Slope is 7/3 and y intercept is -3.
Answer:
a) h = 123/x^2
b) S = x^2 +492/x
c) x ≈ 6.27
d) S'' = 6; area is a minimum (Y)
e) Amin ≈ 117.78 m²
Step-by-step explanation:
a) The volume is given by ...
V = Bh
where B is the area of the base, x^2, and h is the height. Filling in the given volume, and solving for the height, we get:
123 = x^2·h
h = 123/x^2
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b) The surface area is the sum of the area of the base (x^2) and the lateral area, which is the product of the height and the perimeter of the base.

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c) The derivative of the area with respect to x is ...

When this is zero, area is at an extreme.
![0=2x -\dfrac{492}{x^2}\\\\0=x^3-246\\\\x=\sqrt[3]{246}\approx 6.26583](https://tex.z-dn.net/?f=0%3D2x%20-%5Cdfrac%7B492%7D%7Bx%5E2%7D%5C%5C%5C%5C0%3Dx%5E3-246%5C%5C%5C%5Cx%3D%5Csqrt%5B3%5D%7B246%7D%5Capprox%206.26583)
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d) The second derivative is ...

This is positive, so the value of x found represents a minimum of the area function.
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e) The minimum area is ...

The minimum area of metal used is about 117.78 m².
Answer:
Step-by-step explanation:
H(3,2) & J(4, 1)

K(-2,-4) & M(-1 , -5)
![Slope =\dfrac{-5-[-4]}{-1-[-2]}\\\\=\dfrac{-5+4}{-1+2}\\\\= \dfrac{-1}{1}\\\\\\= -1](https://tex.z-dn.net/?f=Slope%20%3D%5Cdfrac%7B-5-%5B-4%5D%7D%7B-1-%5B-2%5D%7D%5C%5C%5C%5C%3D%5Cdfrac%7B-5%2B4%7D%7B-1%2B2%7D%5C%5C%5C%5C%3D%20%5Cdfrac%7B-1%7D%7B1%7D%5C%5C%5C%5C%5C%5C%3D%20-1)
Line HJ and KM have same slopes. So, they are parallel
Answer:
1.82352941176
Step-by-step explanation:
;)
14 x 10^3 = 14,000 (the elephants weight)
So the cat weighs 14 pounds