A ball is kicked off the side of a hill at an angle of elevation of 30 ° . The hill slopes downward 30 ° from the horizontal. Consider a coordinate system in which the origin is the point on the edge of the hill from which the ball is kicked. The path of the ball and the line of declination of the hill can be approximated by y = − x 2 192 + 3 3 x Path of the ball y = − 3 3 x Line of declination of the hill Solve the system to determine where the ball will hit the ground.
A ball is kicked off the side of a hill at an angle of elevation of 30 ° . The hill slopes downward 30 ° from the horizontal. Consider a coordinate system in which the origin is the point on the edge of the hill from which the ball is kicked. The path of the ball and the line of declination of the hill can be approximated by y = − x 2 192 + 3 3 x Path of the ball y = − 3 3 x Line of declination of the hill Solve the system to determine where the ball will hit the ground.
Solution Summary: The author calculates the point where the ball will hit the ground if it is kicked off to the side of the hill at an angle of elevation of 30°.
A ball is kicked off the side of a hill at an angle of elevation of
30
°
.
The hill slopes downward
30
°
from the horizontal. Consider a coordinate system in which the origin is the point on the edge of the hill from which the ball is kicked. The path of the ball and the line of declination of the hill can be approximated by
y
=
−
x
2
192
+
3
3
x
Path of the ball
y
=
−
3
3
x
Line of declination of the hill
Solve the system to determine where the ball will hit the ground.
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
T
1
7. Fill in the blanks to write the calculus problem that would result in the following integral (do
not evaluate the interval). Draw a graph representing the problem.
So
π/2
2 2πxcosx dx
Find the volume of the solid obtained when the region under the curve
on the interval
is rotated about the
axis.
38,189
5. Draw a detailed graph to and set up, but do not evaluate, an integral for the volume of the
solid obtained by rotating the region bounded by the curve: y = cos²x_for_ |x|
≤
and the curve y
y =
about the line
x =
=플
2
80
F3
a
FEB
9
2
7
0
MacBook Air
3
2
stv
DG
Find f(x) and g(x) such that h(x) = (fog)(x) and g(x) = 3 - 5x.
h(x) = (3 –5x)3 – 7(3 −5x)2 + 3(3 −5x) – 1
-
-
-
f(x) = ☐
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