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Arturiano [62]
3 years ago
5

When is 20% off better than 20$ off

Mathematics
1 answer:
Crazy boy [7]3 years ago
7 0

Answer:

Price > 100$

Price > 150$

Step-by-step explanation:

Let us assume that x% off of price y$  is better than x$ off.

Hence, \frac{xy}{1000} > x  

Hence, y > 100

Therefore, when the price is more than 100$, then only x% off on the price is better than x$. (Answer)

Again, assume that 20% off on price y$ is better than 30$ off.

Hence, \frac{20y}{100} > 30

⇒ y > 150$

Therefore, when the price is more than 150$, then only 20% of on the price is better than 30$ off. (Answer)

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Answer:

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Step-by-step explanation:

Let 'D' be the depth of the gutter and 'W' be the width of the gutter, the cross-sectional area as function of depth, A(D), is:

2D+W = 12\\W=12-2D\\A =D*W\\A(D)=-2D^2+12D

The depth for which the derivate of the area function is zero is the depth that yields the maximum cross-sectional area:

A'(D)=0=-4D+12\\D=3\ inches

The cross-sectional area for D = 3 is:

A(3)=-2*3^2+12*3\\A(3) = 18\ in^2

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