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Mariulka [41]
2 years ago
9

The regular price for a pair of jeans is $36.00. The sale price is 25% off the regular price. What is the sale price?

Mathematics
2 answers:
Ilya [14]2 years ago
8 0
36 - 9 = 27$

25% = 9.00

Original price: $36.00
Natali5045456 [20]2 years ago
6 0
27$ is the answer because .25 X 36 = 9
36 - 9 = 27
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The Lagrangian is

L(x,y,\lambda)=x+4y+\lambda(x^2+y^2-9)

with critical points where the partial derivatives vanish.

L_x=1+2\lambda x=0\implies x=-\dfrac1{2\lambda}

L_y=4+2\lambda y=0\implies y=-\dfrac2\lambda

L_\lambda=x^2+y^2-9=0

Substitute x,y into the last equation and solve for \lambda:

\left(-\dfrac1{2\lambda}\right)^2+\left(-\dfrac2\lambda\right)^2=9\implies\lambda=\pm\dfrac{\sqrt{17}}6

Then we get two critical points,

(x,y)=\left(-\dfrac3{\sqrt{17}},-\dfrac{12}{\sqrt{17}}\right)\text{ and }(x,y)=\left(\dfrac3{\sqrt{17}},\dfrac{12}{\sqrt{17}}\right)

We get an absolute maximum of 3\sqrt{17}\approx12.369 at the second point, and an absolute minimum of -3\sqrt{17}\approx-12.369 at the first point.

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Alexeev081 [22]
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Graph attached

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