A coin has a radius of 10 mm. How long will it take the coin to roll through the given angle measure at the given angular velocity? How far will it travel in that time? Round to the nearest tenth.

540°; 6 rev/sec

The coin will take
sec to roll 540° and travels approximately
mm.

t = 1.57 sec

distance, d = 98.65 mm

Step-by-step explanation:

Given an angle of 540°

At 6 revolutions per second, which is the angular velocity.

Radius, r = 10 mm

We are asked to find the time and the distance.

To find the time, let's use the formula:

Where = angle in radians.

Converting 540° to radians, we have:

Therefore, from the formula, let's find t.

time = 1.57

To find the distance, we have:

d = 98.65 mm

Therefore, the time is 1.57 seconds and the distance is 98.65 mm

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.