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:
2x + 3 = 9
Step-by-step explanation:
Three more than twice a number is nine
Twice a number would be 2x
where x is the number
Three more would be + 3
And is means equal sign or “=“
        
                    
             
        
        
        
Answer:
write the equation of the line that passes through (7,6) and (-1,2) in a slope intercept form.
 
        
             
        
        
        
The answer is 31/40
because first you got cane both of the fraction to the same denominator. 
72/80 + 70/80
Add 72+70=142.
142/80 change it to an mixed number and it will be 1 31/40 in simplest form. 
        
                    
             
        
        
        
Answer:
5.34 pages/h
Step-by-step explanation:
4/45 = p/60
p ≈ 5.34