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.
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
There are three options for investing $1150. The first earns 10% compounded annually, the second earns 10% compounded quarterly, and the third earns 10% compounded continuously. Find equations that model each investment growth and
use a graphing utility to graph each model in the same viewing window over a 20-year period. Use the graph to determine which investment yields the highest return after 20 years. What are the differences in earnings among the three
investment?
STEP 1: The formula for compound interest is
A =
nt
= P(1 + − − ) n²,
where n is the number of compoundings per year, t is the number of years, r is the interest rate, P is the principal, and A is the amount (balance) after t years. For continuous compounding, the formula reduces to
A = Pert
Find r and n for each model, and use these values to write A in terms of t for each case.
Annual Model
r=0.10
A = Y(t) = 1150 (1.10)*
n = 1
Quarterly Model
r = 0.10
n = 4
A = Q(t) = 1150(1.025) 4t
Continuous Model
r=0.10
A = C(t) =…
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