A particle has initial position vector (4i + 5j) metres. It moves with a constant velocity of (3i – 2j) m/s. Find its position vector after 7 seconds.

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Q: Problem 1: Prove A = {m e Z: m mod 6 = 2} is a proper subset of B = {n EZ:n is even}.

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Q: 11. 3北 x(t) = e to

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Q: Q4: Solve the following recurrence relation an = 3an-1+2" for n > 1, with ao = 1

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Q: Question 5 Write down the quadratic form corresponding to the matrix. [1 2 -31 A =0 3 lo o -21 2

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Q: Determine which (if any) of the following series are conditionally convergent. (-2)"+1 n+ 7n A. 00…

A: We want to find conditionally convergent series.

Q: Problem 3. Which gives the Laplace transforms of the given time-domain function?         4 ln [(s^2…

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Q: Given f(x)= x² + 3x – 1 and g(x)= 2.x +1; what is (f og)x) %3D

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Q: Find a basis for the eigenspace corresponding to the eigenvalue of A given below. 7 - 1 0 - 5 0 4 A…

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Q: 3. Let ī= {r„} be a sequence of real numbers. State the definition of the limitpoint set of T.

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Q: et A = {2,3,4, 7, 19, 21} and define < on A by x < y if and only if (y – 1)|(x – 1). a. Show that…

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Q: Find the standard matrix of the linear operator M : R R' that fi

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Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y"…

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Q: One of the two tables below shows data that can best be modeled by a linear function, and the other…

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Q: Problem 16. With all sets appropriately defined, only one of the following two statements is always…

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Q: 5. Find the value o(1) for a solution (x) to the initial value problem: (1+ 2x)y" + 4xy'- 4y = 0;…

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Q: A student borrows ​$3000 at 15​% for 6 months to pay tuition. Find the total amount due using simple…

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Q: (-1)"x2" Σ (2n)! +00 1. For all x E R, cos x = n=0 a. Find a power series that is equal to x cos(x²)…

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Q: b) x?y" + (cosx)y' + xy = 0

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Q: Derive the conclusion using Rules of Inference. 3æ N(x) Væ (N(x) → I(x)) :. Bx I(æ) 1. Statement…

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Q: If A and B are sets; A and B denote the complements of the sets A and B, then set (A- B)U(B –…

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Q: A mortgage balance of ​$27,000 is to be repaid over a 12​-year term by equal monthly payments at…

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Q: Use the method of Laplace transforms to solve the given initial value problem. Here, x', y', and z'…

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Q: A space has the line element, ds? = v*du? +u*dv² . Determine whether this space is flat or curved.

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Q: Find the Fourier Series expansion of the graph and its characteristics given below. sin t, 0<t <a f…

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Q: Determine whether the given series converges or diverges. If it converges, find its sum. 8 2 1+- *-1

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Q: Suppose f" exists and is bounded on Co,0), Prove that if bam fa)=0, then bim fGx)=0.

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Q: Compute the exact sum of the following: n j 4 ΣΣΣ&- ) j=1 k=3 j=2

A: Sum of summations

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Q: 1. Encode LOVE (Use capital letters. No space) 2. Find the decoding formula. Select the letter only…

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Q: Show that the column vectors (1,1,2,4), (2,-1,-5,2), (1,-1,-4,0) and (2,1,1,6) vectors in R are…

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