Verify that the two lines are parallel, and find the distance between the lines. (Round your answer to three decimal places.) L₁: x=2-t, y = 3 + 4t, z = 4 + 4t L₂: x = 2t, y = 1 - 8t, z = 4 - 8t

Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

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Q: I 44. Solve the initial value problem: EL y""-2y"-y' + 2y = 0; y(0) = 2, y'(0) = 3, y"(0) = 5.

A: The solution is given below

Q: Find the largest open intervals where the function is concave upward. f(x) = x 3-3x2 - 4x + 5 O None…

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Q: If $500 is invested at 4% interest, compounded annually, then after n years the investment is worth…

A: We need to find out that after 6 years what will be the invested amount become.

Q: Find all the polar coordinates of the point: (9,7).

A: Our Aim is to find the polar coordinates of the point 9, π4.Solution⇒Since, we know that the polar…

Q: Find the local maximum and minimum values and saddle point(s) of the function. If you have…

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Q: 2 x ln((2x)²) dx 1

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Q: +∞ Σ n=1 (x + 1)n η n? + 1]

A: Given: an=x+1n3nn2+1 Now,           limn→∞an+1an=limn→∞x+1n+13n+1n+12+1x+1n3nn2+1…

Q: Determine any planes that are parallel or identical. (Select all that apply.) P₁: -30x + 120y + 60z…

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Q: 3. Find the formula for the following sequences i. An explicit formula for 2, 6, 18, 54, 162,....…

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Q: Activity no. 3. 1. At 2:00p.m., a thermometer reading is 80°F is taken outside where the air…

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Q: Find the general solution of the given second-order differential equation y" 6y' +10y = 0 y(x) =

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Q: Let f(x, y, z)= = fz(x, y, z)= fy(x, y, z)= fz(x, y, z)= 2² - 2y² I y² + 4z² Then

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Q: et a = = = ci + j and b = 4i + 20j. Find c so that a and b are orthogonal. i

A: Please refer to the image below

Q: Find the general solution of the given differential equation. dy dx y(x) = = 3y 3y² 2 + Cx Give the…

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Q: The first three Taylor polynomials for f(x)=√9+x centered at 0 are po (x)=3, P₁ (x)=3+, and…

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Q: An (D²-2D +1) y = x e sinx X Ans, y tết xếể xsinx-2 cosx = + e

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer…

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Q: If r(t) = (2e³t, 4e-3t, 4te³t), find T(0), r"(0), and r'(t) r"(t). T(0) = r"(0) = r'(t) r"(t) =

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Q: The indicated function y(x) is a solution of the associated homogeneous equation. Use the method of…

A: The given equation is;  y''-3y'+2y=5e3x.

Q: What is the difference between the linearization, L(x), of f at a, and the linear approximation (or…

A: Given question:- What is the difference between the linearization, L(x), of f at a, and the linear…

Q: Determine whether the series converges or diverges. Select the correct answer. O diverges Oneither O…

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: Solve the following ODES by Inverse Operator method. 2X -X • (D²³+1) y = 3 + 2*² + 5 € Ans : y = C₁…

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Q: Make a sketch of the region and its bounding curves. Find the area of the region. The region inside…

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Q: 5. Find the 6th term of the recursive sequence defined by a₁ = 0, an+1=2a₁ +3.

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Q: 9 -25 -49 + 8 = 2*+* 3X 2X - 2X Ans: y = c + czxe + cze L 25 -3X e + x + x + ½

A: See this solution in below

Q: (a) Evaluate the double integral Je emax{z²,y²} where R = {(x, y) |0 ≤ x ≤ 1,0 ≤ y ≤ 1} is the unit…

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Q: Find an equation of the line that passes through the point and has the indicated slope. Point slope…

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Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i, j…

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Q: Replace the Cartesian equation x² + y² equation. OA) r sin² 0 = 4 cos 0 B) r = 4 sin 0 Oc) r = 4 cos…

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Q: 2 Solve the following ODES by Inverse Operator m. ℗ 2 (D³² +1) y = cos x Ans & Y = C₁ C3 x + C₂ sinx…

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Q: Question Find dy and evaluate when x = -1 and dx = 0.1 for the function y = 7x² + 5x + 4. Provide…

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Q: Graph the conic section. Identify the vertices, foci, directrices, and asymptotes. Use a graphing…

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Q: Consider the following functions. f₁(x) = 0, f₂(x) = x, f(x) = ex g(x) = C₁f₁(x) + C₂f₂(x) + C₂f3(x)…

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Q: A force of 480 newtons stretches a spring 3 meters. A mass of 40 kilograms is attached to the end of…

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Q: find the vertical asymptotes of the graph of the function f(x)=ln(x+3)

A: x=a is said to be a vertical asymptote of a function y=f(x) iff as x tends to a f(x) tends to ∞ or…

Q: Use the Taylor series to find the first four nonzero terms of the Taylor series for the function In…

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Q: Find the area of the triangle with vertices P(1,5,-2), Q(0,0,0) and R(4, 5, 1). NOTE: Enter the…

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Q: The given differential equation is already in standard form, as the coefficient of the highest order…

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Q: 3/2 1/2 q q 1 2 dq

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Q: र P=Ae+Bex What yp

A: We can answer the question as below.

Q: Problem 1.5 Use the following graph of y = f(x) to graph each function g. (a) g(x) = f(x) – 1 (b)…

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Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

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Q: For the function f(x) = 2x² +1, it is given that 6.². ſª f(x) dx = At what value c does the function…

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Q: Describe at least two (2) similarities found in methods of integration and methods of…

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Q: Express the following limit as an integral. lim 1-00- TL i=1 (2 (27)¹ + 3) 8-91 Ar over [1,6]

A: Note : As  per our guidelines we are supposed to answer only one question if there are multiple…

Q: 1. Does the definite integral [a,b]? Why or why not? 2. How would you calculate the total area of…

A: Here we have to use the concept of integration

Q: USE A DOUBLE INTEGRAL TO FIND THE VOLUME OF THE INDICATED SOLID Z 52 F2 z = 6-24 0≤x≤4 0≤4≤2

A: We will use concept of double integral to solve this.

Q: 2. Integrate: x² In x dx a. In x+c. b. [(In x)² ++c c. [(Inx)² - Inx+]+c d. none of these

A: The given integral is x2lnx.