Write 21/4 as a decimal. Round to three decimal places
2 answers:
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9514 1404 393
Answer:
- maximum: 2
- minimum: -6
Step-by-step explanation:
The extrema will be at the ends of the interval or at a critical point within the interval.
The derivative of the function is ...
f'(x) = 3x² -4x -4 = (x -2)(3x +2)
It is zero at x=-2/3 and at x=2. Only the latter critical point is in the interval. Since the leading coefficient of this cubic is positive, the right-most critical point is a local minimum. The coordinates of interest in this interval are ...
f(0) = 2
f(2) = ((2 -2)(2) -4)(2) +2 = -8 +2 = -6
f(3) = ((3 -2)(3) -4)(3) +2 = -3 +2 = -1
The absolute maximum on the interval is f(0) = 2.
The absolute minimum on the interval is f(2) = -6.
Given:
θ = 60°
Radius = 8 in
To find:
The area of the shaded segment.
Solution:
Vertically opposite angles are congruent.
Angle for the shaded segment = 60°
<u>Area of the sector:</u>
A = 33.5 in²
Area of the sector = 33.5 in²
<u>Area of triangle:</u>
A = 32 in²
Area of the triangle = 32 in²
Area of segment = Area of sector - Area of triangle
= 33.5 in² - 32 in²
= 1.5 in²
The area of the shaded segment is 1.5 square inches.