1. [4(cos 12° + i sin 12°)]³. 3. [√3 (cos 25° + i sin 25°)].

Q: min C(L,K) = 2L+3K s.t. F(L,K) = LK ≥ 10, L≥ 0, K≥ 0. x,y

A: minx,yC(L,K) = 2L+3K s.t. F(L,K) = LK≥10, L≥0, K≥0. The constraints in the above cost-minimisation…

Q: y=-3x+5 -10 -8 -6 -4 -2 10 8 6 4 2 -2 -4 -6 -8 -10 2 4 6 8 10

A: Given :  y =-3x+5

Q: Find the volume of the region under the surface z = corners (0, 0, 0), (6, 0, 0) and (0, 3, 0). 824…

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Q: Consider the following integer nonlinear programming problem. 23 Maximize Z = x₁x2x3, subject to x₁…

A: We have        x1 + 2x2 + 3x3 <= 10     x1 can be atmost 10      X2 atmost be 5       x3 can…

Q: Based on the figure below, approximately how many orders of magnitude bigger is the genome of…

A: Given,A figure showing genome size in log for different genomes.To find: Order of magnitude of the…

Q: Let f(x)=√3x-2 on the interval [2/3, 1] Revolve the region between the curve, y=1 and y-axis about…

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Q: Numerical Integration: c2 1 S Jo √x 1. =dx

A: We will first solve the given integral directly and then apply numerical integration. Consider:…

Q: Let C be the curve of intersection of the paraboloid x² + y² = z and the cylinder (a) Determine the…

A: a) For the intersection of the curves,  x2+y2=z, x24+(y-1)2=1 let y=t ⇒x24=1-(t-1)2…

Q: The general solution of (D³-4D²)y=0 is A y=C₁ + ₂x + c3e4x By=c₁+ c₂e²x + c3e-²x Ⓒy=c₁+ c₂x + c3e-4x…

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Q: 9. To solve tek ₁ [theat] = 10. Let cos(√2t)]= you may use: n! (s = a)n+¹ II. [teat] = (-1){(f(t)}

A: Note: since you have posted multiple questions. As per our guidelines we are supposed to solve only…

Q: 5. Find H(s) = 19 s+2 1 3s-5 + 7 $5

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Q: Find the surface area generated by y = x³; x = 0 and x = 3 and is revolved on x-axis.

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Q: Find the Z Transform of given signal x(n) = n²u(n)

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Q: Show that the Bessel functions J, (v ≥ 0) satisfy where A, are the positive zeros of J,,. [* IJs…

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Q: f(t) 1

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Q: From a table inside a room with current temperature of 26 degrees Celsius, a left over Fried Chicken…

A: Here we will use Newton's rate of cooling If temperature of  body after time t is T then rate of…

Q: Two matrices A and B are given. Calculate whichever of the matrices AB and BA is defined. A=…

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Q: The score in a game in a television show can be represented by the discrete random variable X with…

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Q: B/A block of ice in the shape of a right circular cone is melting in such a way that both its height…

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Q: Part I: PARAMETRIC EQUATIONS. Find the second derivative of y with respect to x from the parametric…

A: This is a problem of application of calculus.

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. [² yex…

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Q: k 21. The following differential equation describes an electrical circuit with I the current at time…

A: The solution is given as

Q: 1. (D³ - 3D²D + 3)y = 0

A: To Solve: (D3-3D2-D+3)y=0.

Q: Evaluate. 1²9 dx 2 + X

A:

Q: Draw a sketch of the given arc C and evaluate S [(x² −2y)dx + (2x + y²)dy]. 2. C is the line segment…

A: Given integral: ∫Cx2-2ydx+2x+y2dy C is a line segment from  12,1 to 54,0 54,0 to 54,2   To find:…

Q: 4. When solving for the solution of higher order differential equations, the presence of x in the…

A: NOTE:Kindly repost the other question as a separate question.  When solving for the solution of…

Q: Q1/A/ Solve the following. Choose five only In(x+2) 1. f dx 2x+4 2. f x² ex dx 3. f tan³x dx 12 4. S…

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Q: Evaluate. [16si 16sin-4x cos³-4x dx

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Q: What is the y=x excos 2x? (A (B) (D²+5)² C D²+5 D (D²-2D+5)² D²-2D+5 annihilator for G

A: Solution

Q: What is the general solution for the differential equation y" + y' = cos x + 4e¯*? A. y = Cx +…

A: Solution:

Q: For a certain battery company, the life span of the batteries follows a normal distribution. What…

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Q: What is the general solution of xy(xy5-1)dx + x²(1+xy5)dy=0 ?

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Q: Based on known series, give the first four nonzero terms of the Maclaurin series for this function.…

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Q: Let Zg = {0,1,2,3,4,5,6,7}. Denote by xg the operation "multiplication modulo 8" where a xg b is the…

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Q: 20) The figure below gives the US consumption of petroleum over a 10 year period. Estimate the…

A: The given chart is  To find: the average consumption .

Q: Solve: y""(t)- y" (t) + y' (t)- y(t) = H(t); y(0) = 0; y'(0) = y" (0) = 1; where H(t) (t+3,0 ≤ t <1…

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Q: 8.M.2 One can define a bilinear form on R2 by the formula ‹ [ 8 ], [ 8 ]› = ac − 3ad − 3bc + 7bd. a)…

A: We have to find the Gram matrix G of the given bilinear form. Then, we can proceed further.

Q: 2A T -t + A, 2A --t + A, T -T t≤c 2 T 0 Osts 1/2

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Q: 1 √√√x+x Solve the integral: S ® h1+x+c A C Gin|5+x²³| +c (B) : C © Bhl1+xel c C) + C 5 5 D) -n|1+x'…

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Q: Solve the quadratic equation: 2 z² − (3 + j5)z +j8-5=0 -

A: To Solve: the complex quadratic equation z2-(3+5j)z+8j-5=0.

Q: S. (22² 2. 2 (2x² – 3x) dx

A: ∫25 2x2-3x Apply the Sum Rule:    ∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx =∫252x2dx-∫253xdx

Q: Find the maximum and minimum values of the function f(x, y, z)= 3x - y - 3z subject to the…

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Q: Solve the DE sinx siny dx + cosx cosy dy = 0 by separation of variables. (A) cos y sin x =C sin y B…

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Q: A contour map is shown for a function f on the square R = [0, 4] × [0, 4] 12 12 Use the Midpoint…

A: Solution:-

Q: Evaluate the following iterated integral: LS xy(2y + 1) dy dx.

A: Evaluation of the double integrals

Q: Find a power series solution of y" + (1+x²)y=0 13 a. ao(1-x². - + x² + ...) + a₁(x-²1²x³- 24 720 13…

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Q: The general solution of (D²-2D+1)y=2sin x A) y=ce*+C2xeX+sinx B) y=c1eX+C2xex+cosx y=C1eX +C,XeX…

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Q: The general solution of (D³-5D2-6D)y=0 is Ay=c₁еx+c₂e²x + c3e³x By=c₁+c₂e²x + C 2x 3x cy=c₁+c₂ex+ C…

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Q: Determine the intervals on which f is increasing or decreasing, assuming that given figure is the…

A: Solution :-

Q: Which of the following statements is/are true about non-Euclidean geometries? I. In non-Euclidean…

A: