Find the volume of the cylinder, then the volume of the empty space. Finally, we subtract these.
V = pi * r^2 * h
V = 3.14 * 3^2 * 12
V = 339.12
So the volume of the bottle of lotion is 339.12.
V = pi * r^2 * h
V = 3.14 * 0.5^2 * 12
V = 9.42
So the volume of the empty space in the bottle of lotion is 9.42.
Subtract these:
339.12 - 9.42 = 329.7
This is an example of a composite function which can be simplified to g(fx). Literally input f(x) into the x of g(x), leading to the answer of 80x^2-120x+42
A is the correct answer
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From the Quotient-Remainder Theorem follows that for every f(x) there exist unique polynomials q(x) and r(x) such that:
,
where r(x) is called remainder.
If r(x)=0, then f(x)=h(x)q(x) and q(x) is adivisor. If q(x) is of form q(x)=x-a, then a is a root of f(x).
x = the number of hot dogs
2.50x - 150 = 300
[You sell each hot dog for $2.50, you spent $150, you want to make $300]
2.50x - 150 = 300 Add 150 on both sides
2.50x = 450 Divide 2.50 on both sides
x = 180
You have to sell 180 hot dogs to make a profit of $300
[proof]
2.50x - 150 = 300
2.50(180) - 150 = 300
450 - 150 = 300
300 = 300