1. Let z1 = 2-i and z2 = 1+i. Use the parallelogram law to construct each of the following vectors. (a) zi +22 (b) z1 - 22 (e) 221 - 322

Q: A curve C is defined by the parametric equations x = 1- t2 y = t – t3 (a) Show that C has two…

A: To check concavity we eliminate t of the parametric equation and we see that the curve is union of…

Q: Police investigators and forensic scientists can often predict the height of a suspect just from a…

A: The least squares regression technique uses a dataset to determine a linear function: y=a+bx such…

Q: Use the method of undetermined coefficients to solve the initial value problem. y" + 4y = P + 4e',…

A: Given differential equation is y'' + 4y = t2 + 4et with y(0) = 0, y'(0) = 9

Q: Q2/Evaluate SR SV - 2x2)dA Where Ris the region bounded by |x| + lyl = 1?

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Q: Use the vertical line test to determine whether the curve is a function. Xmin = -2 Ymin = -6 Xmax =…

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Q: a) State the time interval(s) when the object is moving: i) away from the origin ii) towards the…

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Q: If A, B, and C are n x n invertible matrices, does the equation C-1(A + X)B¬ = In have a solution,…

A: Matrix multiplication and inverse of the Matrix , pre and post multiplication of the Matrix

Q: Find the general solution of the differential equation y" – 4y' – 21y = -47t + 42t². NOTE: Use t as…

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Q: Prove that the nonzero row vectors ofa matrix in row-echelon form are linearly independent. Let = A…

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Q: Can the Fundamental Theorem of Calculus be used to find /. Sin dx? -x sin x O Yes, f(x) = 1 is…

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Q: Exercise. A curve C is described by the vector-valued function p(t) = (t, 4 – 21,² +2). Exercise.…

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Q: Compute [x] and [x] for the following value of x. 32.999 32 [x] = 33 %3! %3D

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Q: 2 -1 . Let A -2 3 (a) Find the eigenvalues and corresponding eigenvectors of A. (b) Find a…

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Q: Find a particular solution yp = Yp(x) of the following DE d'y dx? 16y = 48x + 16x + 26

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Q: 1.17)Change (1101101) to cleci mal

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Q: 4. Solve the homogeneous differential equation x'dy+(y² +xykdx = 0.

A: To solve the given homogeneous differential equation.

Q: Determine the minimal number n of terms of the series 2i-1 actan z = lim p(z) = (-1)+1- 2i – 1 %3D…

A: The given series is arctanx=limn→∞px=∑i=1∞-1i+1x2i-12i-1. therefore putting x=1, we have:…

Q: Use the vertical line test to determine whether the curve is a function. Xmin = -10 Ymin = -100 Xmax…

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Q: Exercise 3.13. Letf:A B be a one-to-one correspohde also a one-to-one correspondence. 1. Prove that…

A: Introduction: A function is referred to as one-to-one correspondence if it is both one-one and onto.…

Q: - = + t, y = t? + 5, -2 sts 2 y y 10 -10 -5 -5 5 10

A: In this question, the concept of the parametric equation is applied. Parametric Equation  A set of…

Q: 10. Prove that if f(x) solves a linear homogeneous differential equation with constant coef-…

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Q: 7. Which angles are supplementary? O 22 and 23 O 23 and 24 O 41 and 22 O 4 and 25 3. 2.

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Q: Suppose the position of a particle is given by parametric equations x(t) = 4t and y(t) = 2t2-1. (a)…

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Q: 7 Prove by induction, showing all of your algebra steps: (-1) + 4 + (-9) +.….. + (-1)"n² = (-1)°n(n…

A: 7 We have to prove that −1+4+−9+....+−1nn2=−1nnn+12 by principal of induction method. First check…

Q: The base of a three-dimensional figure is bound by the graph x = cos(y) + 1 on the interval [-n, r].…

A: Option(2) is correct answer.

