If T: R2 R³ is a linear transformation for which -8 ¹(B)- ¹-H and T(H) = then:

Q: dy 9. = dt du y t 21 +2, y(1) = 3

A: As student asked to solve question 9. So, we solve question 9. Given differential equation is linear…

Q: Find all values of x so that the triangle with vertices A-(x, -5, -2), B-(2,-8,-4), and C-(4, -9,-5)…

A: The  area of a triangle with vertices  A(x,-5,-2)  , B2,-8,-4 , C(4,-9,-5) is  '1' .  (.). Area of…

Q: 5. For real numbers x and y, recall that max(x, y) is the bigger number between x andy and min(x, y)…

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Q: 4.) Determine the x-intervals where the function f(x) = x²+2x is increasing and decreasing. Also…

A: Given function  f(x) = x2+2x Now to determined where is the function is increasing and decreasing

Q: Section III 10 Short-Answer Questions 21. For a sequence {a}. S is the sum of the first n terms of…

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Q: Find the least positive integer that Yields the remainders 1,3 and 5 when divided by 5, 7, and 9…

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Q: Suppose ƒ: R → Z, where f(x) = [x+¹] i. Graph the function f(x). ii. If A = {x: 1 ≤ x ≤ 3}, find…

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Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

A: The indicated function y1x is a solution of the given differential equation. Use reduction of order…

Q: 10. Using the first principle of math induction, prove that, for n positive integer n³ + 2n is…

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Q: A regression analysis between sales (Y) and advertising (X) (both in dollars) resulted in the…

A: Given that the regression analysis between sales Y and advertising X resulted in the following…

Q: The volume of the tetrahedron enclosed by the coordinates planes and the plane 2x+4y-z = 6 is given…

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Q: b) { / - n (-1)") n+2

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Q: wer: Find the determinant of the following 2 x 2 matrix. ¯–1 -7] -6 -3

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Q: a = -4 -3 -1 0 and b = -7 -3 11 -12 Use the Gram-Schmidt procedure to determine an orthonormal basis…

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Q: ABC is a triangle of 45 sq in. P is a point on AB such that AP is two-thirds of AB and PQ is drawn…

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Q: If A is an n x n matrix and the equation Ax=b has more than one solution for some b, then the…

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Q: Let L. be the line passing through the point P-(4, -3, 1) with direction vector a-[-4, 1, 1], and…

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Q: Consider two brine tanks connected as shown in the figure below Tank 1 contains xit) pounds of salt…

A: There are two tanks, Tank 1 contains x(t) pounds of salt in100 gal of brine and tank 2 contains y(t)…

Q: Let La be the line passing through the points Q-(3, 1, 1) and Q₂ (0, 2, 3). Find a value of k so the…

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Q: Q6. Using Laplace Transforms. determine the solution to the following integral equation. t f(t) =…

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Q: Find: L-1[- لته – دي 1 53

A: We have to find the inverse Laplace transformation of the function 1s3-a3 i.e. ℒ-11s3-a3 .

Q: Use any numerical method to solve the given coupled equation system: y′ + 2xz = x2, y(0) = 1 z′′′…

A: Introduction: A numerical method is a technique for solving mathematical problems using numerical…

Q: A film class is making movies in groups. Three digicams are available and each movie must be shot…

A: Given that a film class making movies in groups. Three digicams available and each movie must be…

Q: xy-3y=-24×70 ×(1)=1,y(1):4,ゾ(1)=-52; 1/10=4x221,×,×53 y(x)=

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Q: 9. For n positive integer, prove the following using the first principle of math. induction 2 + 6 +…

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Q: During the summer months Terry makes and sells necklaces on the beach. Terry notices that if he…

A: Price p 8 12 16 Number of necklaces sold n 30 23 12

Q: The weekly profit P for a widget producer is a function of the number n of widgets sold. The formula…

A: The given profit function P=-3+2.1n-0.2n2, where P is measured in thousands of dollars, n is…

Q: Determine whether S is a basis for R3. If it is, write u = (8, 3, 8) as a linear combination of the…

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Q: Q1: A: Find the Laplace Transformer for the following function [8 sin²t cos²t] t L

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Q: Consider the sequence (yn) defined recursively by, Y0 = 2 for n ≥ 0, _Yn+1 = Yn². Show that for all…

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Q: Find the mass and center of mass of the trianular lamina shown below, if the density function is…

A: We have to find the mass and center of mass of the given lamina. The density function is P(x,y)=16x

Q: For each of the following statements, choose whether it is True or False. Correct answers are worth…

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Q: A, B, and C are 4x4 matrices; and det(A)=-4, det(B)=3, and det(C)=-1 then compute et(2B2CTATB³)=0

A: Given that if A, B, and C 4×4 matrices; and det(A)=-4, det (B)=3, and det(C)=-1. To compute:…

Q: Evaluate the integral [[F.n dA for the data F= [y³, a³, 2³], S S: x² + 4y² = 4, x ≥ 0, y ≥ 0,0 ≤ z ≤…

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Q: @ Analyse the following equations graphically and sketch drow the fixed points, and classify their…

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Q: Transform the differential equation y" +10y" - 25y' - 250y=9e-t y(0)=0 y' (0) = 0 y" (0) = 1 into an…

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Q: P₁₁ = P₁2 = P₁3 = P₂2 = P₂3 = DE P32 = P3 3 = -9 What is the projection p of the vector b = -7 P₂1 =…

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Q: consider the following. B = {(2, -1), (-1, 1)}, B'= {(-12, 0), (-4, 4)}, [3] (a) Find the transition…

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Q: 2. Solve the initial value problems 2.1 x²y + xy + y = 0, y(1) = 1, y'(1)=2 2.2 x²y"-3xy' + 4y= 0,…

A: (2.1)  Given IVP is x2y'' + xy' + y = 0   ,    y1 = 1 ,  y'1 = 2                    Tis is…

Q: Find the products AB and BA to determine whether B is the multiplicative inverse of A. -2 -2…

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Q: Write an augmented matrix for the following system of equations. 2x 3y + 3z = -7 9x 6y + 5z = 3 3y…

A: We will find out the required augmented matrix.

Q: Consider the following two matrices Select one: O a. O b. O c. O d. O e. both (A) and (B) are in…

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Q: x² +7 6.) Given the function f(x) = -7 a.) Find any vertical asymptotes. (If none exist then simply…

A: 6. (a) -: Vertical Asymptote-: Those vertical lines that corresponds to the zeroes of the…

Q: 3.) Find the absolute maximum and minimum of the function f(x) = Give your solution to each as…

A: There are some following steps to find the absolute max and min of f(x).(a)  Find all critical…

Q: 5. Compute the Jordan canonical form for the matrix 1 0 0 00-2 01 3

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Q: Problem #2: If 0 in the image below, find a normal vector for the plane whose magnitude is 1 and…

A: This is a plane containing z axis. This means the equation of the plane can be written as  x+λy=0…

Q: 9. find the global maximum and the global minimum of the function f(x, y) = ln(x² + y + 1), over the…

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Q: Using the integration by parts, integrate the function below with respect to a in the range of x = 0…

A: Solution :

Q: Consider the graph below with vertex set {a,b,c,d,e,f,g,h,i,j} b Which of the following are…

A: To check which of the following graphs are  subgraph of above graph.

Q: 3. Show that there exist 100 consecutive positive integers that are not perfect squares.

A: Here we have to show that there exists 100 consecutive positive integer that are not perfect square.…