Answer:
183
Step-by-step explanation:
The absolute value of a number is the number's distance from zero, which will always be a positive value. To find the absolute value of a number, drop the negative sign if there is one to make the number positive.
C.<span>She used an incorrect formula. The formula should be the change in </span>y<span>-values with respect to the change in the </span>x<span>-values.
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Answer: a
Step-by-step explanation:
The volume of a sphere is 
So, if the small sphere has radius
and the largest sphere has radius
, their volumes are

So, their ratio is

The maxima of f(x) occur at its critical points, where f '(x) is zero or undefined. We're given f '(x) is continuous, so we only care about the first case. Looking at the plot, we see that f '(x) = 0 when x = -4, x = 0, and x = 5.
Notice that f '(x) ≥ 0 for all x in the interval [0, 5]. This means f(x) is strictly increasing, and so the absolute maximum of f(x) over [0, 5] occurs at x = 5.
By the fundamental theorem of calculus,

The definite integral corresponds to the area of a trapezoid with height 2 and "bases" of length 5 and 2, so

