Let c(x) represent the cost of producing x items and p(x) be the sale price per item if x items are sold. the profit p(x) of selling x items is p(x)=xp(x)-c(x) (revenue minus costs). the average profit per item when x items are sold is p(x)/(x) and the marginal profit is dp/dx. the marginal profit approximates the profit obtained by selling one more item given that x items have already been sold. consider the following cost functions c and price function p. c(x)=-0.02x^2+40x+80, p(x)=100, a=500a) what is the profit function p. p(x)=? b) find the average profit function and marginal profit function. average profit function: p(x)/(x)=? marginal profit function: dp/dx=? c

(a) Profit function P(x) = 0.02x^2+60x-80

(b) Average profit P(x)/x = P/x = 0.02x+60-80/x

Marginal profit dP/dx = 0.04x+60

Step-by-step explanation:

Cost function: C(x) = -0.02x^2+40x+80

Price function: p(x) = 100

(a) The profit function P(x) = x*p(x)-C(x) can be expressed as:

(b)Average profit function: P(x)/x

Marginal profit function: dP/dx

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180