Uppose that the dollar cost of producing x appliances is c(x)equals900plus80xminus0.2xsquare d. a. Find the average cost per appliance of producing the first 150 appliances. b. Find the marginal cost when 150 appliances are produced. c. Show that the marginal cost wh

Answer with Step-by-step explanation:

We are given that

C(x)=

a.x=150

Substitute the value of x

Total cost of 150 appliances=$8400

Average cost per appliance==$56

b.Differentiate w.r.t x

Substitute x=150

Marginal cost when 150 appliances are produced

$20

c.Cost of 151 appliances=$8419.8

Cost of 151th appliance=Cost of 151 appliances-Cost of 150 appliances

Cost of 151th appliance=$8419.8-$8400=$20

Hence, the marginal cost when 150 appliances are produced is approximately equal to the cost of producing one more appliance after the first 150 have been made .

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step-by-step explanation:

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.