Q: Question 24 of 25 Convert the ordered pair in rectangular coordinates to polar coordinates with r<0…

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Q: Find the solution. dy + 5y=2r?y4 dx A cy-1 = - +x15 -2. - cx 15 y = 23 -x²+ cx !5 13 (D y = -x+cx13…

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Q: (a) Find the f(q* + + en - 10n + q5 jda (b) () Find the derivative of In (3q"- 10) dq. Using the…

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Q: Find the general solution of the differential equation y" + (wo)?y = cos(wt), w? + (wo)?. NOTE: Use…

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Q: 9. Solve the following Linear Programming Problem by graphing it, and using the method of corners.…

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Q: Two airplanes leave an airport at the same time. An hour later, the planes are 168 km apart. If one…

A: Introduction: The law of cosines for the triangle with sides a, b, c and angles A, B, C is given by,…

Q: Q8. a) Determine an algebraic expression that represents instantaneous rate of change at the point x…

A: Instenatinueous rate of change of the function at point

Q: Water is running out of a conical funnel at the rate of 1 in3/ sec. If the radius of the base of the…

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Q: 1+a 1 1 1 1+b 1.1 1 + 1 Prove that 1 = abcd 1+ 1 + a 1+c 1 1 1 1 1+d

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Q: 5. A curve has equation y3 + sin 2y = 2x – x². (a) Use implicit differentiation to show that y' = -1…

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Q: Step 2 () * - () • (::)() one must find : et et dt insort glan () ) in the at tt 7- e et dt gives: -…

A: Please check next step.- also consider giving precise question from now on.

Q: a) Draw a rectangle whose perimeter is greater than the value of the area in the space below. (use a…

A: formula perimeter= 2x length +2x width  area = length x width

Q: 10. Assume / || m. Find the value of x. (r+72)° (3x) O 24 O 20 O 27 O 18

A: Solution :  Given angles  (x+72)° , (3x)°

Q: Find the determinant by row reduction to echelon form. -5 -5 5 -6 -5 5 -2 3 5 Use row operations to…

A: It is given that A=-5-55-6-55-235. We have to find the determinant of the matrix A by row reduction…

Q: 1. Four friends (including Adam) were at the company picnic. Each friend had a different drink (one…

A: Answer: Adam-Water-Lime.David-Soda-Vanilla.Mary-Juice-Strawberry.Wilma-Tea-Lemon Explanation: step…

Q: If two functions are defined as: g: from (1,2,3} to {a,b,c}, and g(3) = a, g(2) = b, g(1) = c h:…

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Q: Given y4) – 9y" – 81y" + 729y' = t² – 10 +t sin t, determine a suitable form for Y(t) if the method…

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Q: 4. Find x so that x + 6, x + 12 and x + 15 are consecutive terms of a Geometric Progression. 5. Find…

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Q: Find the solution of the initial value problem y" + 6y/ + 10y = 0, = 0, y'() = 4. (t) =| How does…

A: Given differential equation is y'' + 6y' + 10y = 0

Q: The table gives the readings from a laboratory experiment 1 4 Y 120 90 60 70 b+x A curve of the form…

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Q: Suppose A E M,n (R)and B. Find the eigenvalues of B = | A in terms LA 2A. of the eigenvalues of A.

A: Given A∈MnR and B=0AA2A. We have to find the eigenvalue of B in terms of A. The eigenvalues of the…

Q: 3. 3. 15

A: Solution

Q: (b) A right-angled triangle has sides of length 3 and æ, and a hypotenuse of length e. Given that (2…

A: Given a right angle triangle has sides of length 3 and x and a Hypotenuse of length l. Given that…

Q: The second term of a geometric sequence is 6 and the fourth term is 96. Find the possible values of…

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

Q: 1. Exercise. Suppose that the curve C in the zy-plane is traced out by the vector-valued function…

A: We have to find derivative of vector.