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scoundrel [369]
3 years ago
5

At Store ABC, one can of Fruit Cocktail cost $1.30 each. At another store, XYZ store, that sells in bulk, a case of 12 cans of F

ruit Cocktail is $15.50. Which one is the better buy: Store ABC or Store XYZ?
Advanced Placement (AP)
1 answer:
Murljashka [212]3 years ago
4 0
ABC charges 1.30 for 1 can but xyz charges 15.50 for 12 cans take 15.50 divided by 12 and the answer is 1.29 so xyz is the better buy
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Answer:

Explanation:

Alright so the way to do this is to use properties of integrals to make our life easier.

So we have:

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So lets break this up into two different integrals that represent the same area.

\int\limits^4_0 {f(x)} \, dx - \int\limits^1_0 {f(x)} \, dx = \int\limits^4_1 {f(x)} \, dx

Lets think about what is going on up there. The integral from four to zero gives us the area under the curve of f(x) from four to zero. If we subtract this from the integral from one to zero (the area under f from one to zero) we are left with the area under f from four to one! Hence:

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\int\limits^4_1 {(3f(x)+2)} \, dx = 3\int\limits^4_1{f(x)} \, dx + 2\int\limits^4_1 {} \, dx

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