The general solution of the 1st-order ODE, (x + 3y - 2)y' = e=3(x+3y-2)² - y - 1/3(x - 2) is

Q: Questions No.3 and No.4 refer to the following: Let f(z) = 5-2z. If g(z) is a function with…

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Q: 13. Prove that if n ≥ 2, then 2" - 1 is not divisible by n. Hint: Let p be the smallest prime that…

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Q: They now have a very prosperous year because Tanya is Expecting Twin Girls. For Baby "A" Tanya's…

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Q: For 0 st≤ 7, a particle moves along the x-axis. The velocity of the particle is given by v(t) =…

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Q: Find all the values of the following: (1) (1-√√/3i) Place all answers in the following blank,…

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Q: 2s + 16 s² + 4s + 13

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Q: Fill in the missing terms for the geometric sequence. n 0 1 2 3 An 16 64

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Q: 12.1 Sampling, Frequency Distributions, and Graphs A store surveyed their customers to find out…

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Q: bute the order of 10 modulo 13. Compute the period of th /13.

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Q: Give an example of an equivalence relation R on the set Q such that there are exactly three distinct…

A: We take the help of the signum function

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Q: Euclid's Game starts with two unequal positive numbers on the board. For this problem, assume that…

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Q: E. Does the set of all positive rationals form a group with the multiplication operation? Either…

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Q: Generic Corp, a manufacturer of doodads, has a daily marginal cost function of C'(x) = 0.65(0.12x +…

A: Daily marginal cost functionC′(x)=0.65(0.12x+0.17)(0.06x2+0.17x+7)−2/7

Q: dx dt dy dt = x + 2y = 4x + 3y

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Q: B. Let S and T be sets of real numbers, and define S. T to be {x.y:x e Sandy € T}. Show that if S…

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Q: Let H be a normal subgroup of Sn. (a) Show that if H contains a 2-cycle then H = Sn. (b) Show that…

A: Let H be a normal subgroup of Sn.We need to show that if H contains a 2−cycle then H=Sn.We need to…

Q: Let m be a positive integer not divisible by 2 or 5. Prove that the decimal expansion of the…

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Q: 12. Show that the arc length L of a curve whose spherical coordinates are p = p(t), 0 = 0(t) and =…

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Q: Problem 1 Consider the vector field F: R2 R2 defined as F(x, y) = to each point (x, y) on the plane,…

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Q: Let F be a field. Compute the determinant of the following matrix in Fax: z 111 1r00 10x0 1000 1 0 0…

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Q: Let f.:A→R, j=1,2,... be a sequence of functions. When we say that the series f. converges uniformly…

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Q: There is an equation that describes the cost function of Ridge, where j runs from 0 to p. So if p is…

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Q: Consider the set of all smooth functions on R as C° (R) := {ƒ : R → R | f(n) exists and it is…

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Q: Let F be a field, and consider the group G := 1 a b {6 {(₁; ;) = 01 с : a, b, c E F ≤ GL3 (F). : a,…

A: Center of group is set of all elements which commute with all elements of G

Q: Let F be a field, and consider the group 1 a b ((:)ker) 01 C 0 0 1 Find the centre Z(G) of the group…

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Q: F(@) = ? -1 f(t) 1

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Q: Use the Laplace transform to solve the initial-value problem, y" + 4y = 1-u(t − 1); y(0) = 0, y'(0)…

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Q: A jar contains 17 differently coloured balls. If you remove two balls, one at a time, how many…

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Q: Calculate the iterated integral integral [[ ³³√² + y^'dady. 0

A: That is evaluate ∫x3x4+y4dx .To evaluate this put the substitution x4+y4=z⟹4x3dx=dz…

Q: Solve the wave equation on half-line (x > 0): Utt-c²Uzz = 0 u(x,0) = sin r u₁(x,0) = c cos x u(0, t)…

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Q: 3. The following relations are equivalence relations (you don't need to prove this). In each case…

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Q: System: y > x² 2 y < 9

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Q: Problem 4.70. 1. Construct sets A, B, and C, and functions f and g that show that fog can be…

A: Let us consider the sets

Q: Determine the Laplace transform of the given function. a) f(t)=2+tª c) f(t)=sinh(5t) b) f(t) = 3…

A: Note: We will be solving part 2(c) as mentioned in the text.The given function is .We know that .We…

Q: Meta Tasks Task 1. Show that if f is monotonic on the interval [a, b] then f e R[a, b].

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Q: Prove that S tan ar tan¹ Br x2 da = 1 log 2 (a + 3)α+³7 Qa38 , a>0, B

A: Note: In the given identity, it should be instead of .We need to prove that , where .Let .

Q: 4. Solve the equation subject to the given conditions. dy dx a) - 3y = 5, y(0) = 2

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Q: Let A(2, -3) and B(-2,1) be vertices of a triangle ABC. If the centroid of this triangle moves on…

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Q: Suppose you have two alloys: (A), with 7 ounces of silver per pound, (B), with 14 ounces of silver…

A: To solve this problem using Leonardo’s method of double false position, we need to make two false…

Q: Proofs Task 4 (portfolio). Let an be a sequence decreasing to zero. Prove that En-1(-1)"an…

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Q: Use mathematical induction to prove that any integer amount of postage of 18 cents or more can be…

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Q: Compute the following matrix. 32 BABI + 3 1 0 -4 -3 -2 2 1 2 34 5 6

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Q: 1. a) Copy and complete the table below: Original Function First derivative Second Derivative…

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Q: 2. (Section 17.2) Evaluate point (-2,0, 37). Judz y dx − x dy + 3y dz if curve C is the part of (t)…

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Q: Determine the equation of the straight line in slope-intercept form that passes through point A (4,…

A: The slope of a line that passes through the two points (a,b) and (c,d) is given by : If the slopes…

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Q: Graph the integrand, and use area to evaluate the definite integral √ √64-x² dx. -8 8 ja √ √64-x²…

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