Page 33 - Calculus Workbook For Dummies

17
Chapter 1: Getting Down the Basics: Algebra and Geometry

5. If it floats your boat, you may also want to express the answer symbolically.
Because x can equal a number in the left region or a number in the right region, this is an or
solution which means union ,h. When you want to include everything from both regions
^
on the number line, you want the union of the two regions. So, the symbolic answer is
16
x < - , x > 4
3
If only the middle region were shaded, you’d have an and or intersection +h problem. When
^
you only want the section of the number line where the two regions overlap, you use the inter-
section of the two regions. Using the above number line points, for example, you would write
the middle-region solution like
16
x < - and x > 4 or
3
16
x < - + x > 4 or
3
16
- < < 4
x
3
You say “to-may-to,” I say “to-mah-to.”
2
2
While we’re on the subject of absolute value, don’t forget that x = x . x does not
equal x! .
=
q Fill in the two missing lengths for the sides of the triangle. a = 5 and b 5 3
This is a 30°-60°-90° triangle — Well, duhh!
r Fill in the two missing lengths for the sides of the triangle.

8 8 3
a = or
3 3
16 16 3
b = or
3 3
Another 30°-60°-90° triangle.

s Fill in the two missing lengths for the sides of the triangle. a = 6 and b = 6 2
Make sure you know your 45°-45°-90° triangle.
25 3
t a. What’s the total area of the pentagon? 50 + 2 .
10 10
The square is by (because half a square is a 45°-45°-90° triangle), so the area is
2 2
10 $ 10 = 100 = 50. The equilateral triangle has a base of 10 , or 5 2, so its height is 5 6
2 2 2 2 2
(because half of an equilateral triangle is a 30°-60°-90° triangle). So the area of the triangle is
J N
1 ` 5 2 K j 5 6 O = 25 12 = 50 3 = 25 3 . The total area is thus 50 + 25 3 .
2 K 2 O 4 4 2 2
L P
b. What’s the perimeter? The answer is 25.
10
The sides of the square are , or 5 2, as are the sides of the equilateral triangle.
2
The pentagon has five sides, so the perimeter is 5 5 2 or 25 2.
$
,