Consider circle o, in which arc xy measures 16π cm. the length of a radius of the circle is 32 cm. what is the circumference of the circle? π units what is the ratio of the arc length to the circumference? what is the measure of central angle xoy?

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°

What is the circumference of the circle?

64π units

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

1/4

What is the measure of central angle XOY?

90 degrees  

Step-by-step explanation:

I got it right on edg

(2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

step-by-step explanation:

simplify the following:

x/x^2 + 3 x + 2 - (x (x + 1))/(x + 2)

combine powers. x/x^2 = x^(1 - 2):

x^(1 - 2) + 3 x + 2 - (x (x + 1))/(x + 2)

1 - 2 = -1:

x^(-1) + 3 x + 2 - (x (x + 1))/(x + 2)

put each term in 1/x + 3 x + 2 - (x (x + 1))/(x + 2) over the common denominator x (x + 2): 1/x + 3 x + 2 - (x (x + 1))/(x + 2) = (x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)):

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2))

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)) = ((x + 2) + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2)):

(2 + x + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

3 x^2 (x + 2) = 3 x^3 + 6 x^2:

(2 + x + 3 x^3 + 6 x^2 + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

2 x (x + 2) = 2 x^2 + 4 x:

(2 + x + 6 x^2 + 3 x^3 + 2 x^2 + 4 x - x^2 (x + 1))/(x (x + 2))

-x^2 (x + 1) = -x^2 - x^3:

(-x^2 - x^3 + 3 x^3 + 6 x^2 + 2 x^2 + 4 x + x + 2)/(x (x + 2))

grouping like terms, 3 x^3 - x^3 + 6 x^2 + 2 x^2 - x^2 + 4 x + x + 2 = (3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2:

((3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

3 x^3 - x^3 = 2 x^3:

(2 x^3 + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

6 x^2 + 2 x^2 - x^2 = 7 x^2:

(2 x^3 + 7 x^2 + (x + 4 x) + 2)/(x (x + 2))

x + 4 x = 5 x:

answer:   (2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

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