A player in a video game must knock out a target located 84 pixels above and 156 pixels to the left of his position. Choose a polar coordinate system with the player at the pole and the polar axis extending to the player’s right. Find the polar coordinates of the target (this determines the distance and angle at which the player should fire his gun). Find r to the nearest pixel and θ in degree measure to the nearest tenth of a degree.
A player in a video game must knock out a target located 84 pixels above and 156 pixels to the left of his position. Choose a polar coordinate system with the player at the pole and the polar axis extending to the player’s right. Find the polar coordinates of the target (this determines the distance and angle at which the player should fire his gun). Find r to the nearest pixel and θ in degree measure to the nearest tenth of a degree.
Solution Summary: The author explains how to calculate the polar coordinates of the target in a video game.
A player in a video game must knock out a target located
84
pixels above and
156
pixels to the left of his position. Choose a polar coordinate system with the player at the pole and the polar axis extending to the player’s right. Find the polar coordinates of the target (this determines the distance and angle at which the player should fire his gun). Find
r
to the nearest pixel and
θ
in degree measure to the nearest tenth of a degree.
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.
Given lim x-4 f (x) = 1,limx-49 (x) = 10, and lim→-4 h (x) = -7 use the limit properties
to find lim→-4
1
[2h (x) — h(x) + 7 f(x)] :
-
h(x)+7f(x)
3
O DNE
17. Suppose we know that the graph below is the graph of a solution to dy/dt = f(t).
(a) How much of the slope field can
you sketch from this information?
[Hint: Note that the differential
equation depends only on t.]
(b) What can you say about the solu-
tion with y(0) = 2? (For example,
can you sketch the graph of this so-
lution?)
y(0) = 1
y
AN
(b) Find the (instantaneous) rate of change of y at x = 5.
In the previous part, we found the average rate of change for several intervals of decreasing size starting at x = 5. The instantaneous rate of
change of fat x = 5 is the limit of the average rate of change over the interval [x, x + h] as h approaches 0. This is given by the derivative in the
following limit.
lim
h→0
-
f(x + h) − f(x)
h
The first step to find this limit is to compute f(x + h). Recall that this means replacing the input variable x with the expression x + h in the rule
defining f.
f(x + h) = (x + h)² - 5(x+ h)
=
2xh+h2_
x² + 2xh + h² 5✔
-
5
)x - 5h
Step 4
-
The second step for finding the derivative of fat x is to find the difference f(x + h) − f(x).
-
f(x + h) f(x) =
= (x²
x² + 2xh + h² -
])-
=
2x
+ h² - 5h
])x-5h) - (x² - 5x)
=
]) (2x + h - 5)
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Polar Coordinates Basic Introduction, Conversion to Rectangular, How to Plot Points, Negative R Valu; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=aSdaT62ndYE;License: Standard YouTube License, CC-BY