I can answer any questions from the standard four semester Calulus sequence. Derivatives, partial derivatives, chain rule, single and multiple integrals, change of variable, sequences and series, vector integration (Green`s Theorem, Stokes, and Gauss) and applications. Pre-Calculus, Linear Algebra and Finite Math questions are also welcome.
Ph.D. in Mathematics and many years teaching undergraduate courses at three state universities.
B.S. , M.S. , Ph.D.
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It means neither one determines the other. If you are told one , you can't figure out the other. For example , a person's height and age are independent variables. If I tell you that a man is 30 years
Days and students are independent variables . Neither directly nor inversely proportional. Total dorm charges are directly proportional to the product of students and days. 18 is correct
(x-1)(x-2)(x-3)(x-4)(x-5)(x-6)(x-7) = x^7 - 28x^6 + 322x^5 - 1960x^4 + 6769x^3 - 13132x^2 + 13068x - 5040 so n^7 - 28n^6 + 322n^5 - 1960n^4 + 6769n^3 - 13132n^2 + 13068n = 5040 for
10^a = 3 10^b = 2 (5^a)(2^a) = 3 (5^b)(2^b) = 2 5^b = 2^(1-b) 5^(b/(1-b)) = 2 (5^a)(5^(ab/(1-b))) = 3 5^(a/(1-b)) = 3 Multiply left sides and right sides of 5^(b/(1-b))
Proportion , ratio and fraction all are the same thing. a/b is a proportion a/b = c/d is an equation that shows that two proportions are the same . 4/12 = 2/6 = 1/3 are three proportions that
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