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Subsection 2.1 Angles and Circles Exercises
A circle has its center at
\((5, -12)\text{,}\) and contains the origin
\((0,0)\text{.}\)
Draw a diagram of the circle in the
\(xy\) -plane.
Write the equation of the circle.
Find the circumference and area of the circle.
Find the length of the arc of the circle cut out by an angle of
\(\frac{\pi}{3}\) radians.
Find the area of the sector of the circle cut out by an angle of
\(\frac{\pi}{3}\) radians.
A circle has its center at
\((-2, 5)\text{,}\) and contains the point
\((3,5)\text{.}\)
Draw a diagram of the circle in the
\(xy\) -plane.
Write the equation of the circle.
Find the circumference and area of the circle.
Find the length of the arc of the circle cut out by an angle of
\(\frac{\pi}{4}\) radians.
Find the area of the sector of the circle cut out by an angle of
\(\frac{\pi}{4}\) radians.
A park has a circular walking path with a diameter of 250 meters.
Draw a diagram of the path in the
\(xy\) -plane.
Write the equation to describe the walking path in your diagram.
Find the distance traveled by someone walking once around the entire path.
Find the distance traveled by someone walking counterclockwise along the path from the easternmost point of the path to the northernmost point of the path.
Find the distance traveled by someone walking
straight through the park from the easternmost point of the path to the northernmost point of the path.
A Ferris wheel has a diameter of 10 meters, and is mounted so that the bottom of the wheel is 1 meter off the ground. A rider boards the wheel from the 6 o’clock position and the ride turns counterclockwise as seen by the operator.
Draw a diagram of the Ferris wheel in the
\(xy\) -plane.
Write an equation to describe the points on the Ferris wheel.
Find the distance traveled by someone riding through one complete turn of the wheel.
Find the distance traveled by someone ridlng from the boarding position to the 11 o’clock position.
The wheel makes 1 turn every 30 seconds. A rider boards the wheel and travels a distance of 8 meters (along the arc). How long did this take?
A carousel (merry-go-round) has a diameter of 18 meters. The ride turns counterclockwise.
Draw a diagram of the carousel in the
\(xy\) -plane, with the center of the carousel at the origin.
Write an equation to describe the points on the edge of the carousel.
Find the distance traveled by someone riding a horse at the outer rim of the carousel through one complete turn.
Find the distance traveled by someone riding a horse 2 meters from the outer rim as they make
\(\frac{1}{3}\) of a turn.
The carousel makes 1 turn every 40 seconds. A rider on the outer rim boards the wheel and travels a distance of 15 meters. How long did this take?
First-class US mail flat envelopes can be shipped for $.98 for the first ounce, and $.21 for each additional ounce.
Write a function equation that gives the cost to ship an envelope weighing
\(w\) ounces.
What is the cost to ship an envelope weighing 10 ounces?
Customers are advised to ship via other methods if the cost of the envelope will be more than $3.50. What is the maximum weight that should be shipped via first-class flat envelope?
