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
Answer:
Step-by-step explanation:
Generally equation of a line is given as
y=mx+c
Then given the point (x, y)=(0,2)
Therefore x=0 and y=2
y=mx+c
2=m×0+c
2=0+c
Then, c=2
Then intercept is 2
Also given the point (x, y)=(3,4)
x=3 and y=4 and c=2
y=mx+c
4=m×3+2
4=3m+2
4-2=3m
2=3m
Then, m=2/3
Then, the slope of the graph is 2/3
y=mx+c
Now, m=2/3 and c=2
The general equation of the line becomes
y=2/3x+2
Multiply through by 3
3y=2x+6
Then this is the equation of the line
Answer:
Surface area
103.109in²
Step-by-step explanation:
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