Question 8 Let W be the subspace spanned by the u's. Find the distance from y to W. y = 02√3 18 O√626 03√2 O 626 U₁ 0 U₂ W

Q: a. Calculate the first four derivatives of sin(x²) and hence find the fourth order Tay- lor…

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Q: Sequence of Subsets Let A₁, A₂,..., A₁00 be a se of Some set B. Suppose that all these subsets are…

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Q: Part: b:Diagonalize the following matrix if possible whose eigenvalues are given to be 0, 1, 1. 0 A…

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Q: IV. Let F be a vector-valued function such that 1 F'(t) = (te', ; 1 + 1.31²) and F(0) = (-1, 0, -2).…

A: Given information F→'t = t et,  11+t2 ,  3 t2 and F→0 = -1, 0, -2

Q: 6. Let S be the region bounded above by the paraboloid z = 1 - x² - y² and below by the ry-plane.…

A: Introduction: Apart from Cartesian coordinate system, a triple integral can also be evaluated by…

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A: The graph of y=f(x)-a shifts a units downward to  the graph of y=f(x). Where a>0. The graph of…

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Q: Let the space curve be the intersection of two surfaces z = x² + y² and y² + z² = 1. Draw this curve…

A: As per the question we are given two 3d surfaces defined by the equations : z = x2 + y2   ;   y2 +…

Q: Ifk = 25, what is the period of a cos ine or a sine funciton? O 45 45 25 45 45 2π

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Q: A teacher gave her students the following list of words. Number 1 2 3 4 5 Word RADAR LONDON POPCORN…

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Q: A function f is approximated by a cubic spline defined by : (1 + 2x -x³ (2-(x-1)-3(x-1)² + (x-1)³…

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Q: Use truth tables to determine whether or not the following arguments are valid:  a) Either sales or…

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Q: 4. Determine whether each series is convergent or divergent. If it is convergent, find its sum. ∞ 2)…

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Q: 9. Given the bases B = {1+2t, 2+t} and C = {1-t, 2-3t) of P₁. Find the change of coordinates matrix…

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Q: Let f(x) = 4x + 5 and g(x) = 5x² + 2x. After simplifying, (fog)(x) = =

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Q: [A] 3 2 1 |01 - 2 3 4

A: The given matrix is A=32101-2134 and we are asking to find the determinant of A .

Q: Joyce removes the pennies from her purse. Now her bag contains 12 nickels, 26 dimes, and 14…

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Q: Using intermediate value theorem, the equation x³ O None of the choices O 10,1[ O 13,4[ O 12,3[ - 3x…

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Q: Find the angle between the given vectors:  a) u=(3,4), v=(5,-12); = x1y1 +x2y2 b) u(1,1,1),…

A: Sol:- a) u=(3,4), v=(5,-12); <u,v> = x1y1 +x2y2 i.e a)  u=(3,4,0), v=(5,-12,0); <u,v> =…

Q: Plot the points on the same three-dimensional coordinate system. (a) (3, 4, 1) (b) (-2, 3, 7) 8 8 00

A: Using the graphing calculator point the plot on the graph

Q: 9. Find, by inspection, the value of r that solves the exponential equation 2 = 64. A. 32. B. 8. C.…

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Q: bl A field mouse population satisfies the Initial Value Problem: dp = 0.5p-400. p(0) = 600. dt (a)…

A: Given That :  Differential Equation is  dpdt=.5p -400 ,p(0)=600 To find : time at which population…

Q: Find (u - 3v) · (3u – v), given that u u = 9, u v = 6, and v . v = 8.

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Q: This question examines your understanding of bases of linear vector spaces. Please tick all correct…

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Q: Q17. Consider the graph with the following vertices, edges, and weights (weights are stated as the…

A: We use kruskal's algorithm to find the total weight of minimum spanning tree.

Q: h(x) = Σ bu(t) sin (mat). 4 Please choose the correct option: does your answer only include odd…

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Q: 1) Compute y (0.5) with y!!! xy¹ = (1-x) ex by Taylor series y (o)=yl (o)=y" (a)=1₂h = 0.5 16 Euler…

A: Given That :  y"'-x y'=(1-x)ex y(0)=y'(0)=y"(0)=1, h=.5 To Find : compute y(.5) using Taylors series…

Q: A function is approximated by a cubic spline defined by: {"="64" (4 + 6(x-1) + 4(x-1)² An…

A: Sol:- Consider the function in the range of (0,1) ∫011+x+x2+x3dxApply the Sum Rule:…

Q: Given that u= O O No answer text provided. O O O ---B H - 157/R HR 5 and v= 6 Find a unit vector in…

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Q: 2x 3. Find the constant a so that (x) = xe²x is a solution to y' + ay - e²x 4 3 O 1 O -1 -2 = 0.

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Q: The graph of f(t) is given below. f(t) a b Match the graph below with one of the given functions. a…

A: Two graphs are given.

Q: 4. The y-intercept of the function y = 7+1 is - D. y = ¹/. A. y = 1. B. y = 2. C. y = 7.

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: The function S(x) that approximates a function f is defined on the interval [1,3] by: (1 + 2x -x³…

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Q: 2. Find the discontinuities, if any, for the following functions. For each discontinuity, indicate…

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Q: Let f: M₂ (R) i. ii. iii. M₂(R) be defined by f (A) = A - AT. Show that f is a linear operator Find…

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Q: Let a, b € Z and both nonzero. Prove that gcd(a, b) x lcm(a, b) = |ab|.

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Q: Consider the differential equation 2x²y" + (x²+x)y' - y = 0. (a) Without solving this differential…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: The function S(x) is defined on the interval [1,3] by: (1+2x-x³ S(x) = (2-(x-1)-3(x-1)² + (x-1)³…

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Q: Solve the initial value problem below using the method of Laplace transforms. y" - 3y'-10y = 0, y(0)…

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Q: There are 8 different textbooks on a shelf. The number of ways the books can be arranged if the…

A: Given there are 8 different books on a shelf.

Q: Consider the following vectors. u = (5, 0), V v = (1, 1) Find the lengths of u, v, and u + v. ||u||…

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Q: What is the parent function of y = (x + 2)(x − 8) Oy=x² Oy=x4 Oy=x³ Oy=x

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Q: 3.49. Find the inverse Laplace transform of the following X(s): (a) X(s)-- .Re(s) > -1 (b) X(x)= (c)…

A: Given  a   Xs=1ss+12 , Res>-1b  Xs=1ss+12 , -1<Res<0c   Xs=1ss+12 , Res<-1 To find :…

Q: (a) Let f(x)=√√2x+1. Use definition of the derivative Equation 3.4 to compute f'(x). (No other…

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Q: llowing: [Ln(3+j5)]sin(-2-j)

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