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:
the slope is 0
Step-by-step explanation:
Answer:
8 units
Step-by-step explanation:
» <u>Concepts</u>
Parallelogram Side Theorem states that the opposite sides of a parallelogram are congruent, meaning they have the same length.
» <u>Application</u>
In this case, we're asked to apply the theorem to find the value of q and then find the length of AB. Thus, we have to set up the equation 4q - 8 = q + 4.
» <u>Solving</u>
Step 1: Subtract q from both sides.
Step 2: Add 8 to both sides.
Step 3: Divide both sides by 3.
Step 4: Plug in the value of q for side AB.
Therefore, the answer is 8 units.

we can divide the equation on (x+1) and if we have a real solutons (x+1) is a factor
is a factor because the remainder is 0
so the new form of the equation is
Answer:

Step-by-step explanation:
