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3 years ago

Gasoline costs 2.21 euro per liter in France. What is the price in dollars per gallon

Mathematics

1 answer:

Daniel [21]3 years ago

4 0

1G is equivalent to 3.7854L

Now you multiply that by the cost per L in Euros:

2.21(3.7854) = 8.365734

Now convert it to USD:

8.365734(2.21) = 18.48 USD per gallon

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FIXED

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What % of 400 is 85?

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21.25% because 85/400 = .2125 which is 21.25%

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3 years ago

Write an inequality to represent the possible<br> combinations of x cupcakes and y cakes sold.

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Answer:

The inequality for this would be n ≥ 20.

We know this because it must be larger than 40. We also know it can possibly be equal because the statement says "at least".

Step-by-step explanation:

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2 years ago

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3 years ago

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2 years ago

This extreme value problem has a solution with both a maximum value and a minimum value. use lagrange multipliers to find the ex

harina [27]

$L(x,y,z,\lambda)=8x+8y+4z+\lambda(4x^2+4y^2+4z^2-36)$

$L_x=8+8\lambda x=0\implies 1+\lambda x=0$
$L_y=8+8\lambda y=0\implies 1+\lambda y=0$
$L_z=4+8\lambda z=0\implies 1+2\lambda z=0$
$L_\lambda=4x^2+4y^2+4z^2-36=0\implies x^2+y^2+z^2=9$

$yL_x=y+\lambda xy=0$
$xL_y=x+\lambda xy=0$
$\implies yL_x-xL_y=y-x=0\implies y=x$

$2zL_x=2z+2\lambda xz=0$
$xL_z=x+2\lambda xz=0$
$\implies 2zL_x-xL_z=2z-x=0\implies x=2z$

$2zL_y=2z+2\lambda yz=0$
$yL_z=y+2\lambda yz=0$
$\implies 2zL_y-yL_z=2z-y=0\implies y=2z$

$x=y=2z\implies x^2+y^2+z^2=9\iff 4z^2+4z^2+z^2=9z^2=9\implies z=\pm1$

$z=\pm1\implies y=x=\pm2$

So we have two critical points, (2, 2, 1) and (-2, -2, -1), which respectively give a max of 36 and a min of -36.

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3 years ago