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lisabon 2012 [21]
2 years ago
10

Please help me due today and i really need help brainliest goes to the person who answers correctly and first this is really har

d

Mathematics
1 answer:
Andrei [34K]2 years ago
6 0
1). the submarine is descending 100 feet per minute. this is because the line decreases 100 on the y axis when the x axis increases by 1.
2). the submarine is descending 50 feet per minute. this is because the line decreases 50 on the y axis when the x axis increases by 1.
3). y=15x this is because the slope increases by 15 on the y axis when 1 is increased on the x axis. the y intercept is 0. this means that every hour of piano lessons they get paid $15.

I hope this helps, and hopefully I’m right :)
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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

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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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