If the perimeter of a sector is 4 times its radius, then the radian measure of the central angle of the sector is (A) 2. (B) 4.(C)2/π.(D)4/π.(E) impossible to determine without knowing the radius.

The radian measure of all three angles in a triangle can be integers. Justify your answer.

Calculate the force of gravity between Earth

$$\left( \text { mass } = 6.0 \times 10 ^ { 24 } \mathrm { kg } \right)$$

and the moon

$$(mass = 7.4 \times 10 ^ { 22 } \mathrm { kg } ).$$

The average Earth-moon distance is

$$3.8 \times 10 ^ { 8 } m$$

Find the sum. -72 + (-30)

Sarah and Matteo are told that the perimeter of a sector of a circle is 10 times the length of the circle’s radius. Sarah thinks that the radian measure of the sector’s central angle is 8 radians. Mateo thinks that there is not enough information given to solve the problem. Is either of them correct? Explain your reasoning.

Find the slope of the line through the given points. Tell whether the slope is positive, negative, zero, or undefined. (6, 3), (6, -1)

Two boats start at the same point and speed away along courses that form a 110° angle. If one boat travels at 24 miles per hour and the other boat travels at 32 miles per hour, how far apart are the boats after 30 minutes? (A) 21 miles (B) 22 miles (C) 23 miles (D) 24 miles (E) 25 miles

The propellers of the Amazon Paradise have a radius of 1.2 m. At full throttle the propellers turn at 135 rpm. What is the linear speed (in meters per second) of a point on a blade halfway between the center of the propeller and the tip of the blade?

The concentric circles on an archery target are 6 inches apart. The inner circle (red) has a perimeter of 37.7 inches. What is the perimeter of the next-largest (yellow) circle?

What voltage produces a 6 A current in a circuit that has a total resistance of 3 Ω?

The propellers of the Amazon Paradise have a radius of 1.2 m. At full throttle the propellers turn at 135 rpm. What is the linear speed of the tip of the propeller blade in meters per second?

How many numbers between 0 and 2π solve the equation 3cos²x+cosx=2? (A) None ,(B) One, (C) Two, (D) Three, (E) Four.

A simple pulley with the given radius r used to lift heavy objects is positioned 10 feet above ground level. Given that the pulley rotates , determine the height to which the object is lifted.

$$r = 4 in., θ = 720°$$

To the nearest inch, find the perimeter of a 10-degree sector cut from a circular disc of radius 11 inches.