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Goryan [66]
3 years ago
14

Simplify the expression |ab^3| , if: a 0

Mathematics
1 answer:
Nutka1998 [239]3 years ago
5 0

Answer:[45] i think

Step-by-step explanation:

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The absolute value of -183 is _______.
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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.

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Please help WILL MARK BRAINLIEST I need the right answer​
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Answer: a

Step-by-step explanation:

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2 years ago
The radius of the large sphere is double the radius of the small sphere. How many times is the volume of the large sphere than t
kobusy [5.1K]

The volume of a sphere is \cfrac{4}{3}\ \pi r^3

So, if the small sphere has radius r and the largest sphere has radius 2r, their volumes are

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So, their ratio is

\cfrac{V_2}{V_1} = \cfrac{\frac{4}{3}\ \pi 8r^3}{\frac{4}{3}\ \pi r^3} = 8

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3 years ago
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The graph of f ′ (x), the derivative of f(x), is continuous for all x and consists of five line segments as shown below. Given f
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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,

\displaystyle f(5) = f(0) + \int_0^5 f'(x) \, dx

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

\displaystyle \int_0^5 f'(x) \, dx = \frac{5+2}2 \times 2 = 7

\implies \max\{f(x) \mid 0\le x \le5\} = f(5) = f(0) + 7 = \boxed{13}

8 0
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