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:
-2 3/4
Step-by-step explanation:
i gotchu
(a) Differentiate each of the components to get r'(t). The rule is
.. d/dt (a*e^(bt)) = a*b*e^(bt)
The answer you have shown is the correct one.
(b) See the figure. The red curve is the position r(t) for 0 ≤ t ≤ 2. The dashed orange line is the tangent line, whose equation is
.. L(t) = r(0) +r'(0)*t = (2 +2t)i +(3 -3t)j
(B) 8 less than the product of 3 and n
Here, we are given an equation 3n - 8
Let us consider each of the options one by one
(A) the product of 3, n and 8 will be written as 24n. Hence this isn't the correct answer.
(B) 8 less than the product of 3 and n will be written as 3n - 8. This matches our equation and hence is the correct answer.
(C) n minus 8 times 3 will be written as 24 - n. Hence, this is also incorrect.
(D) 3 times n less than 8 will be written as 8 - 3n. Thus, this is also eliminated.
Therefore, option B is the correct answer.
Learn more about expressing equations here-
brainly.com/question/4344214
#SPJ9
c) Combine 2+3 to get 5. 100-(5x5) equals 100-25. 100-25 is 75. The answer is 75.
d) Combine 2+3 to get 5. Combine 1+4 to get 5, which is 25. The answer is 5.
g) Combine 4+6 to get 10. Combine 70+-6 to get 64. Take the root of 64, leaving you with 10-8. Combine 10 + -8 to get 2. The answer is 2.
h) Combine 5+4 to get 9. Take the root of 36, leaving you with 18 + 6. Combine 18 + 6 to get 24. The answer is 24.
5. [15 + 22 + 53] divided by [12 + 18] = [90] divided by [30] = 3 ribbons each.
6. (4 x 12) + (6 x 8) = 96 total.
