Velamur Quiz 8 *Note: Inflection points are not on Exam 2.

Velamur Quiz 9 *Note: Inflection points are not on Exam 2.

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Recall that each central angle measure corresponds to a *terminal point*, expressed as x- and y-coordinates. For example, the terminal point of 270° is (0,-1). Define a function that models this relationship and graph it in degrees. Then graph it in radians.

After you’ve drawn your graphs, check out the applets here. Are any of them demonstrating the function that you just graphed? What’s the name of that function?

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2. The area of a sector of a circle with a central angle of 2 radians is . Find the radius of the circle.

3.

Will & the Wheel from InkyMind on Vimeo.

How fast is the wheel turning? How fast is Will running?

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a.

b.

c. -1

d. -2

e. -1

2. 45

3.

4. unknown angle is 43 degrees, unknown sides are 18 feet and 13 feet

5. 39

6. The fire is 182.3 miles from station A and 128.7 miles from station B.

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2. A potter forms a piece of clay into a cylinder. As he rolls it, the length, , of the cylinder increases and the radius, , decreases. If the length of the cylinder is increasing at 0.1 cm per second, find the rate at which the radius is changing when the radius is 1 cm and the length is 5 cm.

3. A certain quantity of gas occupies a volume of 20cc at a pressure of 1 atmosphere. The gas expands without the addition of heat, so, for some constant , its pressure, , and volume, , satisfy the equation . (a) Find the rate of change of pressure with respect to volume. (b) The volume is increasing at 2cc/min when the volume is 30cc. At that moment, is the pressure increasing or decreasing? How fast?

4. (a) A hemispherical bowl of radius 10cm contains water to a depth of cm. Find the radius of the surface of the water as a function of . (b) The water level drops at a rate of 0.1 cm per hour. At the what rate is the radius of the water decreasing when the depth is 5 cm?

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