If the city bus through Austin travels at 40 miles per hour, how many miles
1 answer:
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Answer:
Option C,
Step-by-step explanation:
We can find the correct answer by plugging in the x and y values of a point on the graph into each option, then finding the one that gives a true statement as a result.
For example, one point on the graph is (30,4). We can substitute 30 for the x and 4 for the y in option C's equation, . Then, simplify:
4 does equal 4, so when we substitute a point from the graph into this equation, the result is a true statement. Thus, option C is the answer.
Let x represent the side length of the square end, and let d represent the dimension that is the sum of length and girth. Then the volume V is given by
V = x²(d -4x)
Volume will be maximized when the derivative of V is zero.
dV/dx = 0 = -12x² +2dx
0 = -2x(6x -d)
This has solutions
x = 0, x = d/6
a) The largest possible volume is
(d/6)²(d -4d/6) = 2(d/6)³
= 2(108 in/6)³ = 11,664 in³
b) The dimensions of the package with largest volume are
d/6 = 18 inches square by
d -4d/6 = d/3 = 36 inches long
V = x²(d -4x)
Volume will be maximized when the derivative of V is zero.
dV/dx = 0 = -12x² +2dx
0 = -2x(6x -d)
This has solutions
x = 0, x = d/6
a) The largest possible volume is
(d/6)²(d -4d/6) = 2(d/6)³
= 2(108 in/6)³ = 11,664 in³
b) The dimensions of the package with largest volume are
d/6 = 18 inches square by
d -4d/6 = d/3 = 36 inches long