Little League Baseball Refer to Problem 110. Overlay a rectangular coordinate system on a Little League baseball diamond so that the origin is at home plate, the positive x -axis lies in the direction from home plate to first base, and the positive y -axis lies in the direction from home plate to third base. (a) What are the coordinates of first base, second base, and third base? Use feet as the unit of measurement. (b) If the right fielder is located at ( 180 , 20 ) , how far is it from there to second base? (c) If the center fielder is located at ( 220 , 220 ) , how far is it from there to third base?
Little League Baseball Refer to Problem 110. Overlay a rectangular coordinate system on a Little League baseball diamond so that the origin is at home plate, the positive x -axis lies in the direction from home plate to first base, and the positive y -axis lies in the direction from home plate to third base. (a) What are the coordinates of first base, second base, and third base? Use feet as the unit of measurement. (b) If the right fielder is located at ( 180 , 20 ) , how far is it from there to second base? (c) If the center fielder is located at ( 220 , 220 ) , how far is it from there to third base?
Little League Baseball Refer to Problem 110. Overlay a rectangular coordinate system on a Little League baseball diamond so that the origin is at home plate, the positive
lies in the direction from home plate to first base, and the positive
lies in the direction from home plate to third base.
(a) What are the coordinates of first base, second base, and third base? Use feet as the unit of measurement.
(b) If the right fielder is located at
, how far is it from there to second base?
(c) If the center fielder is located at
, how far is it from there to third base?
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)
Macbook Pro
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.