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2 years ago

PLEASE HELP!!! find the length of arc LN. Round to the nearest hundredth. SHOW WORK....

Mathematics

1 answer:

patriot [66]2 years ago

6 0

9514 1404 393

Answer:

15.71 units

Step-by-step explanation:

The arc length is given by the formula ...

s = rθ

where r represents the radius, and θ represents the central angle in radians.

The angle of 60° is π/3 radians, so the arc length is ...

s = 15(π/3) = 5π ≈ 15.71 . . . units

LN ≈ 15.71 units

<em>Note</em>: if you use 3.14 for π, you will get 15.70.

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3 years ago

The measure of angle P is five less than four times the measure of angle Q. Of angle P and angle Q are supplementary angles, fin

Andru [333]

Answer:

m∠P=140°

Step-by-step explanation:

Given:

∠P and ∠Q are supplementary angles.

The measure of angle P is five less than four times the measure of angle Q.

To find m∠P

Solution:

The measure of angle P can be given as:

A) $m\angle P=4(m\angle Q-5)$

And

B) $m\angle P+ m\angle Q=180$ [Definition of supplementary angles]

Substituting equation A into B.

$4(m\angle Q-5)+ m\angle Q=180$

Solving for $m\angle Q$

Using distribution:

$4m\angle Q-20+ m\angle Q=180$

Simplifying by combining like terms.

$5m\angle Q-20=180$

Adding 20 to both sides.

$5m\angle Q-20+20=180+20$

$5m\angle Q=200$

Dividing both sides by 5.

$\frac{5m\angle Q}{5}=\frac{200}{5}$

$m\angle Q=40$

Substituting $m\angle Q=40$ in equation B.

$m\angle P+ 40=180$

Subtracting both sides by 40.

$m\angle P+ 40-40=180-40$

$m\angle P=140$

Thus, we have:

m∠P=140° (Answer)

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