Suppose that a rectangle is bounded by the x -axis and the graph of y = cos x . a. Write a function that represents the area A x of the rectangle for. 0 < x < π 2 b. Complete the table. a. Graph the function from part (a) on the viewing window: 0 , π 2 , π 6 by − 3 , 3 , 1 and approximate the values of x for which the area is 1 square unit Round to 2 decimal places. b. In calculus, we can show that the maximum value of the area of the rectangle will occur at values of x for which 2 cos x − 2 x sin x = 0 . Confirm this result by graphing y = 2 cos x − 2 x sin x and the function from part (a) on the same viewing window. What do you notice?
Suppose that a rectangle is bounded by the x -axis and the graph of y = cos x . a. Write a function that represents the area A x of the rectangle for. 0 < x < π 2 b. Complete the table. a. Graph the function from part (a) on the viewing window: 0 , π 2 , π 6 by − 3 , 3 , 1 and approximate the values of x for which the area is 1 square unit Round to 2 decimal places. b. In calculus, we can show that the maximum value of the area of the rectangle will occur at values of x for which 2 cos x − 2 x sin x = 0 . Confirm this result by graphing y = 2 cos x − 2 x sin x and the function from part (a) on the same viewing window. What do you notice?
Solution Summary: The author analyzes the function that represents the area of the rectangle for 0xpi 2.
Suppose that a rectangle is bounded by the x-axis and the graph of
y
=
cos
x
.
a. Write a function that represents the area
A
x
of the rectangle for.
0
<
x
<
π
2
b. Complete the table.
a. Graph the function from part (a) on the viewing window:
0
,
π
2
,
π
6
by
−
3
,
3
,
1
and approximate the values of
x
for which the area is
1
square unit Round to
2
decimal places.
b. In calculus, we can show that the maximum value of the area of the rectangle will occur at values of
x
for which
2
cos
x
−
2
x
sin
x
=
0
. Confirm this result by graphing
y
=
2
cos
x
−
2
x
sin
x
and the function from part (a) on the same viewing window. What do you notice?
find the zeros of the function algebraically:
f(x) = 9x2 - 3x - 2
Rylee's car is stuck in the mud. Roman and Shanice come along in a truck to help pull her out. They attach
one end of a tow strap to the front of the car and the other end to the truck's trailer hitch, and the truck
starts to pull. Meanwhile, Roman and Shanice get behind the car and push. The truck generates a
horizontal force of 377 lb on the car. Roman and Shanice are pushing at a slight upward angle and generate
a force of 119 lb on the car. These forces can be represented by vectors, as shown in the figure below. The
angle between these vectors is 20.2°. Find the resultant force (the vector sum), then give its magnitude
and its direction angle from the positive x-axis.
119 lb
20.2°
377 lb
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