Find the distance the point P(0, 2, 8) is to the line through the two points Q(1,-1,4), and R(-1,-4, 5).

Q: One root of the equation 2x + x³ + 4x + 2 = 0 is O a) 1/1/2 Ob) -2 Oc) - 1/12 d) 2

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Q: Find the least-squares line given the matrix products ATA 608.4 5942.2 A¹b- = y = Ex: 1.2 +Ex: 1.2 €…

A: Let us to find a least square line for the set of values {(xi,yi):i=1,2,⋯,n}Let the equation of line…

Q: Consider the set S composed of the points on the line segment S₁ between points (-1,0) and (2,0) and…

A: Given that S1 is the line segment joining (−1,0) and (2,0). And, S2 is the line segment joining…

Q: Let a, b ∊ R, and suppose that for every ɛ>0 we have a≤b + ɛ. Show that a≤b.

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Q: Objective Function Subject To Kmax.= y₁ + 2y2 Y₁ + y₂ ≤ 0.7 Y₁-Y2 ≥ Log2 0≤y₁ ≤1 0≤y₂ ≤1 y ≥0…

A: Objective function subjected to

Q: Compute the work done by the vector field F(x, y, z) = (1+²) moving a particle: 1+2, 2², 2yz) when…

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Q: YouWhy is it 8×1/2 and not 8-1/2? Please explain. Thank you. Phi(8)=8(1-1/2).

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Q: x² y + 10 x y" + 14 y = 0 in (0, +∞). Compute the wronskian of the solutions ₁ Yr Ys W(x) = * € (0,…

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Q: 12. Briefly explain how the bisection method can be used to solve a nonlinear equation f(x) = 0, if…

A: In the above question, we need to explain the bisection method to find the roots of a nonlinear…

Q: (b) Let = {A; : i EN} be an indexed family of sets with the property that A₁ A₂ 22 A, 2..., that is,…

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Q: (c) Prove that m is prime if and only if y(m) = m - 1.

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Q: If 2x³-9x² + 4x-7 is divided by x-3 to give a quotient of 2x²-3x - 5 and a remainder of -22, then…

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Q: Tove that S L { cosh at} = 35 ₁² s>lal > 5-a² 2

A: In this question, we will find the Laplace transformation.

Q: A Cartesian and a polar graph of 3 1=2 - 5 cos (40) are given. Identify the points on the polar…

A: From the given polar curve of Given that a polar graph is periodic with a period,The point A is…

Q: 1. A car travels at a constant speed and burns g(x) liters of gas per kilometer, where x is the…

A: 1. Given that a car travels at a constant speed and burns g(x) liters of gas per kilometer,…

Q: ∞ Write out the first few terms of the series Σ n=0 The first term is (-1)" 4 What is the series'…

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Q: Expand the given set to form a basis for R³. (IC) BO

A: Given set  We have to expand the basis for

Q: 17. Let S denote the part of the cylindrical surface x² + y² = 9 that is between the planes z = -1…

A: A parametrization of the surface S is \)" data-mce-style="cursor: default;">S(u,v)=<3cos⁡u ,…

Q: In each of Problems 6 through 8: a. Find the solution of the given initial value problem. b. Sketch…

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Q: Determine the number of permutations (arrangements) possible of 7 things taken 3 at a time.

A: We have to determine the number of possible permutations of 7 things taken  at a time.So,

Q: Find the particular solution of the differential equation x²y" + 8xy' +12y = 1x 4 y'(1) = 42.…

A: We have to solve the differential equation.

Q: Assume the domain of the field plot below is R2 a) Identify, if possible, a point in the plane where…

A: We have to answer the following questions on the basis of the given vector field.

Q: Let the function x(1) be given by the conditions x (0) = 1 and x (1) = 1x(1) + 2[x(1)]² Determine…

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Q: 1. Find all solutions of the congruence 5x+3x²+x+3 = 0 mod 30.

A: The congruence .To Find:Solution of the above congruence.

Q: 1) A) Show that the set of all odd integers is countable, by producing a 1-1 Function F From J onto…

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Q: Assume all matrices are invertible. Note that c cannot exist by itself in a matrix equation. Solve…

A: Given, all matrix are invertible.XA = cX + IAlso c can't exist by itself in a matrix equation.

Q: For the signal below, sketch the following signals O (g) (4-t) (h) x(1/4) -t -2≤t≤0 0≤t≤4 otherwise…

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Q: A regional municipality is studying a water supply plan for its tri-city and surrounding area to the…

A: Present worth at year 2030Hence, present worth at year 2030 will be $158.147096 million

Q: Find kif 2x + 1 is a factor of kx3 + 7x² + kx-3. a) k = -2 b) k = 2 Oc) k = 1 O d) none of the above

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Q: Each elements of a finite field F with p" elements satisfies the equation XP = x. n

A: We have to show that each elements of a finite field F with pn elements satisfies the equation .

Q: Find a 3 x 3 matrix A that has eigenvalues λ = 0, 12, -12, with corresponding eigenvectors 400…

A: We have to find a  matrix that has eigenvalues , with the corresponding eigenvectorsWe know thatIf A…

Q: Solve (y - 3)² = -54 for y y=3± √6i y = 3±3i y=3±3√6i y = 3+ 6i

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Q: d²x dt² solve for x. 2 + w³²x = F sin wt

A: Given differential equation isd2X/dt2  + w2X = F0 sinwt

Q: 1. Prove that the function f(x) = x² sin x + 4x 3 has exactly one root in [0, 2]. Perform the…

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Q: Pivot once as indicated in the given simplex cableau. Read the solution from the result. Pivot…

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Q: Show that if f: A→B and E, F are subsets of A then f(E∪F) = f(E)∪f(F) and f(E∩F) ⊆ f(E)∩f(F).

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Q: Calculate the residual value of an oven in a bakery, whose installed cost is $40000.  The machine is…

A: Installed cost is The machine is depreciated for  year at a rate of

Q: The data in the table below, also shown in the figure, is taken from the CDC growth tables for…

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Q: Problem #4: Suppose that a matrix A has characteristic polynomial p() = 24 - 32³ +62² 15. Consider…

A: (i). Given characteristic polynomial is p(λ)=λ4−3λ3+6λ2−15.If λ=2 is an eigenvalue of A then…

Q: The given T is a linear transformation from R2 into R2. Show that T is invertible and find a formula…

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Q: Solve the initial-value problem where f(t)= = 2: y'-y = f(t), y(0) = 1 0 ≤t≤1 t≥1 1: in the…

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Q: A large tract of land is being surveyed and divided into smaller parcels for sale. When parcels of…

A: Given information:Parcels of  leave  leftover.Parcels of  leave  leftover.Parcels of…

Q: Let S be a nonempty subset of R that is bounded below. Prove that inf S= -sup{-s:s∊S}

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Q: Maximize p = 10x + 20y + 15z subject to x + 2y + z≤ 20 2y - z≥ 5 2x - y + z≥ 10 x ≥ 0, y ≥ 0, z ≥ 0.…

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Q: Suppose that a fourth order differential equation has a solution y = -8e4x cos(x). (a) Find such a…

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Q: 5. Marc is asked to simplify the expression √3-√75. He says that since the radical you -------- ----…

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Q: Source Demand 1 2 3 4 1 108 M M M 10 2 1.09 1.11 M M 19 Destination 3 1.11 1.13 1.1 M 29 4 1.13 114…

A: Supply and demand are as follows:To Find:Using the transportation simplex method, determine the cost…

Q: B.C. IC. Solve completely to the final form of the solution as a Fourier Series the heat equation…

A: Using seperation of variables method:Let u(x,t)=X(x)T(t)From the conditions :u(0,t)=u(1,t)⇒…

Q: We learned how the diagonal on the unit square lead Pythagoras to discover not all magnitudes are…

A: We first draw the diagram using ruler and label the figure.

Q: Determine whether the given limits exist and find their values. Give a clear explanation.

A: We have to find