College mathematics

COLLEGE MATHEMATICS

College Mathematics

Section 4 .7

22 58 116 ) Radius is half the diameter , so Section 5 .1 Each term has a z . 16 2 (2 (2 (2 , 40 2 (2 (2 (5 , 72 2 (2 (2 (3 (3

Each term has 23 as a common factor

Thus the GCF of these three terms is 8z

Section 5 .2

NOTE : There is no common binomial in this problem

It is either miswritten , or this is what the instructor intended

Section 5 .3 First , find

factors of 24 that have a difference of 5

24 2 2 2 3 , 24 8 3 . These factors have a difference of 5

Section 5 .4 a 15 , b -17 , c -4 ac -60 -60 -20 3 -20 3 -17

Thus , the two integers are -20 and 3 ac -30

b -7 factors of -30 that add to -7 are -10 and 3 Thus 15x2 - 7x - 2 factors to (5x 1 (3x-2

Since 3 is prime , 3x has to be in one term and x in the other . 10 factors

as 5 2 or 10 1 . we will try 5 2 first

102 ac 108 , b 21 108 factors to 12 9 , which sums to 21

Section 5 .5 (x 3 ) is a factor (x 3 (x2 x3 3x2 (x 3 (bx bx2 3bx

3x2 bx2 2x2 , therefore b -1 (x 3 (x2 - x - 2 (x 3 (x 1 (x-2

factors to (x 3 (x 1 (x-2 ac -48 , b 2 -48 -6 8 , diff 2 106 110

Volume equals length width height

cm3

And we know that the width is y-6 cm . This is a factor of the above equation We know that a 1 , and that -72 c -6 . Therefore c 12 Therefore , -13 b - 6 . b -7 Factors of 12 that add to -7 are -4 and -3 Thus the new length and height are y - 4 cm and y - 3 cm , though we do not know

which is which

Section 5 .6

18 ) Thus , h 3 /2 or h -1

32

First , the products have to equal zero , so we put it in standard form Thus , w ? or w -1 /2

44 Thus , the three solutions are m 0 , m -3 , or m 1

60

Using ac method Thus , the solution is h 3 or h 6 66

The diagonal divides the rectangle into two equal right triangles

we are given c 10 , thus c2 100

We also know that on side is 2 meters longer than the other

Thus , one side is x , and the other side is x 2

So :Using the ac method Thus the length of the sides is 6 meters and 8 meters

90

This is also a right triangle . The hypotenuse is the distance the train is from

the car . One leg is the distance the car is from the tracks , and the other is the

distance the train is from the road

Thus Therefore the train is 40 meters from the track

92...