(A) Why does the Law of Sines have an ambiguous case when solving for angles, while the Law of Cosines does not?

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Q: (26) Let f(x) = x?e=*. For what value(s) of x does f(x) have a horizontal tangent? (a) Find the…

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A: Given the differential equation y""' - y"" = 0. Here the auxiliary equation is r5 - r4 = 0. implies…

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A: Solution:

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A: Solution for 3:  Prove that: cos2z+sin2z=1; let, for acute angle z   now,take LHS =cos2z+sin2z

Q: Advanced Math In 2 6. Using the substitution u = sinhx, evaluate the definite integral cosh' x dx.

A: The solution is given as

Q: 1) (1, 120°) 90° 120° 60° 150° 30° 180° 0- 210° 330° 240° 300° 270° 4. 3. 2.

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Q: .What transformation would map the pre-image onto the image? Are they congruent? preimage age 20-9-8…

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Q: NIIVISIDIE D 4. Prove that v3 is not rational. 5 Provo

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Q: SOLVE FOR INVERSE LAPLACE TRANSFORM 6s – 4 - s2 4s + 20

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Q: Q5) Solve the equation with y (0,1) = y (1,1) = 0 y (x,0) = sin x ! = 0,0 sxSI 8. ду (х .0) and…

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Q: Sketch the graph and show all extrema, inflection points, and asymptotes where applicable. 1) f(x) =…

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Q: If any point D is taken on the base BC of an isosceles triangle ABC and DEF is drawn perpendicular…

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Q: 1. Which of the following permutations in S, is odd? (a) 53124 (b) 51423 (c) 51234 (ed) 54231

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Q: Construct the dual problem associated with the primal problem. Solve the primal problem.

A: Given,      Minimise C=2x+8ysubject to                 x+2y≥4              3x+2y≥6 and      x, y ≥0

Q: Problem 23. Answer using Cauchy's Theorem. Given that C is a simple closed path, evaluate each of…

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Q: "rove that function f(x, y) = is a convex function. For this purpose, compute the Hessian matrix of…

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Q: The value of the triple integral (x + y)dV where E is the E portion of x + y + z? 0 < y, is in the…

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Q: 2. Find the volume of solid generated by revolving te area enclosed by: x=y2+1, x=0, y=0 and y=2…

A: The area enclosed by x=y2+1, x=0, y=0 and y=0 The shaded portion is the required region

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A: Introduction: The formula of work done from point a to b is given by, W=∫abkxdx Where is constant.

Q: Evaluate the inverse laplace transform: F(s)=4s-2/s^2-6s+18

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Q: 2. Radar stations are positioned 12.5 miles away from one another on an east-west line. A signal…

A: We will use sin rule  For a ∆ABC  If a,b,c represents opposite sides of angle A,B,C then…

Q: Prove the statements: Use mathematical induction to show that E, ar*-1 a(1-r") for all integers n >…

A: Show that ∑k=1nark-1=a1-rn1-r for all integers n≥1, where r≠1. Prove the equation is true for n=1.…

Q: Use only the Stokes’ theorem to evaluate  integralC(−z − y)dx + (x − z)dy + (x − y)dz where C is the…

A: Solution: given  F=-z-y,x-z,x-yand C is the intersection of ; z=x2+y2 and z=y First, we solve the…

Q: 2. (a) Find the derivative y', given: (i) y = (x² + 1) arctan r – x; Answer: (ii) y = cosh(2x log…

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Q: Which of the following is a nonhomogeneous linear differential equation with constant coefficients?…

A: Recall the standard form of nonhomogeneous Linear differential equations with constant coefficient

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Q: 2 0 The total of the Eigenvalues (A, + 22 + A) for the matrix 1 4 -1 is -1 2 О а. 5 O b. 13 O c.…

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Q: Q4)(a) Find the maximum eigen value for the system A = with initial vector x' (0) = (0.0299 l)

A: Using power method to find the maximum eigenvalue.

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Q: 1. Use the following table to estimate the area between f(x) and the x-axis on the interval 75xS 27.…

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Q: Find the laplace transform of the following: a.) f(t) = teatcosbt b.) f(t) = 7t + 6et - 2et - 10…

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Q: Q4) Solve the boundary value problem y - 3y' + 2y = 0 with y'(1) = 1, y(3) = 2e - e² h = 0.5 %3D

A: Solution :-

Q: COMPLEX ANALYSIS 5. Evaluate the following line integral v) dz where C is the simple closed path…

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Q: 3. Let R be the region below bounded by the parabola y = 4 – x2 and the lines 3x – 2y + 3 = 0 and y…

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Q: Estimate the true percent relative error for the first derivative of the function, y = cos(sin(x)+…

A: We have to find 1st derivative using central difference method and then calculate true percent…