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The triangle shown here is called Pascal’s triangle. Can you guess what the next two rows at the bottom are? Compare these numbers with the coefficients of binomial expansions.
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Chapter B.3 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
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- condition: Throughout this question, n is a positive integer satisfying the following (n) = 2³ × 17 × q, gcd(n,6) = 1, q = 2(mod3) is an odd prime. (a) Show that 17†n. - (b) Show that 17|(p − 1) for some prime factor p of n.arrow_forwardI bought sparrows at 3 for a penny, turtle doves at 2 for a penny, and doves at 2 pence each. If I spent 30 pence buying 30 birds and bought at least one of each kind of bird, how many birds of each kind did I buy?arrow_forward- Prove that if (n − 1)! + 1 is divisible by n (> 1), then n must be prime.arrow_forward
- Chrom ESS $425 5. Ar Dive for x 21) Name 1. Classify the triangles based on their side lengths and angle measures. 89° 30° Acute Scalene Right Scalene 130° Date A +100 Obtuse Equiangular Isosceles Equilateral What additional information would you need to prove these triangles congruent by ASA? If marrow_forwardFrom the differential equation y′ = x + sin(y):a) A solution curve passes through the point (1, π/2). What is its slope at that point?b) Justify why for x > 1 the solutions are increasing.c) Show that the concavity of each solution has the function 1 + x cos(y) + 1/2 sin(2y).Justify each of the steps.d) A solution curve passes through the point (0, 0). Show that the curve has a minimumrelative at (0, 0).arrow_forwardQ/ Qfind the incidence matrix for the graph K₁ UCarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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