Verify that the points are vertices of a parallelogram and find its area A(2,-3,1) B(6,5,-1) C(7,2,2) D(3,-6,4)

Q: 2. (a) Use the method of Laplace transforms to find the solution y(t) of the initial value problem…

A: The given problem is to find the solution for the given initial value problem with given initial…

Q: Q-5: a) Find the area of the region enclosed by the two graphs y = e²x and y = 1-x, on [0,1]. b) L…

A: Sol:- aThe area between curves definitionThe area between curves is the area between a curve fx and…

Q: Find the volume of the solid region Q cut from the sphere x²+y?+z?=4 by the cylinder r = 2 sine

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Q: Solve the linear system using Gaussian elimination 2x₁ + 4x₂2x3 = 0 3x₁ + 5x₂ = 1

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Q: A parametrization of all the points on the sphere a + y² + z? = 1 that are such that y > 0 is given…

A: Find the parametrization of points on sphere x2+y2+z2=1, where y≥0. The equation x2+y2+z2=12…

Q: Approximate 22 dr with six intervals and the trapezoid rule.

A: The trapezoid rule can be defined as: ∫abydx=h2(y0+2(y1+y2+y3+...+yn-1)+yn), where h=b-aNand N is…

Q: 10. Let w = f(x, y, z) = xe. If x = t², y = 1-t₁ z = 1 + 2t, use the partial dw dt derivatives and…

A: Using the chain rule and rule of partial derivative and get the required derivative.Final solution…

Q: Find the directional derivative of f(r,y, z) = e² cos(Tyz) at (0, 1, ) in 2-1 -y-1= I-2 the…

A: To Find: Directional derivative

Q: 4) Consider a rod of length meters with density 8(x) =(2-cos x) kg/m over the interval 0sxS4. a)…

A: Solve the above questions.

Q: 16. A flower farmer predicts that 85 % of the rose in the bushes he plants will grow rose buds that…

A: Since you have asked multiple questions  , we will solve the first question for you .If  you want a…

Q: Use the long division method to find the result when x¹ x³ + 9x² - 11x + 21 is divided by x2 + 4. If…

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Q: ath 2110Q need it. convert the following triple integral from Cartesian coordinates to cylindrical…

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Q: Consider the following data representing the price of laptop computers (in dollars). 1465, 1151,…

A: Please see the answer below.

Q: 4. The velocity of a speed boat in ft/sec at selected times is given in the table. t 10 15 20 25 30…

A: (a) Acceleration = Change in velocitychange in time

Q: Assume that the function f : R → R is differentiable. 1. Show that the function u(x, y) = f(x+y)e¬¤…

A: (1) To show:  u(x,y)=f(x+y)e-x is a solution of ∂u∂x-∂u∂y=-u. (2) To find: A function f such that…

Q: For time, 1, in hours, 0 ≤ ≤ 1, a bug is crawling at a velocity, u, in meters/hour given by V= 11.…

A: Consider the given equation, v=21+t and, a=0, b=1,and ∆t=0.2 So, we get the intervals, 0,0.2,…

Q: cIn(2) Major Topic 1. (a) Compute dx er + 3 (b) Compute dr 1+ 76 (c) Find the equation for the…

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Q: Use polar coordinates to find the volume of the solid region bounded above by the hemisphere z = /…

A: Given  The solid region bounded above by the Hemisphere z=25-x2-y2 and below by the circular region…

Q: 2.) Write the solution set of the given homogenous System in parametric vector form. 2x1 + 2x2 + 4x3…

A: We are given the homogeneous system and we have to solve the given system in parametric from.

Q: Solve the initial value problem below using the method of Laplace tr y" - 4y' +29y=87e4t, y(0) = 3,…

A: The given initial value problem

Q: A manufacturer produces both widgets and gadgets. Widgets generate a profit of $75 each and gadgets…

A: Given data into tabular form. Raw material A&B for each widgets 8 units of A 1 unit of B…

Q: A, average velocity between t = 3 and 1 = 9. B, average velocity between t= 15 and t = 18. C,…

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Q: needed to be solved correclty in 15 minutes and get the thumbs up please show neat and clean work…

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Q: Ask Bard to solve the IVP: y" + 4y = 0, y(0) = 3, y'(0) = 0. and check if its answer is correct.

A: We have to solve the initial value problemy'' + 4y = 0, y(0) = 3, y''(0) = 0 and check if its answer…

Q: (Q1) (a) Count the number of arrangements of the word FEBRUARY that satisfy all of the following…

A: Given the word FEBRUARY

Q: 5 students are selected at random from your class of 100 students to attend an event. What is the…

A: 5 Students are selected randomly from 100 students to attend event.  The total number of ways to…

Q: Find the volume of the solid bounded by the planes z = 0, z = 4, and y = 9 and the parabolic…

A: We have to find the volume of the solid bounded by the plane z=0, z=4 and y=9 and the parabolic…

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

A: First we solve for critical point find the partial derivative with respect to X and y separately and…

Q: Find the minimum value of f (x,y,z) = 2x2 + y? + 3z? subject to the constraint 2x - 3y - 4z = 49

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Q: Kindly solve ASAP in 30 minutes and get the thumbs up please show me neat and clean work for it by…

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Q: The graph of the function f is shown below. Which statement best describes the value of f'(-1)?…

A: Please see the below picture for detailed solution.

Q: 11. Find the first four nonzero terms in a power series expansion of the solution to the given…

A: