Q1: Find the equation of the pi ne containing the points A(0,0,0), B(2,0,-1) and C(2,-1,0) then find the distance from the point (1,4,0) to the piane.

Q: Determine whether S = {1-1,2t +31², 1²-21³,2+1³} is a basis for P3.

A: DEFINITION OF A BASIS-: A SET OF VECTORS v1,v2,v3,.......vn IS SAAD TO BE BASIS FOR A VECTOR SPACE V…

Q: Question 2 ( a) Evaluate L{eot} b) Evaluate C{(t−2)² + sin 6t + cos 7t} c) Use the Laplace transform…

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Q: A fluid has density 900 kg/m³ and flows with velocity = xi+yj + zk, where x, y, and z are measured…

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Q: A local television station sent out questionnaires to determine if viewers would rather see reruns…

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Q: Evaluate the integral fef ds, where f(x, y) = y cos(2x) and C is the triangle with vertices at the…

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Q: frequency 8 4 2 1 2 3 4 5 6 Do the data appear to be normally distributed? Explain. O Yes, the…

A: The dice is rolled: So, the outcomes can be 1, 2, 3, 4, 5, 6 So, Die Rolled frequency 1 7 2 5…

Q: A. Find the tangent plane at x = 1/3, y = 2/3 of the surface z = ²+ln(x+y). B. Estimate z(.25, .60)…

A: x=13, y=23 Equation of surface: z=yx+lnx+y

Q: Problem 1: Use cofactors Cij = (-1)i+j det(M;;) to find all cofactors of the following matrix A and…

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Q: Find the area of the region enclosed by y = 0.75 and = 5.5 - y². -4 -3 -2 -1 1 1 -2 -3 1 2 3 4 n Q…

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Q: What are the strongly connected components of the digraph below? Your answer should consist of a…

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Q: 4. Evaluate the double integral given by [f 1 -dyda I

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Q: Draw the graph and find the Fourier transform of f(t)=e-at, a>0.

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Q: Use the vectorized Euler method with h-0.25 to find an approximation for the solution to the given…

A: Given; y''=5t6-5y6, y0=0, y'0=-1 on 0,1

Q: Show that 43|(6¹00 +7197).

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: 11. The mean age of a class of twenty-five students is 23.2 years. How old would a twenty-sixth…

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Q: Determine whether each of the following series are absolutely convergent, conditionally convergent,…

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Q: Determine the value of n required to approximate using the Simpson's rule. E S e² dr to within 10-4…

A: Given: The given integral is ∫01x e2x dx. Also, it is given that E≤b-a5180n4maxf4x,   a≤x≤b. To…

Q: Use the Laplace transform to solve the given initial-boundary-value problems. U₁ = Uxx, u(0,1)= 0,…

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Q: Subject Name: Linear Algebra Tips: please solve problem-1 and must do it handwriting on a paper

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Q: 8. Find the centroid of the region bounded by y x and y = x².

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Q: Limit calculations. For each real-valued sequence, explain whether it is convergent, divergent to…

A: The given sequences are, c) sn=-2n·n-12n·n2-2n+1 d) sn=2 sin nn2+2. We have to check the convergence…

Q: Evaluate the indefinite integral as a power series. [x² x8 In(1 + x) dx 00 f(x) = c + Σ n = 1 What…

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Q: Problem 4. Conduct linearization of the system near its stationary points and determine their…

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Q: COS b) MTX -L The functions sin orthogonal set on -L≤x≤L, then show (MIX) cos (nIX) L COS L for m=…

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Q: (b) Prove that E-o(-1)* )= 0 for all positive integers m.

A: We have to prove ∑k=0n-1kkn=0 for all positive integer n

Q: Please do fast

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Q: 5. Consider the following linear programming problem: Minimize: C = 4x₁ + 5x2 subject to: 2x1 + x₂ ≥…

A: Given information Linear programming problem:- Minimize:  C=4x1 +5x2subject to:    2x1+x2 ≥12  x1+x2…

Q: If f+g is are differentiable at x0, then prove f and g differentiable at x0 ww

A: We are given that the function (f+g) is differentiable at x0. one has to show that f and g both will…

Q: Let → F = . Use Stokes' Theorem to evaluate SSS curl → F.d S, where S is the hemisphere x^2 + y^2 +…

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Q: = 1+ =1+=+=+. 2 3 +=(n = N), then prove n (2) + S(n-1) = (nS(n) − n) or (nS(n-1) - + - ...

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Q: Define a binary relation =3 on Z by x=3 y if x - y is divisible by 3. 1. Prove that 3 is an…

A: There is a relation on Z such that x is related to y if (x - y) is divisible by 3. Our aim is to…

Q: Prove the following via Mathematical Induction. Show your solutions. Prove 13 + 23 + 33 + … + n3 =…

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Q: 3. Determine half range Fourier sine series for f(x)=e^x in 0<x<m

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Q: determine terms up to and including x5 in two linearly independent power series solutions of the…

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Q: Suppose f(x) is the function represented by the following graph. Based only on the information you…

A: The Taylor series of the function: f(x) about x=a is defined as: f(x)=∑n=0∞f(n)(a)n!(x−a)n. We need…

Q: By sketching level sets, show graphically the location of the points at which the function…

A: Given the function fx,y=x3-y with a constraint x4+y2=1. The level sets are given by fx,y=k, k∈ℝ. We…

Q: H be the set of all points (x, y) in ℝ2 such that x2 + xy 3y2 = 3. Show that H is a closed subset of…

A: Answer given below.

Q: (c) Find a power series representation for fx arctan(x) dx. You can use the sigma notation or the…

A: Here we use series for arctan x. Also in the last question we use Taylor error approximation.

Q: Find all the eigenvalues and the corresponding eigenvectors of the matrix A = = 6 2 -2 2-2 5 O 7

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Q: (11) 11. Prove by induction that 1 1 1+ + + 22 3² + - 2.

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Q: 6. SET-UP the double integral which gives the vol- ume of the solid in the first octant enclosed by…

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Q: Problem 1: Find the linear combination 2a +33 + 4y = b. Then write b as a matrix-vector…

A: Given that        α=111, β=011,  γ=001 We need to find the given linear combination.

Q: Let λ ER and consider the matrix J = 1 0 X 0 0 00 1 0 0 λ 1 0 0 X € M4. (a) Show that A is the only…

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Q: Prove 6n + 4 is divisible by 5 for all positive integers.

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: 4. Solve the recurrence relation an = 5an-1-6an-2 (n> 1) subject to the initial conditions ao = 1,…

A: Given recurrence relation an=5an-1-6an-2 subject to  a0=1a1=1

Q: Complete the following: (Round your answer to the nearest cent.) Item Apple iPod List price Single…

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Q: dependent: --8--8---8---8 V3 = VI 1 0 V2 = 2 V4= 3 4 Solve c₁v₁ + c₂2+ C3V3+ C4V4 = 0 or Ax = 0. The…

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Q: -31+1 e Sinat

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: 7 Julie Ring wants to buy a new line of Tonka trucks for her shop. Manufacturer A offers a 14/8…

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Q: 16.4 Euler's Method 16-23 In Exercises 5-10, find the orthogonal trajectories of the family of…

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