CHECK POINT 3 The toll to a bridge costs $2. If you use the bridge x times in a month, the monthly cost, y , is y = 2 x . With a $10 discount pass, the toll is reduced to $l. The monthly cost, y , of using the bridge x times in a month with the discount pass is y = 10 + x . a. Let x = 0 , 2 , 4 , 6 , 8 , 10 , and 12. Make tables of values showing seven solutions of y = 2 x and seven solutions of y = 10 + x . b. Graph the equations in the same rectangular coordinate system . c. What are the coordinates of the intersection point for the two graphs? Interpret the coordinates in practical terms.
CHECK POINT 3 The toll to a bridge costs $2. If you use the bridge x times in a month, the monthly cost, y , is y = 2 x . With a $10 discount pass, the toll is reduced to $l. The monthly cost, y , of using the bridge x times in a month with the discount pass is y = 10 + x . a. Let x = 0 , 2 , 4 , 6 , 8 , 10 , and 12. Make tables of values showing seven solutions of y = 2 x and seven solutions of y = 10 + x . b. Graph the equations in the same rectangular coordinate system . c. What are the coordinates of the intersection point for the two graphs? Interpret the coordinates in practical terms.
Solution Summary: The author explains how to determine the table for the equations y=2x and
CHECK POINT 3 The toll to a bridge costs $2. If you use the bridge x times in a month, the monthly cost, y, is
y
=
2
x
. With a $10 discount pass, the toll is reduced to $l. The monthly cost, y, of using the bridge x times in a month with the discount pass is
y
=
10
+
x
.
a. Let
x
=
0
,
2
,
4
,
6
,
8
,
10
, and 12. Make tables of values showing seven solutions of
y
=
2
x
and seven solutions of
y
=
10
+
x
.
b. Graph the equations in the same rectangular coordinate system.
c. What are the coordinates of the intersection point for the two graphs? Interpret the coordinates in practical terms.
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.
RK
119
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Match the surfaces (a) - (f) below with the contour diagrams (1) - (6) below those.
(a) Surface (a) matches contour 5 V
V
(b) Surface (b) matches contour 2 V
(c) Surface (c) matches contour 1
(d) Surface (d) matches contour 6 V
(e) Surface (e) matches contour 4 V
(f) Surface (f) matches contour 3 V
(4)
(1)
-0.25
(a)
(b)
(c)
(d)
(e)
y
y
2.5
0.5
1.5
1.5
1.5
y
.3
0.25
OC
0.25
-0.25
(2)
X
1.5
ZI
(f)
y
0.01
0.01
(3)
☑
X
0.01
0.01
0.2
0.2
(5)
0 x
0.5
(6)
0.25
X
X
0.25
0.5
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At least one of the answers above is NOT correct.
The figure shows a hill with two paths, A and B.
(a) What is the elevation change along each path? 400
9400
✓ feet
(b) Which path ascends more rapidly? A v
(c) On which path will you probably have a better view of the surrounding
countryside (assuming that trees do not block your view)? A V
(d) Along which path is there more likely to be a stream?
A V
Note: You can earn 50% partial credit for 2-3 correct answers.
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9800'
A
10000
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B
0
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4)
28. (a) Under what conditions do we say that two random variables X and Y are
independent?
(b) Demonstrate that if X and Y are independent, then it follows that E(XY) =
E(X)E(Y);
(e) Show by a counter example that the converse of (ii) is not necessarily true.
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