got is greater than the volume of the box, so it won’t all fit.
4 0
2 years ago
Read 2 more answers
60 POINTS!!!! PLEASE HELP URGENT
sammy [17]

Using linear combination method to solve the system of equations 3x - 8y = 7  and x + 2y = -7 is (x, y) = (-3, -2)

<h3><u>Solution:</u></h3>

Given that, a system of equations are:

3x – 8y = 7 ⇒ (1) and x + 2y = - 7 ⇒ (2)

We have to solve the system of equations using linear combination method and find their solution.

Linear combination is the process of adding two algebraic equations so that one of the variables is eliminated. Addition or subtraction can be used to perform a linear combination.

Now, let us multiply equation (2) with 4 so that y coefficients will be equal numerically.

4x + 8y = -28 ⇒ (3)

Now, add (1) and (3)  

3x – 8y = 7  

4x + 8y = - 28  

----------------

7x + 0 = - 21  

7x = -21  

x = - 3  

Now, substitute "x" value in (2)

(2) ⇒ -3 + 2y = - 7  

2y = 3 – 7  

2y = - 4  

y = -2

Hence, the solution for the given two system of equations is (-3, -2)

3 0
3 years ago
A town has accumulated 3 inches of snow, and the snow depth is increasing by 4 inches every
maxonik [38]
3 hours. I think. X represents the # of hours and they equal the same after exactly 3 hours.

8 0
3 years ago
What is the answer to or help me learn what 54-6÷2+6=
JulijaS [17]
You would use, Order of Operations, A.K.A PEMDAS.
Parenthesis, Exponets, Multiplication, Division, Addition, Subtraction
Follow that order and you do the work yourself, you would never learn by asking other's for the answer. >:) 
From: Dark Angel
5 0
3 years ago
Read 2 more answers
Snap company issues 10% five year bonds on january 1 of this year, with a par value of 120,000 and semiannual interest payments
mezya [45]

Answer:

<h3>$189,292.92</h3>

Step-by-step explanation:

Using the compound interest formula to get the equivalent amount after 5 years;

A = P(1+r/n)^nt

P is the principal = 120,000

r is the rate = 10% = 0.1

t is the time = 5 years

n is the time of compounding = 1/2  = 0.5(semi annual interest)

Substitute into the formula;

A = 120,000(1+0.1/0.5)^(5)(0.5)

A = 120,000(1+0.2)^2.5

A = 120,000(1.2)^2.5

A = 120,000(1.5774)

A =  189,292.92

Hence the company issue is $189,292.92

4 0
3 years ago
Other questions:
  • Ralph buys a desk that regularly sells for $250 and a desk chair that regularly sells for $145. both items are on sale at 15% of
    11·1 answer
  • How do I solve this Physics equation?
    15·1 answer
  • Write an algebraic expression that is equivalent to the expression.<br><br> cos⁡(arcsin⁡ (x-h)/r )
    15·1 answer
  • I am totally stuck on this problem please help
    11·1 answer
  • How is the graph of y=2x^2+3 different from the graph of y=x^2-9x+20 shown below?
    15·1 answer
  • How to find the area of the seating area
    9·2 answers
  • Luke was asked to compute the length of AB. What is Luke's error?
    7·1 answer
  • (20m + 3) - (7 m - 5)<br> Find the difference
    6·2 answers
  • What is a variable in mathematics?
    9·2 answers
  • Question 2(Multiple Choice Worth 1 points)<br> (01.04 LC)<br><br> Solve for x: −2x − 4 &gt; 8
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!