A coffee roaster is designing a coffee can that can be modeled with a right cylinder for its new Breakfast Blend. Breakfast Blend costs the roaster $0.03 per cubic inch to produce. The roaster wants the can to contain an amount of
coffee that will cost him no more than $7.50 to produce. Given that the height of the can is to be equal to its diameter,
what is the maximum height allowable for the can? Round to the nearest tenth of an inch,

a; x = 0.5

step-by-step explanation:

-10x = -5

x = 0.5

x^2 + 81

we can factor this using difference of square binomials.

rewrite the equation:

x^2 - (-81)

factor:

(a^2 - b^2) = (√a^2 + √b^2)(√a^2 - √b^2)

(x^2 - (-81) = (x + √-81)(x - √-81)

we can remove the - from under the radical by multiplying it by i.

(x^2 - (-81) = (x + i√81)(x - i√81)

(x^2 - (-81) = (x + 9i)(x - 9i)

we can check our answer by using foil:

x^2 - 9ix + 9ix - 81i^2

x^2 - 81^2

i^2 = -1

x^2 + 81