th 6) Let t, be the k" triangular number. Prove that t, + 4 k + 10 is k k also triangular.

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Q: 5. Solve d²y dy dx² dx +2 + 5y = sin 2x, given that y(0)=3, y'(0)=0.

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Q: |: Use Mashematizel Induethon to solve bhe followbing; j I(2") + 2(2²) + 3(2-³)+.. .+ n(2^)…

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Q: What are the roots of the graphed function? A(-4) BI-2.-3) C 11.5)

A: We know, roots of a function f(x) are those values of x for which f(x)=0 Or those values of x for…

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Q: Suppose s and t are distinct natural numbers. Show that lcm(s, t) + lcm(s+1, t+1) > 2st/(sqr(|s −…

A: Given: s and t are distinct natural numbersTo prove: lcm(s, t)+lcm(s+1, t+1)>2sts-t

Q: Q2: Suppose A = {Set of natural number less than 9}, B = {Even natural number less than 12 } and C =…

A: A = { Set of natural number less than 9} B = { Even natural number less than 12} C = { Multiples of…

Q: Prove that there is no triangular number which is one less than a multiple of 11.

A: Introduction: A triangular number is a positive integer that is the average of two integers. For…

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A: We will verify that there is no magic square of order 2 using the proof by contradiction.

Q: [1 1) If A = 3 15 2] 4 6] B = [-3 -21 -5 314 4 253 3. [P 91 Find: D = r s tu

A: NOTE: Refresh your page if you can't see any equations. . here we have

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Q: bute 80 identical pencils in a class consisting of 10 boys and 20 girls in such a way that each of…

A: Given:- Number of boys=10 Number of girls = 20 Number of Pencils=80

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Q: 3) Find integers x and y such that 13x + 15y = 1.

A: We see, 15 - 13 = 2              => k(15 - 13) = 2k for any integer k              => 15 k -…

Q: 3. (a) Solve the differential equation (x+1) ª¹ = y +e³(x+1)² . dx (b) Form the differential…

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Q: f U1 and U2 are both upper triangular matrices, and L1 and L2 are lower triangular which of the…

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Q: To avoid collisions with invasive species of aliens, new imperial regulations allow only positive…

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Q: Find all natural numbers m and n with properties GCD(m,n) = 8 and LCM(m, п) — 168. %3D

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Q: Find the 66th term of the triangular numbers {1, 3, 6, …}.

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Q: Simplify. X y y X x+y 2х y У х x+y 2х II

A: Simplify          [(x/y)-(y/x)]/{(x+y)/2x}

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Q: C Show that dim 9 (√2, 3²/3) = Q(

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Q: The number t = 1 + 2 + 1 + 2 + ... + n is called the nth triangular number (so called because t,…

A: As per the question we have to prove that there are infinitely many triangular numbers which are…

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Q: k-1 d) Compute k=1 60 e) Compute > (5k +4) k 1 2/3

A: