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natali 33 [55]
2 years ago
13

Diane's bird feeder holds 2/3 of a cup of birdseed. Diane is filling the bird feeder with a scoop that holds 1/3 of a cup. How m

any scoops of birdseed will Diane put into the feeder?
Please explain.
Mathematics
2 answers:
Butoxors [25]2 years ago
8 0

2 cups because you just have divide 1/3 from 2/3

Lubov Fominskaja [6]2 years ago
5 0

So, we have this given info: Her scoop holds 1/3 cups and the bird feeder holds 2/3 cups. 2/3 is double the amount of 1/3, meaning 2 1/3s is 2/3. She would have to put 2 scoops of bird seeds into the bird feeder.

Answer: 2 cups of bird seeds

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so hmmm seemingly the graphs meet at -2 and +2 and 0, let's check

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so f(x) = g(x) at those points, so let's take the integral of the top - bottom functions for both intervals, namely f(x) - g(x) from -2 to 0 and g(x) - f(x) from 0 to +2.

\stackrel{f(x)}{2x^3-x^2-5x}~~ - ~~[\stackrel{g(x)}{-x^2+3x}]\implies 2x^3-x^2-5x+x^2-3x \\\\\\ 2x^3-8x\implies 2(x^3-4x)\implies \displaystyle 2\int\limits_{-2}^{0} (x^3-4x)dx \implies 2\left[ \cfrac{x^4}{4}-2x^2 \right]_{-2}^{0}\implies \boxed{8} \\\\[-0.35em] ~\dotfill

\stackrel{g(x)}{-x^2+3x}~~ - ~~[\stackrel{f(x)}{2x^3-x^2-5x}]\implies -x^2+3x-2x^3+x^2+5x \\\\\\ -2x^3+8x\implies 2(-x^3+4x) \\\\\\ \displaystyle 2\int\limits_{0}^{2} (-x^3+4x)dx \implies 2\left[ -\cfrac{x^4}{4}+2x^2 \right]_{0}^{2}\implies \boxed{8} ~\hfill \boxed{\stackrel{\textit{total area}}{8~~ + ~~8~~ = ~~16}}

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