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MI - 4 Teacher (circle): NC NC NC 1) Condie Problem Set: 6 Dowling Loo means you have to show all work done by hand, with no calculator use. Find exact value for log(100!) – log(99!). 2) Given MAX with mA 36 , x 17, and a 13 , solve for the length of side m to the nearest tenth. 3) Solve each equation for n: 2n 2n 1 a) 13 7 n 2 n3 NC ID Number____________ Mods: __________ 4) 3n 1 3n 1 b) 4 n n 1 Find the sum of each series, leaving complex answers in a + bi form. You may again assume that for complex numbers a bi, with a bi 1 our formula for the sum of infinite geometric series is valid. i a) n 1 2 5) 1 i b) n 1 2 n n In triangle ABC, a 12, b 10, and c 9 . Find the measure of the largest angle in triangle ABC. f ( x) f ( x) . 2 Determine (if possible), whether g is an even function or an odd function. Show your reasoning. NC 6) NC 7) Let f be a function whose domain includes all real numbers. Define g ( x) Erik wants to form 4-digit integers using only the digits 1, 2, 3, and 4. He is allowed to repeat digits. What is the probability that he forms a 4-digit integer where at least one digit repeats? Express your answer as a common fraction. PS 6.1 Rev. 16 MI - 4 Teacher (circle): NC Problem Set: 6 Dowling Loo Condie ID Number____________ Mods: __________ 8) Suppose that an isosceles triangle has two sides of length a and one side of length c. a. Find the area of the triangle in terms of a and c. Simplify as much as you can. b. A well-known formula for the area of a triangle is called Hero’s Formula. It is given by s(s a)(s b)(s c), where s abc . 2 Use this formula to find the area of the isosceles triangle from part a. Note: You may not use this formula in part a. NC 9) The sum of a number, a, and its reciprocal is 1. Let an be the sum of the nth power of a and its reciprocal. That is, an a n 1 . an a. Find the sequence an n 1 3 b. Find the value of a6 NC 2x 4 10) Let f ( x) ln . 3x a. Find the domain of f. b. Find all x for which f ( x ) 0 NC 11) Find the last two digits of the number 112016 . PS 6.2 Rev. 16