Let a be a number a 0. Solve the following initial value problem. -2 *- ( ²3 -1 ) x x(0) - (2) = X, = 6

Q: Question 2: Given the function f(x, y) = sin(x + y), at the point P(π/3, π/4), What unit direction…

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Q: The graph of f(y) is given below. Use it to answer the following. Let y' (t) = f(y). Identify the W…

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Q: Using the Laplace transform pairs and the Laplace transform theorems, derive the Laplace transforms…

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Q: 37. Optimal garden A rectangular flower garden with an area of 30 m2 is surrounded by a grass border…

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Q: Find the differential equation by eliminating the arbitrary constant y=(x+c)e¯* State the dependent…

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Q: . (a) Let f: X→ Y and g: Y→ Z be functions. Show that go f: X→ Z is a function too. (b) If f: X→ Y…

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Q: Find a function of the form y = A sin(kx) + Cor y = A cos(kx) + C whose graph matches the function…

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Q: 10. In 2013, the population of a city was 715,000, with an annual growth rate of 0.013% a) Find a…

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Q: The value of Mr. Gong's Mercedes Benz after t years is given by v = 53700 (0.8) (A: a) Find the…

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Q: The matrix has eigenvalues -4,-1, and 2. Find its eigenvectors. A = - -1 0 3 -3 6 2 -6 3 -4

A: The characteristic equation of matrix A is defined as |A-λI|=0. The eigenvalues of the matrix are…

Q: Your client has been given a trust fund valued at $1.64 million. She cannot access the money until…

A: The trust fund valued $1.64 million. The money will be available from 65 years old after 15 years.…

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Q: your answers! You may freely use all limit laws covered in this course. Do not use any results not…

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Q: If f: R→ [0, ∞) is a function such that f(x - 1) + f(x + 1) = √3 f(x), then prove that f(x) is…

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Q: Consider the following system of three linear equations in three unknowns: x₁ + x₂ + ax₂ = 1 = x₂ +…

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Q: Please do B and C

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Q: Let T: R³ → R³ be the linear transformation defined by T((x, y, z)) = (x+z, −y — z, 2r+y+3z). a.…

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Q: Let denote the vector space of polynomials in the variable x of degree n or less with real…

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Q: M Estimate the average rate of change from z=3 to z=7. Enter your estimate as a decimal number (not…

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Q: Determine the coefficient of x³8 in the multinomial theorem expansion of (1+x²+x²+x6)³.

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Q: Let U = { 10, 11, 12, 13, 14, 15, 16}, A = { 10, 11, 13, 14). Use the roster method to write the set…

A: U={10,11,12,13,14,15, 16}  A={10,11 ,13, 14} Here A' = set of those elements which belongs to U but…

Q: 9. List the ordered pairs in the equivalence relation on A = {1, 2, 3, 4, 5} associated with these…

A: Equivalence relation is relatuon which is reflexive, symmetric and transitive.

Q: 2a 1.² 1.²² 0 2ax-r² dydx

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Q: (b) (bn), where bn := n (1 +212) " for all n € N. Hint: Consider bn.

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Q: n (₁+) (+) () ---- () = 10

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Q: 1. The growth of a population of a fishpond is proportional to its current population. A pond…

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Q: Exercise What is the integral closure of ZZ in Q[FI]

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Q: Let o: R → S be a ring homomorphism. Now let M be a subring of R and N a subring of S. Prove (M) is…

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Q: Buch B. ZG where yzx is...... solution of hema... DE

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Q: 3. Prove for each of the following sequences that it converges, and determine its limit. Fully…

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Q: The odds in favor of Nolan getting promoted are 5:2. Find the probability that Nolan gets promoted.…

A: The odds in favour of Nolan getting promoted are 5:2

Q: If f: R→ [0, ∞) is a function such that f(x - 1) + f(x + 1) = √3 f(x), then prove that f(x) is…

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Q: 5 The inverse Laplace transform of F(s) = 5² - 2s+5 1 f(t) = 5e²¹ sin 2t f(t) = 5e¹ sin 2t 5 f(t) =…

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Q: 25₁ ( 1 , ² ; ³ ; x ²) = + sin ²¹ x

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Q: Consider the function f(x) = x-[x]--, if x # I 9 where 0, if xEI [.] denotes the fractional integral…

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Q: Find the following limits. You may use any theorem we have proved, such as Arithmetic of Limits.…

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Q: What is the reflection rule for the triangle and image with coordinates A(9,12),B(-2,-15), c(3,8),…

A: The triangle is formed by the vertices 9,12,-2,-15,3,8 The image of the triangle is formed by the…

Q: (a) Suppose A (B+C) is a 2X3 matrix. Find the appropriate dimensions of A, B, and C. (b) Define…

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Q: 1. Suppose that the demand function is y=-3x + 54. A. What is the highest price a consumer would pay…

A: This is the question from Mathematical Economics.

Q: A research group is looking at fans at a football game. For some reason, they need to make sure that…

A: Here we take worst case possible. So, first we take 10 fans assuming that we have 5-5 fans of both…

Q: y' = 5x(y + 2)³

A: Given differential equation  is y' =5x(y+2)3. This can be solved by separation of variable.

Q: Find the following limits. You may use any theorem we have proved, such as Arithmetic of Limits.…

A: We will use substitution method to find the limit.

Q: y" - 3y + 2y = f(x). (a) Suppose that in Eq.(2), f(x) = 0. (i) Write down the order and degree of…

A: Given: y''-3y'+2y=fx  a f(x)=0  (b) f(x)=4x To find: (a) Degree and order of given differential…

Q: C X6n-4 = X6n-7 + X6n-66n-7 X6n-6 + X6n-9

A: Given: The information that leads to the required proof.We need to show the equations marked in red…

Q: "S[. 10. 10 2x-1 16 S[cate 7XH - 21 7² dx = 5 In (2x-1) - 3 -зе + 7x+1 15 Cos (2x+3) B (2x+1)+ - 8…

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Q: Angle vertical to <3 is

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Q: X6n-4 = X6n-3 = X6n-2 = h II n-1 f3i+1p-f3i-1h f3i+29-f3ik f3i-1p-f3i-3h, (S f3iq-f3i-2k) i=0 n-1 k…

A: Given: The information that leads to the required proof.We need to show the equations marked in…

Q: Royal Furniture bought a sofa for $940. The sofa had a $1,540 list price. What was the trade…

A: Given cost of sofa  bought is $ 940 List price of sofa is $ 1540 The discount on sofa is = 1540-940=…

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A: From given integral 1st we will find range of values of x,y,z then will find equations of planes…

Q: For the following integral, reverse the order of integration and evaluate the integral. 1/4 1/2 SS…

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