K is the midpoint of JL. Given the jk =2x+7 and KL = 4x+1, find x

Answers:

1. The circumference of the circle is 64 ∏ cm.

2. The ratio of the arc length to the circumference is 1/4.

3. The measure of central angle XOY is ∏/2 radians or 90°

Solution:

Length of the arc XY: La = 16∏ cm

Length of a radius of the circle: r = 32 cm

1. What is the circumference of the circle?

Circumference of the circle: L=?

L=2∏r

Replacing r by 32 cm in the formula above:

L=2∏ (32 cm)

Multilying:

L=64∏ cm

2. What is the ratio of the arc length to the circumference?

Ratio of the arc length to the circumference: r=?

r=La/L

Replacing La by 16∏ cm and L by 64∏ cm in the formula above:

r = (16∏ cm) / (64∏ cm)

r=16/64

Simplifying the fraction dividing the numerator and denominator by 16:

r= (16/16) / (64/16)

r=1/4

3. What is the measure of central angle XOY?

Central angle XOY: A=?

A=La/r

Replacing La by 16∏ cm and r by 32 cm in the formula above:

A= (16∏ cm) / (32 cm)

A= 16∏ / 32 radians

Simplifying the fraction dividing the numerator and denominator by 16:

A= (16∏/16) / (32/16) radians

A= ∏/2 radians equivalent to 90°

A= ∏/2 radians = 90°