A child kicks a rock off the side of a hill at an angle of elevation of 60 ° . 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 rock is kicked. The path of the rock and the line of declination of the hill can be approximated by y = − x 2 36 + 3 x Path of the rock y = − 3 3 x Line of declination of the hill Solve the system to determine where the rock will hit the ground.
A child kicks a rock off the side of a hill at an angle of elevation of 60 ° . 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 rock is kicked. The path of the rock and the line of declination of the hill can be approximated by y = − x 2 36 + 3 x Path of the rock y = − 3 3 x Line of declination of the hill Solve the system to determine where the rock will hit the ground.
A child kicks a rock off the side of a hill at an angle of elevation of
60
°
.
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 rock is kicked. The path of the rock and the line of declination of the hill can be approximated by
y
=
−
x
2
36
+
3
x
Path of the rock
y
=
−
3
3
x
Line of declination of the hill
Solve the system to determine where the rock 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.
Find a plane containing the point (3, -3, 1) and the line of intersection of the planes 2x + 3y - 3z = 14
and -3x - y + z = −21.
The equation of the plane is:
Determine whether the lines
L₁ : F(t) = (−2, 3, −1)t + (0,2,-3) and
L2 : ƒ(s) = (2, −3, 1)s + (−10, 17, -8)
intersect. If they do, find the point of intersection.
● They intersect at the point
They are skew lines
They are parallel or equal
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