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Unformatted text preview: MAC1114 - Homework 1
Due Thursday, January 13
1. Finish the statement: If angles
angles 2. (cf. 16π
5 Sec. and 28π
10 α and β are coterminal, then α=β+ (be thorough!). Are the coterminal? Show why or why not. 4.1 #114) A motorized pulley with a radius of 1 inch runs at 1600 revolutions per minute. The pulley is connected to a pulley on a saw arbor with a radius of 4 inches. Find the linear speed of the saw blade in inches per minute.
3. Jemma has just installed a sprinkling system in her back yard, which is a 30 ft. by 40 ft. rectangle. Sprinklers are positioned at the corners of the yard; they are directed towards the center of the yard,
spray a distance of 15 ft, rotate through a 120◦ angle, and they each pump 2 gallons of water per minute. A typical sprinkler cycle lasts 40 minutes. Tap water costs 2 cents per gallon. (a) What fraction of Jemma's yard will be missed by all four sprinklers? (b) How much money would go to waste (due watering the fence, other people's yards, etc.) if she ran the sprinklers right now?
(c) If Jemma adjusts her sprinklers to rotate through a 90◦ angle (so no water is wasted) and increases their spray distance just enough to ensure that the whole yard is covered (note: some parts may
be watered by multiple sprinklers), how much will it cost to run her sprinklers? 1 ...
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