CHALLENGE PROBLEM SESSIONSpokane Math Circle

10.28.12

2007-08 PREALGEBRA #40

A circle of radius 2 inches rolls along the entire perimeter of a right triangle with sides 8, and 16 inches. How many inches are traveled by the center of the circle?

THINGS TO KNOW FIRST

30-60-90 triangles Arc lengths using angles

30-60-90 TRIANGLES

Will always be in the ratio of 1::2 http://www.mathopenref.com/triangle306090.html Need proof? Use Pythagoras () on an

equilateral triangle:

ARC LENGTH

Circumference of a circle? How to use angle/circumference to find arc

length?

NOW SOLVE!

A circle of radius 2 inches rolls along the entire perimeter of a right triangle with sides 8, and 16 inches. How many inches are traveled by the center of the circle?

FINAL ANSWER?

4𝜋+24+8√3

2011-2012 7TH/8TH GRADE #38

Find the equation, in slope-intercept form, of the line perpendicular to 4x – 3y = 18 and intersecting the point (8, 5).

THINGS TO KNOW FIRST

One variable equations (linear equations) Slope relationships

LINEAR EQUATIONS

Slope (m) is defined as or rise over run. Common forms of linear equations: Slope-intercept form: Point-slope form:

PERPENDICULAR/PARALLEL LINES

Slope of line parallel to? Slope of line perpendicular to?

NOW SOLVE!

Tina is offered a job with two options for pay. In the first option, she will make $5000 per month with no raises. In the second option, she will start at $3000 per month and get a raise of $500 at the beginning of every year. How much more money, in dollars, will she have made in five years if she chooses the higher paying option?

NOW SOLVE!

Find the equation, in slope-intercept form, of the line perpendicular to 4x – 3y = 18 and intersecting the point (8, 5).

FINAL ANSWER?

𝑦=−34𝑥+11