f(x)= 4 sin(4(x-5))+5 parent function: f(x)=sinx do the transformation table for the function above (use three tables and make sure it's detailed)

Q: Find the differential equation such that y(x) = c₁(x-4)³ + c₂! 64x² d²y + +60x+y=0 dx² dx 64(x-4)²…

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Q: Let S = { 1 - (-¹)" | n € N}. Determine inf S and sup S. Justify. n

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Q: 5. Use transformations to sketch the function y=-3log10 (x-1) +2.

A: We have y=-3log10x-1+2 Now, if the original function is y1=log10x, then we apply various…

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Q: a² a³. 5. Ifbb²b³-1 = 0, show that abc = 1. lc c² c³-1

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Q: 3. Answer the following questions. Show all solution steps: x3 y6 z4 a. Simplify: ÷ 2(x4y7)⁰ xm y2…

A: (a) we have to simplify x2x4y70÷x3y6z4xmy2z-5 also, m=2 Then x2x4y70÷x3y6z4x2y2z-5

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Q: e al HIIL equ U VILII the discrete topology T, then (X,T) is compact. * O True O False

A: Given that X be an infinite set equipped with the discrete topology T.

Q: -8s +8 s288 +1 you obtain an equivalent expression given by: s-4 a ~ { ( 2 = ²4 ) ² = 2 ² } + 82 -¹…

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Q: a) Write the standard form of the quadratic function whose graph is a parabola with the given vertex…

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Q: . Find inverse Laplace:

A: Note: As per Bartleby guidelines, we cannot author handwritten answers, so I am giving type written…

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Q: Let S = { 1 - (-1)" n | n € N}. Determine inf S and sup S. Justify.

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Q: 1. Show that a frination f: Tamb]-> R differentiable at xolamb) is and only if are it's lower and…

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Q: x(n) = a¹sin (w¸n) u(n)

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Q: Determine the dimension of the span of each set. 6 3 12 - A = span ({0}) 2 - -1 4 20 10 40 dim (A) =…

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Q: 5Q. Solve the differential equation 2y" + xy' + y = 0 by power series method.

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Q: (a) Sketch the graph of the line equation: 2 y = x-1

A: Graph of the line equation

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Q: dy ² dx d²y dx² ey

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Q: 4. (a) Find the general solution of the system x₁ = 4x17x2, x2 = 7x1 + 4x₂. (b) Let a and b be real…

A: We solve by eigenvalues and eigenvectors method.

Q: 5. Given a piecewise function 4, f(t): = { 1, 0≤t 2. Express f(t) in the form of unit step function.…

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Q: 2) Find an explicit solution for each of the following intial-value problems, also give its interval…

A: we have to find the solution of given differential equations and its interval of definition.

Q: QUESTION 6 Find the indicated vector. Let u = [²] = [3²] V= 9 9 Find 7 v - 6 u.

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Q: Ex.7 The area of the surface ∑ = {(x,y,z) €R® : (x² + ²) < 1, z = 9 + xy} is: (A) - 5 (B) 4개 2 (C)…

A: Using polar coordinates.

Q: consider a closed rectangular box with a squar base. if base side is measured with error at 2% and…

A: The rectangular box has a square base. Let the base side be x Then the base area is x2 The Sum of…

Q: = 2√√5 +11i in polar form and also represent it graphically 2Q. Express the complex number z = Hence…

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Q: Ва ut = Zuxx – ucot )=32 т и (ч, t ) = 52 та heat equation Ic = 4 (xio)= 5x+2 осхи

A: Transform the imhomogeneous boundary conditions to homogeneous boundary conditions and then apply…

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Q: 1.2. In the process of calculating L-¹ given by: -2.L -2s +3 we get an equivalent expression 10s 7 ^…

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Q: 2. Suppose that {f(t)} = F(s) with F a differentiable function and that {f(t)} exists. Then L{-te*…

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Q: Solve e^(3z-7)=1

A: Given,  e3z-7=1 ⇒lne3z-7=ln1   [Taking logarithm both sides] ⇒3z-7=0   [since lnea=a   and   ln1=0]…

Q: max Z= 3x₁ + 2x₂ -X1 + X₂ ≤4 3x₁ + 2x₂ ≤ 125 X1 X₂ ≤3 X1, X₂ ≥ 0

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Q: 12. Consider the function f, such that f and f' are continuous for t≥ 0, defined by (37t - 95 0<t<7…

A: This is a problem of unit step or Heaviside function.

Q: 1 5. If 162-₁ { 10 / ( √5 - 2)²2 +25)}² atbect sen(5t), the value of a cis ds

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Q: a b -2a If det d e f -3, evaluate det Sb 8 c+4b -2d -2g Se Sh f+4e +4h

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Q: Show that the vector field A and B are everywhere perpendicular if A (2.-5,6) and B (6,5,-2)

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Q: Consider the following table. X f(x) X f(x) 0.0 6.5 2.0 7.9 0.4 6.1 2.4 8.5 0.8 6.4 2.8 8.6 1.2 6.6…

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Q: (a) Let n, k € Z with 0 ≤ k ≤n. Write down the formula for the binomial coefficient (7) and use it…

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Q: Scenario 2: The mean content of 25 bottles of brand S mango juice is 255 ml with a standard…

A: Given : μ = 360 ml Ẍ (Mean) = 355 ml σ (Population Standard Deviation)= 9 ml α= 0.01

Q: Find the directions of maximum and minimum change of fat the given point, and the values of the…

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Q: Find the total cost of the down payment at 10% the cost of your house.   House is 170,000

A: Given cost of the house is $170,000 down payment is 10%

Q: 2. Use the method of equation Uariation of parameters to solve the differential dy - k- dx² dx xez…

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Q: 1.047i 4Q. Using De Movier's Theorem find all roots of √/25 e¹

A: The given problem is to find the all roots the given complex expression by using De Movier's…