   Chapter 11.5, Problem 101E

Chapter
Section
Textbook Problem

# EXPLORING CONCEPTSPlanes Consider a line and a point not on the line. How many planes contain the line and the point? Explain.

(a)

To determine

To calculate: The approximate values for z for the provided values of x and y and compare it with the given values of z in the table,

 Year 2005 2006 2007 2008 2009 2010 x 36.4 39 42.4 44.7 43 45.2 y 15.3 16.6 17.4 17.5 17 17.3 z 16.4 18.1 20 20.5 20.1 21.4
Explanation

Given:

Personal consumption expenditures table where x is the expenditures on amusement parks, y is expenditures on live entertainment (excluding sports) and z is the expenditures on spectator sports. The table is as follows:

 Year 2005 2006 2007 2008 2009 2010 x 36.4 39 42.4 44.7 43 45.2 y 15.3 16.6 17.4 17.5 17 17.3 z 16.4 18.1 20 20.5 20.1 21.4

And, the model for the data is given by,

0.46x+0.30yz=4.94

Calculation:

Since, the provided equation for the data is,

0.46x+0.30yz=4.94

Approximate value of z will be calculated by substituting provided values of x and y from the table.

Thus, for the year 2005, substitute x=42.4,y=17.4 in the provided equation,

0.46(36.4)+0.30(15.3)z=4.9416.744+4.59z=4.94z=16.4z=16.4

So, approximated value of z for the year 2005 is 16.4.

For the year 2006, substitute x=39.0,y=16.6 in the provided equation,

0.46(39.0)+0.30(16.6)z=4.9416.744+4.59z=4.94z=17.98z=17.98

So, approximated value of z for the year 2006 is 17.98;

For the year 2007, substitute x=42.4,y=17.4 in the provided equation,

0.46(42.4)+0.30(17.4)z=4.9419.5+5.22z=4.94z=19.78z=19.78

So, approximated value of z for the year 2007 is 19

(b)

To determine

Behavior of recreation type z for the increase in recreation types x and y where the value of x, y and z are given as,

 Year 2005 2006 2007 2008 2009 2010 x 36.4 39 42.4 44.7 43 45.2 y 15.3 16.6 17.4 17.5 17 17.3 z 16.4 18.1 20 20.5 20.1 21.4

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