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.
Find the area of the shaded region.
(a)
5-
y
3
2-
(1,4)
(5,0)
1
3
4
5
6
(b)
3 y
2
Decide whether the problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to
estimate the solution.
STEP 1: Consider the figure in part (a). Since this region is simply a triangle, you may use precalculus methods to solve this part of the problem. First determine the height of the triangle and the length of the triangle's base.
height 4
units
units
base
5
STEP 2: Compute the area of the triangle by employing a formula from precalculus, thus finding the area of the shaded region in part (a).
10
square units
STEP 3: Consider the figure in part (b). Since this region is defined by a complicated curve, the problem seems to require calculus. Find an approximation of the shaded region by using a graphical approach. (Hint: Treat the shaded regi
as…
Solve this differential equation:
dy
0.05y(900 - y)
dt
y(0) = 2
y(t) =
Suppose that you are holding your toy submarine under the water. You release it and it begins to ascend. The
graph models the depth of the submarine as a function of time.
What is the domain and range of the function in the graph?
1-
t (time)
1 2
4/5 6 7
8
-2
-3
456700
-4
-5
-6
-7
d (depth)
-8
D: 00 t≤
R:
Chapter 1 Solutions
Precalculus Enhanced with Graphing Utilities, Books a la Carte Edition Plus NEW MyLab Math -- Access Card Package (7th Edition)
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.