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QUESTION: A pendulum swings through an angle of 20^o each second. If the pendulum is 40 inches long, how far does the tip move each second?

ANSWER: This can be thought of as a circle.

The radius is 40" and the angle is 20°.

The entire circumference is 2•pi*r.

Since pi is roughly 3.1416, r is 40", and the angle is 1/18 of a full circle,

That gives us a value of 251", and that's how far it moves.

---------- FOLLOW-UP ----------

QUESTION: graph each of the following equations:

1)3x-2y=-6

2) -2y>8

3)¦x+2y¦<10

4){y>3 and y-x<5

ANSWER: 1) This is a line, y = 3x/2 + 3.

2) This is the half plane below y = -4.

3) This is a diamond between the corners (-10,0), (5,0), (10,0), and (-5,0).

4) This is the region above y-3 and to the left of the line y = 5+x.

---------- FOLLOW-UP ----------

QUESTION: solve each word problem:

1) find three consecutive even integers whose sum is 84?

2) if the perimeter of a rectangular is 34 yd and the length is 2 yd longer than twice the width, then what are the length and width?

3)Mark plans to fence a rectangular area for rabbits alongside his house. He will use 14 feet of fencing only three sides of the rectangle. if the side that runs parallel to the house is 2 feet longer than either of the other two sides, then what are the dimensions of the rectangular area?

1) If n-1,n, and n+1 are the three consecutive integers, this means that

n-1 + n + n+1 is the sum. Adding these up gives 3n = 84.

Dividing by 3 gives n = 28. This means the numbers are 27, 28, and 29.

2) Take one side as x, then the other side is x+2.

The perimeter is 2x + 2(x+2) = 2x + 2x + 4 = 4x + 4 = 4(x+1).

If this is 34, then 4(x+1) = 34 can be divided by 4, giving x+1 = 8.5.

Subtracting 1 from both sides gives x = 7.5.

3) If the two sides sticking out from the house are x feet long,

that leaves 14-2x feet of fencing for the other side.

If 14-2x is 2 greater than x, we have 14-2x = x + 2.

Adding 2x-2 to both sides gives 14-2 = 2x+x, which is 12 = 3x, so x=4.

This makes the other sides be 14-2x = 14-8 = 6.

Checking, this is 2 more than 4.

Word Problems

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