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Fittoniya [83]
3 years ago
6

Locate the absolute extrema of the function on the closed interval: y = 3x^(2/3) - 2x, [-1, 1]

Mathematics
1 answer:
Alecsey [184]3 years ago
7 0
To get the extrema, derive the function.
You get y' = 2x^-1/3 - 2.
Set this equal to zero, and you get x=0 as the location of a critical point.
Since you are on a closed interval [-1, 1], those points can also have an extrema.
Your min is right, but the max isn't at (1,1). At x=-1, you get y=5 (y = 3(-1)^2/3 -2(-1); (-1)^2/3 = 1, not -1).
Thus, the maximum is at (-1, 5).
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The circumference of a circle is 23π m. What is the area, in square meters? Express your answer in terms of \piπ
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Answer:

Area of the circle =   \frac{529}{4}  π  m²    or      132.25 π  m²

Step-by-step explanation:

To find the area, we will follow the steps below.

First write down the formular for the circumference of a circle, then use the formula to find the radius of the circle after which you can now find the area of the circle.

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C = 2πr

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From the question given, circumference C = 23π

23π = 2π r

Divide both-side of the equation by 2π

23π/2π  =  2πr/2π

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radius =   \frac{23}{2}  m

Formula for calculating the area of a circle is given by;

A = πr²

where A= area of the circle   and   r is the radius of the circle

A = π ( \frac{23}{2} )²

A = \frac{529}{4}  π  m²    or      132.25 π  m²

Area of the circle =   \frac{529}{4}  π  m²    or      132.25 π  m²

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