Let a and b be positive integers. Suppose Q is defined recursively as follows: if a < b Q(a, b) = {Ola %3D (a- b, b) + 1 if b< a Find Q(36, 15).

Q: In the expansion of (x+y)35

A: We use the Binomial Theorem to find the required coefficient in the given question.

Q: Suppose that {an} is defined recursively by: an = (an-1)² - 1 and that ao = 2. Find a2 and az.

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Q: Find the solution to this recursive relation an = an-1+3, a0=1

A: To Find the solution to this recursive relation an = an-1+3, a0=1

Q: Show by an example that (AB)" B™A".

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Q: Determine the coefficient of xaxzx if (x1 + x2 + x3 + x4)1ª is expandec

A: This is given by the multinomial coefficient formula. We state the theorem and then deduce the…

Q: З and an - - 3ап-1 + an-2 for integers n>2. Evaluate and d4: Let a, = 2, a2

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Q: If a = (4, 0, 4), b = (3, 4,-4), and c = (0, 4, 5), show that a x (b x c) = (a x b) x c. 60i + 96j -…

A: Solution: Step-1                         Given if a = 4, 0, 4 ,b = 3, 4, -4, and c = 0, 4, 5, show…

Q: find a if A=8a

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Q: 10 a.) Completely simplify E ()2* i=0 b.) Expand (1 – r)® and simplify. c.) Expand (r +r-1)5 and…

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Q: Show by contraposition that : Vx ERX2-3x - 1020 → x25 or x< - 2

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Q: Let B = [-1 1 4 -3] Find -4B

A: Solution

Q: Convert the following polynomials to factorial poly 1. (x-7)(x-6)(x - 5)(x+4) 2. (x+6) (x + 7)(x +…

A: We have to solve 1. (x-7)(x-6)(x-5)(x+4)2. (x+6)(x+7)(x+8)(x+9)(x-10)

Q: Find the solution to this recursive relation  an=2nan-1, a0=3

A: Given that  an=2nan-1, a0=3 To find the solution of this recursive relation

Q: Express e(1/2-6) in the form a + bj.

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Q: Suppose Zı= 4+4i , Z2= 5 +7i. Evaluate (a) 2 Z1– 4 Z2 Z2 (b) 3 Z1

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Q: Let a=⟨−3,−2,2⟩ and b=⟨−4,−2,0⟩ Compute:

A: Given that          a = &lt;-3, -2, 2 &gt;    and    b = &lt;-4, -2, 0&gt; Here we have to compute…

Q: Suppose the multiplication cx is defined to produce (cx1, 0) instead of (cx1, cx2 ). With the usual…

A: The multiplication cx where x∈ℝ2 is defined as cx=cx1, 0 because x=x1, x2 where x1 and x2 belong to…

Q: Pam is a Disc Jockey. Every week she buys 3 new albums to keep her collection current. She currently…

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Q: For each of the following, perform the indicated computation. (a) (5 ỉ – 7j – 7k) – (-6ỉ – 83 + 7k)…

A: To simplify the vectors:

Q: = 5 Find a3, a4, and as for the recursive formula an = an-1 +3an-2 if a1 = 2 and a2

A: given   recursive formula is an= an-1+3an-2and   a1=2   ,  a2=5then we have to find  a3 , a4  , a5…

Q: x

A: We see that the r-th term of (x+y)27 is given by Cr27xry(27-r)  i.e. the sum of exponent of x and y…

Q: Find x. A (2x – 15)* (2x 15)° - C

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Q: Let a = -27 +53 + 4k. Find a.

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Q: If P (A) = 0.6, P(B)=0.1, and A and B are mutually exclusive, find P (A or B). P(4 or B) = |

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Q: Find the term of (a – 2b)3 that has b in it. |

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Q: Find the following expressions if a = (6r, 0, r), b = (6s, –s, 7s), and c = (2t, 10t, 5). a ·b = 1.…

A: We need to find dot product.

Q: Let a = (1, 3, 8) and b = (7, 3, 4). Compute 5a + 7b

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Q: Which of the following are multiplicative inverses:  (a) 5y/x and 5x/y (b) 5y and 7y (c) 7y/x and…

A: Here we have to find which of the options are multiplicative inverses.

Q: and a3= Recursive : an=an-lor I-udo'b=ub: oilldag

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Q: Is A = [ -5   5   1 ]            [ 0   1   -1 ]            [ 1   -1   0 ] the A-1 = ?

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Q: Show that a6-1 is divisible by 168 whenever (a, 42)=1.

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Q: В Calculate A and B so that + %D 1+x 1-

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Q: Write the cycle (1634)(3645) in S7 as a product of disjoint cycles

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Q: Find all x such that 7x+3 is divisible by 9.

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Q: Compute x3 in two ways: by computing x, and x₂, and by computing P³ 0.1 0.2 -~8 0.9 0.8 -0₁ ₂2-0…

A: The given matrix is, P=0.10.20.90.8,x0=10. The value x3 was obtained from: Now, x1can be computed…