Math League practice: 1/18/21

Math League practice: 1/18/21

A and B test emphasis

Open Ended

Determine exactly the positive solution to

 $3x^2=243$  

Open Ended

Given that

 $\frac{2x^3+14x^2+12x}{4x+4}\div\left(mx+n\right)=x$  

determine the exact value of n

Open Ended

The volume of a sphere whose surface area is 36π can be expressed as nπ.

Find n

The surface area of a sphere is

 $4πr^2$  So  $4πr^2=36π$  , so r = 3

The volume of a sphere is  $\frac{4}{3}πr^3$  

So  $\frac{4}{3}π\left(3\right)^3=36π$  

Thus nπ = 36π, so n = 36

Open Ended

In the circle pictured, minor arcs AB and BC each measure 73˚ and the measure of angle AEB = 82˚.

Determine exactly the measure of arc AD

Intersecting chords BD and CA cut off arcs AB and CD, with the relationship

 $m\angle AEB=\frac{1}{2}\left(m\ AB\ +\ m\ CD\right)$  
82˚ = 1/2 (73 + CD)

164˚ = 73 + CD
91˚ = CD
So arc AD = 360˚ - (91˚ + 146˚) = 123˚