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2 years ago

Suppose you wanted to make an open-topped box out of a flat piece of cardboard that is 25 inches long

Mathematics

2 answers:

grigory [225]2 years ago

7 0

i dont know man

Step-by-step explanation:

...

Artemon [7]2 years ago

6 0

Answer:

5 inches

Step-by-step explanation:

The side of the square you cut has length x.

The total length of the cardboard is 25". Once you cut the two corners, the length of the base of the box is 25 - 2x.

The total width of the cardboard is 20". Once you cut the two corners, the width of the base of the box is 20 - 2x.

The height of the box is x.

The volume of the box is

V = LWH

V = (25 - 2x)(20 - 2x)x

V = (2x - 25)(2x - 20)x

The volume is 750 cu in.

(2x - 25)(2x - 20)x = 750

Now try each value in the choices for x, and see which one works.

Try x = 3

(2(3) - 25)(2(3) - 20)(3) = (-19)(-14)(3) = 798

798 is not equal to 750, so x = 3 does not work.

Try x = 4

(2(4) - 25)(2(4) - 20)(4) = (-17)(-12)(4) = 816

816 is not equal to 750, so x = 4 does not work.

Try x = 5

(2(5) - 25)(2(5) - 20)(5) = (-15)(-10)(5) = 750

750 is equal to 750, so x = 5 does not work.

Answer: 5

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Step-by-step explanation:

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Let's differentiate f(x,y) with respect to y in order to find g(y):

$\frac{\partial f(x,y)}{\partial y}=\frac{\partial }{\partial y} (2*sin(x)+y*cos(x)+g(y))=cos(x)+\frac{dg(y)}{dy}$

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$cos(x)+\frac{dg(y)}{dy}=cos(x)+sin(y)$

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$\frac{dg(y)}{dy}=sin(y)$

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$g(y)=\int\ sin(y) \, dy =-cos(y)$

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Finally the solution is f(x,y)=C1 :

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