Suppose a baby food company has determined that its total revenue r for its food is given by r = − x ^3 + 102 x ^2 + 1575 x where r is measured in dollars and x is the number of units (in thousands) produced. what production level will yield a maximum revenue?

The production level will yield a maximum revenue when production level is approximately equal to 75,000.

Step-by-step explanation:

Revenue is given by  

R(x) =

First, we differentiate R(x) with respect to x, to get,

Equating the first derivative to zero, we get,

Solving, with the help of quadratic formula, we get,

Again differentiation R(x), with respect to x, we get,

At x = 75

Thus, maxima occurs at x = 75 for R(x).

Thus, the production level will yield a maximum revenue when production level is approximately equal to 75,000.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct