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:
2L^2 - 27L + 70 = 0.
Step-by-step explanation:
p = 2(L + W)
27 = 2L + 2W
2W = 27 - 2L
W = (27 - 2L)/2
Substitute for W in the area equation:
A = LW
35 = (27 - 2L) * L / 2
L(27 - 2L) = 70
-2L^2 + 27L - 70 = 0 Multiply through by -1:
2L^2 - 27L + 70 = 0
31 because if you round numbers -29 won’t work if you round it but if you round it by 31 it works
Answer: 320
Step-by-step explanation:
there are 16 tablespoons in one cup so 20*16=320
