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stepan [7]
3 years ago
15

Is this correct? If not please tell the correct answer and how u got it​

Mathematics
1 answer:
ICE Princess25 [194]3 years ago
4 0

Answer:

Its incorrect

Step-by-step explanation:

Area is width times height but in this case its 3 numbers so after you did width time height if I'm not mistaken you multiply that number by 4 so you were supposed to multiply 5 and 6 the answer is 30 and then multiply 30 by 4 which is 120 I think.

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What is the maximum volume in cubic inches of an open box to be made from a 12-inch by 16-inch piece of cardboard by cutting out
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If you start with a 12x16 rectangle and cut square with side length x, when you bend the sides you'll have an inner rectangle with sides 12-2x and 16-2x, and a height of x.

So, the volume will be given by the product of the dimensions, i.e.

(12-2x)(16-2x)x = 4x^3-56x^2+192x

The derivative of this function is

12x^2-112x+192

and it equals zero if and only if

12x^2-112x+192=0 \iff x = \dfrac{14\pm 2\sqrt{13}}{3}

If we evaluate the volume function at these points, we have

f\left(\dfrac{14-2\sqrt{13}}{3}\right) = \dfrac{64}{27}(35+13\sqrt{13})> f\left(\dfrac{14-2\sqrt{13}}{3}\right) = -\dfrac{64}{27}(13\sqrt{13}-35)

So, the maximum volume is given if you cut a square with side length

x=\dfrac{14-2\sqrt{13}}{3}\approx 2.7

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Step-by-step explanation:

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