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
Aleksandr [31]
2 years ago
10

The​ cost, in​ dollars, of producing x belts is given by Upper C (x )equals 594 plus 10 x minus 0.067 x squared. Find the rate a

t which average cost is changing when 576 belts have been produced. When 576 belts have been​ produced, the average cost is changing at nothing dollars per belt belts per dollar for each additional belt.
Mathematics
1 answer:
alexandr402 [8]2 years ago
7 0

Answer:

When 576 belts have been​ produced, the average cost is changing at 0.0652(decreasing) dollar per belt

Step-by-step explanation:

If x is the number of units of a product produced in some time interval then average cost function is given as,  

\overline{C}=\dfrac{C\left(x\right)}{x}

Cost function is given as,  C\left(x\right)=594+10x-0.067x^{2}

Substituting the value in formula for average cost function,  

\overline{C}=\dfrac{594+10x-0.067x^{2}}{x}

Simplifying,

\overline{C}=\dfrac{594}{x}+\dfrac{10x}{x}-\dfrac{0.067x^{2}}{x}

\overline{C}=\dfrac{594}{x}+10-0.067x

To find the rate of average cost that is, \dfrac{d\overline{C}}{dx}. So differentiating function \overline{C} with respect to x,  

\dfrac{d\overline{C}}{dx}=\dfrac{d}{dx}\left (\dfrac{594}{x}+10-0.067x \right )

Applying sum rule and difference rule of derivative,

\dfrac{d\overline{C}}{dx}=\dfrac{d}{dx}\left(\dfrac{594}{x}\right)+\dfrac{d}{dx}\left(10\right)-\dfrac{d}{dx}\left(0.067x\right)

Applying constant multiple rule of derivative,  

\dfrac{d\overline{C}}{dx}=594\dfrac{d}{dx}\left(\dfrac{1}{x}\right)+\dfrac{d}{dx}\left(10\right)-0.067\dfrac{d}{dx}\left(x\right)

Since,  

\dfrac{1}{x}=x^{-1}

\dfrac{d\overline{C}}{dx}=594\dfrac{d}{dx}\left(x^{-1}\right)+\dfrac{d}{dx}\left(10\right)-0.067\dfrac{d}{dx}\left(x\right)

Applying power rule and constant rule of derivative,

\dfrac{d\overline{C}}{dx}=594\left(-1\:x^{-1-1}\right)+0-0.067\left(1\:x^{1-1}\right)

\dfrac{d\overline{C}}{dx}=594\left(-1\:x^{-2}\right)-0.067\left(1\:x^{0}\right)

\dfrac{d\overline{C}}{dx}=594\:x^{-2}-0.067

\dfrac{d\overline{C}}{dx}=\dfrac{594}{x^{2}}-0.067

Substituting the value of x=576,

\dfrac{d\overline{C}}{dx}=594\left(\dfrac{1}{\left(576 \right)^{2}}\right )-0.067

\dfrac{d\overline{C}}{dx}=-0.0652

Negative sign indicates that rate of average cost is decreasing.

Therefore, the average cost is changing at the rate of 0.0652(decreasing) dollar per belt

You might be interested in
Need help finding slope, x-intercept, and y-intercept
butalik [34]

Step-by-step explanation:

count the slope, 5 up in 2.5 horizontal steps, slope = 5/2.5 or 2

x intercept is on the graph, 2.5

y intercept is also on the graph, -5

8 0
2 years ago
Read 2 more answers
PLEASE HELP :’( last one
valina [46]

Answer:

A.3

Step-by-step explanation:

5 0
2 years ago
Mathematics Transform Exponential Functions<br>Please answer
Vitek1552 [10]

Answer:

g(x) = 6 * 3^x

Step-by-step explanation:

This is the answer because the question states that the graph is vertically stretched by a factor of 6. Since the parent function of an exponential function is f(x) = a * 3^(k(x-d)) + c, we plug in 6 for a, where we get g(x) = 6 * 3^x.

6 0
3 years ago
Subtract what she has now from the total she needs. She needs ten. She has one 2 1/3 and 3 1/3 added is 5 2/3
tatiyna

Answer:

4 ⅓

Step-by-step explanation:

10 - 5 ⅔

10 - 5 × 3 + 2/3

10 - 17/3

3 × 10 - 17/3

30 - 17/3

13/3 = 4 ⅓

<u>-TheUnknownScientist</u>

6 0
2 years ago
Solve for x in the parallelogram below.<br> PLEASE HURRY
Elina [12.6K]

Answer:

x=6

Step-by-step explanation:

Hope it was right

7 0
3 years ago
Read 2 more answers
Other questions:
  • What is the domain of the function below? {(0,2),(3,1),(5,2),(8,4)}
    15·1 answer
  • What is the value of 3ab+<br>5b - 6 when a = - 1and b = 3​
    5·2 answers
  • Function- f(x)=-x^2+4x+6
    10·1 answer
  • Help me solve this: <br> 16-x=x
    6·1 answer
  • What percent of 56 is 35 shirts
    11·1 answer
  • 15. A door wedge is shaped like a triangular prism. The wedge is filled with sand. How
    8·2 answers
  • You will get 11 points IF YOU GET THIS RIGHT AND A BRAINLESS!!SO PLEASE HELP :D
    13·1 answer
  • Which is a simplified form of the expression 6(2t – 3) + 3(t + 5)?
    12·2 answers
  • Dmitri buys 23 pound of mixed nuts, 12 pound of chocolate
    12·1 answer
  • Find an equation with a solution of x = 2 of multiplicity 1 , and a solution of x = − 1 of multiplicity 2 .
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!