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:
Total of 9 lengths of 4 inches can be taken out from a board of 3 feet
Step-by-step explanation:
length of board in feet = 3 ft
As
1 ft = 12 inches
So
Length of board in inch = 
= 36 inches
Let no of 4 inches length be = x
The equation become
Total of 9 lengths of 4 inches can be taken out from a board of 3 feet
Answer:
Jodi and Mariah are sisters. Jodi is three years older than Mariah. Using one variable, write an expression to represent the sum of their ages. Make sure to explain what your variable represents.
(3+x)+x
Step-by-step explanation:
x=Mariah
The midpoint is the average of the coordinates of the endpoints.
M = (A + B)/2 = ((1+7)/2, (3+8)/2) = (4, 11/2)
The midpoint of AB is (4, 11/2).
