Answer:
-18 is your answer.
Step-by-step explanation:
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Answer:
17) MC(x) = 35 − 12/x²
18) R(x) = -0.05x² + 80x
Step-by-step explanation:
17) The marginal average cost function (MC) is the derivative of the average cost function (AC).
AC(x) = C(x) / x
MC(x) = d/dx AC(x)
First, find the average cost function:
AC(x) = C(x) / x
AC(x) = (5x + 3)(7x + 4) / x
AC(x) = (35x² + 41x + 12) / x
AC(x) = 35x + 41 + 12/x
Now find the marginal average cost function:
MC(x) = d/dx AC(x)
MC(x) = 35 − 12/x²
18) x is the demand, and p(x) is the price at that demand. Assuming the equation is linear, let's use the points to find the slope:
m = (40 − 50) / (800 − 600)
m = -0.05
Use point-slope form to find the equation of the line:
p(x) − 50 = -0.05 (x − 600)
p(x) − 50 = -0.05x + 30
p(x) = -0.05x + 80
The revenue is the product of price and demand:
R(x) = x p(x)
R(x) = x (-0.05x + 80)
R(x) = -0.05x² + 80x
First we gather all the information we have about the amount of miles that Carolyn runs:
Monday, Wednesday, Friday: 4 1/2 miles
Tuesday, Saturday: 2 3/4 miles
And the question is the amount of miles that she runs in 4 weeks.
So lets begin by calculating the amount of miles she runs in one week, then we just multiply by 4 and we'll have the final answer.
So, we have to add 4 1/2 three times (Monday, Wed, Friday), and 2 3/4 two times (Tuesday, Sat):
1 week Miles = 4 1/2 + 4 1/2 + 4 1/2 + 2 3/4 + 2 3/4
lets add the whole parts and the fraction parts apart:
1 week Miles = (4 + 4 + 4 + 2 + 2) + (1/2 + 1/2 + 1/2 + 3/4 + 3/4)
1 week <span>Miles = (16) + (3/2 + 6/4)
</span>we can reduce the last fraction:
1 week <span>Miles = (16) + (3/2 + 3/2)
</span>1 week <span>Miles = (16) + (6/2)
</span>1 week <span>Miles = (16) + (3)
</span>1 week <span>Miles = 19
</span>therefore Carolyn runs 19 miles each week, so for 4 weeks we have to add 19 four times or multiply it by 4, is the same:
4 weeks <span>Miles = 4*19
</span>4 weeks <span>Miles = 76
hence Carolyn runs 76 miles in 4 weeks.</span>
