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University of Calgary
STAT 217

AMAT 217 Problems for Labs 1.Find the slope of the line tangent to the curve x y e 2 x−y 2 at the point 1,1 on the curve. 6 4 2.Find an equation of the line tangent to the curve y x − 1 2x − 3 5 − 2x at the 4x − 7 13 − 6x 5 point 2,1on the curve. 0 3.A hard boiled egg is removed from a pot of hot water at 101 C and is left to cool 0 in a room where the temperature is maintained at 20 C. After 10 minutes the egg has cooled to a temperature of 74 C. 0 a What is the temperature of the egg after 20 minutes? b When will the egg’s temperature be 36 C? 0 Assume Newton’s Law of Cooling. 4.A cup of boiling water 100 C is placed outside. One minute later the temperature of 0 0 the water is 70 C and after another minute, its temperature is 49 C.What is the outside temperature (the medium)? 5.The half life of a radioactive substance is about 300 years. In how many years will only one − fourth of the original amount remain? 6.Find the half life of a radioactive substance if after 60 days, 75% of the original amount has disintegrated. 7.Find the exact values of i cos1 1 ii sin −1 iii csc −2 2 8.True or False : a tantan 100 100 b tan tan100 100 9.Find exact values of −1 −1 a tantan 100 b cossec 2 −1
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