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.
1.) a.) 12 / 6 = 2
b.) 3 / 2 = 1.5
c.) 16 / 8 =2
d.) Positive
2.) 0 = 0
2 = 13
4 = 26
6 = 39
8 = 52
10 = 65
a.) $6.50
b<span>.) Is increasing
c.) </span>Positive
<span>The sum of the measures of the interior angles of a polygon with n sides is (n – 2)180.The measure of each interior angle of an equiangular n-gon is.<span>If you count one exterior angle at each vertex, the sum of the measures of the exterior angles of a polygon is always 360°</span></span>
If I read correctly, 2456 pennies needs to be divided simply by 3 then rounded to the nearest hundredth. So you would do 2456/3 3 goes into 24 how many times? Then 3 goes into 5 how many times, then continue the pattern. Once you've gotten a decimal to the thousandth, round the number to the hundredth and there you go
We know that the sum of the interior angles of a triangle equals 180, then,in this case we have the following equation:
then, solving for b, we get:
now that we have that b = 41, we can find the measure of each angle:
