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KonstantinChe [14]
3 years ago
7

A square deck has a side length of x + 5. You are expanding the deck so that each side is 4 times as long as the side length of

the original deck. What is the area of the new deck? Show your work and write your answer in standard form.
Mathematics
2 answers:
yaroslaw [1]3 years ago
8 0
If you are expanding the side length x+5 by a multiple of 4, your new side would look like this: 4(x+5) or, simplifying, 4x+20.  The area of this new, bigger square would be found by squaring the 4x+20 to get 16x^2 + 160x + 400
Papessa [141]3 years ago
5 0
Length of a side = 4(x+5). the area is 16(x+5)(x+5)
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x = -1 is local maximum, x = 1 is local minimum

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To find minima and maxima the of the function, we must take the derivative and equalize it to zero to find the roots.

1) f(x) = 6x + 6/x

f\prime(x) = 6 - 6/x^2 = 0 and x \neq 0

So, the roots are x = -1 and x = 1

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The function is decreasing on the interval [-1,0) ∪ (0,1]

x = -1 is local maximum, x = 1 is local minimum.

2) f(x)=6-4/x+2/x^2

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The function is decreasing on the interval (-∞,0) ∪ (0,1]

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3) f(x) = 8x^2/(x-4)

f\prime(x) = (8x^2-64x)/(x-4)^2=0 and x \neq 4

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f\prime(x) = 4/(x-2)^{1/3} has no solution and x = 2 is crtitical point.

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f\prime(x) = (4/\sqrt x)-6 = 0

So the root is x = 4/9

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