O. MacDonald EIO Farms Bay City, MI 48706 May 1, 2016 Math 211 Students Mendocin
ID: 2863684 • Letter: O
Question
O. MacDonald EIO Farms Bay City, MI 48706 May 1, 2016 Math 211 Students Mendocino College Ukiah, Ca Dear Calculus Students, While recently traveling to Arizona to research the raising of roadrunners, I came across a certain Mr. Coyote who mentioned that you were helping him with a problem. He appeared happy, if a little unrested, and thought that you might be able to help me with a problem that I have been unable to solve. You see, I am in love with a doctor who recently treated me at the Hope Springs Eternal Hospital. She is Jonas Salk and Florence Nightingale rolled up into one. Dr. Darlene Clementine has spent a lot of time working with me and I'd like to present her with a gift that lets her know how I feel about her. One of my hobbies is making jewelry. I would like to make a white-gold medallion exactly 2 cm. across that is inlaid with a 6-petal rose in yellow gold for my darling Dr. Clementine. I will know how much yellow gold I will need if I can only find the area of the interior of the rose curveExplanation / Answer
Area = (1/2) r^2 d
Integrate from 0 to pi/3 for one leaf
Area = (1/2) sin^2 (3)/4 d
= (1/8) sin^2 (3) d
= (1/8) (1-cos(6))/2 d
(1-cos(6))/16 d = /16 - sin(6)/16
Let F() = /16 - sin(6)/16
F(pi/3) = pi/48 - 0
F(0) = 0-0
F(pi/3)-F(0) = pi/48-----------------ans.
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