a.
To calculate: The area of the given trapezoid as a function of
The area of the given trapezoid as a function of
Given information: A trapezoid is inscribed inside the upper half of a circle as shown below.
Figure (1)
Formula used: The area of a trapezoid is given by
Calculation:
Draw a perpendicular to find the height of the trapezoid.
Figure (2)
Apply the formula of distance between two points to calculate the length
The radius of circle is
Calculate the value of
Calculate the length of
Calculate the area of trapezoid as a function of
Further simplify.
Thus, the area of the given trapezoid as a function of
b.
To calculate: The value of
The value of
Given information: A trapezoid is inscribed inside the upper half of a circle as shown below.
Figure (3)
Calculation:
From part (a), the area of trapezoid is
Draw the graph of the area function as shown below.
Figure (4)
From the graph, it can be observed that the graph reaches its maximum value for
Thus, the value of
Chapter 5 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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- 3) If a is a positive number, what is the value of the following double integral? 2a Love Lv 2ay-y² .x2 + y2 dadyarrow_forward16. Solve each of the following equations for x. (a) 42x+1 = 64 (b) 27-3815 (c) 92. 27² = 3-1 (d) log x + log(x - 21) = 2 (e) 3 = 14 (f) 2x+1 = 51-2xarrow_forward11. Find the composition fog and gof for the following functions. 2 (a) f(x) = 2x+5, g(x) = x² 2 (b) f(x) = x²+x, g(x) = √√x 1 (c) f(x) = -1/2) 9 9(x) = х = - Xarrow_forward
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