1. The angles between the axes in two coordinate systems are given in the table below 135° 60° 120° 90° 45° 45° 45° 60° 120° Construct the corresponding transformation matrix Q and verify that it is orthogonal.

Q: x3 4. Зx2 dx 3x 8(у + 1) %3D 0 dy у+1

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Q: Answer the following questions about the function whose derivative is given below. a. What are the c...

A: Given: f'(x)=3sinx-32cosx+1, 0≤x≤2π To find: a) Critical points of f. b) The intervals in which f is...

Q: Use the Laplace transform to solve the initial value problem below. y" – 22y' + 121y = t, y(0) = 0, ...

A: Given differential equation is y'' - 22y' + 121y = t with y(0) = 0 ,  y'(0) = 1

Q: a az 3. In R", let Wbe the subset of all vectors v = that satisfy a, -a, = a, – a,. az a4 a) Show th...

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Q: Solve the given initial-value problem. The DE is homogeneous. xy2 dy = y3 – x³, y(1) = 4 dx

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Q: ng of a drug in a person's system t hours after the drug is administered, when does the drug reach p...

A: Note: A stationary point of a function f(x) is a point where the derivative of f(x) is equal to 0.  ...

Q: For the given surface f (x, y) = 2 + sin(xy) at the point (1, 0, 2), find the following: a) Gradient...

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Q: az that satisfy a, -a, = a, – a,. az 3. In R', let Wbe the subset of all vectors v = a4 a) Show that...

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Q: 3! L-1 (s-5)4.

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Q: The unit circle x² + y=1 can be wrriten in parametric form as x = cos(0) and y = sin0. dy Find and h...

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Q: 1. Suppose that a group of illegal counterfeiters print 1,000 copies of fake $20 bills and introduce...

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Q: Consider the region D C R² defined by the inequalities æ² + y² > 1, x² + y² 0, and y <a. Let w be t...

A: Consider the region D⊂ℝ2 defined by the inequalities x2+y2≥1, x2+y2≤4, y≥0, y≤x Let w be the two for...

Q: 1 Let f(x, y) 2 5æ + y - 3y. Зу. 2 Our goal is to find the location and value of the absolute maximu...

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Q: Let f = x? + y² + z² be a zero-form on R. Suppose that P and P2 are two distinct points on a sphere ...

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Q: d) (A – B) = AT - B"

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Q: 3. Let fx) --2x (x² - 9)(x*-1) Determine

A: Please find attachment for the details solution

Q: Evaluate the following integral by appropriate method: L 12+ |x] dx dx Jyz xVx2-1 L, 12x – 1| dx

A: We are entitled to solve only one question at a time. As the question number is not specified, so we...

Q: -) Given Xn+1 = X +2X + 3Xn, shown below (also shown is Xn+1 = X„), and X5 = 0.1, %3D %3D %3D what i...

A: Ki

Q: Consider the following differential equation (E):4y" – 4y' +y = 0. Then the two functions ex/2 and x...

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Q: Let w = y dy A dz – x dz A dx + z dx A dy be a two-form on R°. Evaluate its surface integral I along...

A: w=ydydz-xdzdx+19zdxdy    =yi^-xj^+z9k^i^dydz+j^dzdx+k^dxdy    =∫∫yi^-xj^+z9k^ds→

Q: If you have been hired at an annual salary of $23,000 and expect to receive annual increases of 5%, ...

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Q: Find the roots of the following equation x6 – x - 1 = 0 Using an initial guess of xo =1.5?

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Q: fT: R? → R* is a linear transformation such that 13 7 () - 26 and T then the standard matrix of T is...

A: Introduction: Every linear transformation from a vector space to another vector space has a matrix r...

Q: Convert the equation d°y dy -3 x y 0 dx3 -3. and initial conditions y(0)= 1.11983, y'(0)=0.83697 and...

A: Introduction: A higher order linear differential equation can be converted into a system of first or...

Q: Find the linear approximation of the function at the given point: f(x, y) = 2 sin x – 3 cos y at (0,...

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Q: Now let's have you try to use these formulae. Find the inverse laplace transform of y'(t),y''(t), an...

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Q: 6X

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Q: k and Ĉ = к апd rs along the a ICorteeion

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Q: Instruction: Answer the following question. х3 — 5х2 + 7х — 2 lim | x→2 х — 2 > Indicate if the limi...

A: We have to find the limit of function.

Q: A system of linear equations has an augmented matrix whose row echelon form is 1 −1 2 1 3 0 1 3 ...

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Q: An integrating factor for the differential dy + my = e-m² is dx equation

A: Given differential equation is dydx + my = e-mx

Q: The differential equation y + 3y = (y + 4x) y can be written in differential form: M(x, y) dx + N(x,...

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Q: Consider the region D in t

A: Given, the curves                 y=2x, y=4x, y2=x, and y2=3x To find ∬Dx2x4dA        

Q: {(a, b) | a < b, 2<a<5, 2<bs5}

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Q: Use the table below to determine the Borda winner. Assign the point values to each vote. Number of V...

A: Note: Hi! Thank you for the question, as per the honor code, we are allowed to answer three sub-part...

Q: Siven X(z) = 2 + 6z-1 find x(1) of x[n] 4 2z-2+13z-3 O 1 O 0.5 O-1 O 1.5

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Q: L{t e¬at } =

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Q: Let V be an inner product space over R. Let u1, U2, Uz, U4 E V such that (u;, u;) < 0, i, j = 1, 2, ...

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Q: 4. Consider w = and v =. (a) Write z = as a linear combination of w and v. (1 2 3 (b) Consider the m...

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Q: 27. Find the Inverse Laplace Transform of the following: 150 d. (s? + 2s + 5)(s? – 4s + 8)

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Q: Solve the initial value problem using the Laplace transform. y' = 9y + 6, y(0) = 1 y(t)

A: We solve the given IVP  y'=9y+6.....(1) y(0)=1 by using Laplace transform.  

Q: IfT: R? → R³ is a linear transformation such that 13 16 (:) - T 26 and T then the standard matrix of...

A: Standard basis for R² is given by {(1,0),(0,1)}.

Q: а) b: G' → G such that o o = idg', where idG' is the identity map on G'. Show that o is injective. S...

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Q: a) On = Select correct it converges to 2 converges to I Converges to O • Converges to diverges to Op...

A: a). Given an = 2nn2nn! As n! &lt; 2n   for all n &gt; 1 So limn→∞an = limn→∞2nn2nn! = ∞ Hence Answer...

Q: car travels 180 miles in 3 hours. At this rate, how many miles does the car travel in 1 hour? Practi...

A: We have to find how many miles does the car travel in a hour.

Q: (iv) What price should the company charge to maximize revenue? (v) What price should the company cha...

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Q: 4.14 A rectangular arrangement of numbers or terms having various uses such as transforming coordina...

A: Note:- In this problem some information is missing like,  is D∈ℝ4 or ℝ2. But, Basis for  ℝ2 is alrea...

Q: 5 In(x Create a bucket by rotating around the y axis the curve y contains a liquid with density 840 ...

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Q: Problem 1.27. Find the in-degree and out-degree of each vertex of the following directed graphs a V3...

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Q: Assuming the base b> 1, an exponential function of the form a-b has a domain of [ Select | in which ...

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