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invariable
Definition: (adjective) not changing or subject to change.
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Math Teaser
Problem
A group of 9 friends invest equally in a business opportunity that costs $20,000. If n more friends were to take part evenly in the investment...
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SAT* Tip of the Day
So What?
Math questions involving two equations and two unknowns can usually be combined into one equation with one unknown.
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PSAT: Math Question #4

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Question:
 The length of an arc of a circle equals 
1
8
 of the circle's 
 circumference. What is the diameter of the circle if the length of 
 the arc is   π   ? 


Choices:
A. 2.83
B. 4
C. 6.33
D. 8
E. 10

The correct answer is (D).

Now, it is easy to find the diameter, d, using the formula for the circumference of a circle.

The correct answer is (D).

 Since the length of the arc is   π   , and this length is 
1
8
 of the 
 circumference, the circumference must be 8   π 

Now, it is easy to find the diameter, d, using the formula for the circumference of a circle.

 Circumference   =  2  π  r  =   π  d

Circumference
 =   π  d
8  π   =   π  d
8  π 
 π 
=d
8
=d
 

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