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: 5 inches
Step-by-step explanation:
The x's denote the insects measured so the longest insects would be of lengths:
1³/₄ inch, 1³/₄ inch and 1¹/₂ inch.
Adding them together would require converting them to improper fractions first:
7/4, 7/4, 3/2
Pick a denominator that is both denominators' lowest common multiple = 4
Adding them:
Divide the LCM by the denominator of the fraction and multiply the result by the numerator:
= (7 + 7 + 6) / 4
= 20/4
= 5 inches
Answer:
156 square inches
Step-by-step explanation:
We are given the two quantities
Let
length = l = 13 inches
and
Width = w = 12 inches
The formula for the area of rectangle is:
where l is length and w is width
Putting the values of both that are given
so the area is 156 square inches ..
Answer:
A
Step-by-step explanation:
Answer: (4,-5)
Step-by-step explanation:
8y = -40
(divide by 8)
y = -5
(plug it in to one of the equations)
3x + 6*-5 = -18
3x + -30 = -18
3x = 12
x = 4
