Find an equation of the plane that passes through the point P(-7,–5,5) and has the vector n = (-1,4, 2) as a normal.

Q: particle is moving with the given data. Find the position of the particle. a(t)= 2t+3 , s(0)=4 ,…

A: Given query is to find the position function.

Q: Solve the following system of IVP: -3 3 x' = Ax where A =-2 -1 1 and x(0) 21 %3D 3.

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Q: Sketch the following function and classify the points of discontinuity. y = x for a -2 Input the…

A: Let's find.

Q: Solve for x. 17**8 = 113* x+8 Write the exact answer using either base-10 or base-e logarithms. x =…

A: Basic application of logarithmic properties problem

Q: Find the area of the shaded region. r = V cos20 r = 6 cos 0 NOTE: Enter the exact answer. A

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Q: Given that f(x) = z"h(z) h( – 1) = 2 h'(– 1) = 5 Calculate f'(- 1).

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

A: We have to  find the unit vector in the given direction.

Q: d d. Calculate ri(t) · r2(t)] and x r2(t)] first by differentiating dt dt the product directly and…

A: This is a problem related to cross and dot product of the derivative function. Please find the…

Q: Find the surface area formed when the curve f(x)=x^3 between x=1 & x=3 is rotated around the x-axis

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: a) Determine whether the following differential equation is a type of linear equation or not, i.…

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Q: A particular computing company finds that its weekly profit, in dollars, from the production and…

A: Since multiple subparts are asked, I am answering first 3 subparts. Here we will use first…

Q: 2. Let A = (1,0, 2) and B = (6, -2, 3). Solve for proja B. %3D

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Q: Find the volume of the solid generated by the region bounded by y= x3, y=0 and x= 1 about the y-axis…

A: The region bounded by the curvey=x3, y=0 and x=1 is:

Q: sing the four step rule, find the derivative of y = tan(x) %3D

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Q: Draw the graphs of the given functions. Find their points of intersection. Find the area bounded by…

A: Given curvesy = 4x2y = x2+3

Q: Find the indicated derivative for the function. f′′(x) for f(x)=2x7−9x2+2x−

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Q: Express the given parametric equations of a line using bracket notation and also using i, j. k…

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Q: Work out the product of 2cos60° x 3cos30° in polar and rectangular form.

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Q: Find the inverse Laplace transforms of the functions: 3 (a) F(s) s4 1 (b) F(s) (c) F(s) = s+5 3s+1…

A: We are authorized to answer three subparts at a time, since you have not mentioned which part you…

Q: The motion of a particle is described by the position function s(t) = t3 - 12t2 + 36t, t > O where s…

A: Use the derivative for the finding velocity of the function

Q: 1 hence find u Given that y =u – 5u' and x dx 2(1-15u") a. 3 u 2(15u 1) Ob. 3 u (15u? -1) 2 u'…

A: The objective of the question is evaluate the derivative and choose the correct option.

Q: 1 0.5 -5 -4 -3 -2 1 2 f -0.차 -1 -1.5 -2 5. Is the function continuous at x = -3? 6. Is the function…

A: topic - continuity of a function

Q: Se*V9-e2x dx

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Q: Find all cube roots of the complex number 64(cos (219°) + i sin (219°). Leave answers in polar form…

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Q: Linear equation of order one: dy- (x² – 2xy ldx = 0

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Q: Solve by integrating factors found by inspection: y (x2 - y2 + 1)dx - x (x2 - y2 - 1) dy = 0

A: To solve: y(x2 - y2 + 1)dx - x(x2 - y2 - 1)dy = 0 ⇒yx2 dx- y3 dx+ y dx - x3dy +xy2dy +xdy = 0

Q: If the series 1(-1)" 2 were approximated using its first k terms, what would be the smallest number…

A: We have to find the smallest number of k such that the error bound would guarantee an error of not…

Q: An open rectangular box has an area of 441 cm2. If its length must be 3 times its width, find its…

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Q: S(sec; - sin) do

A: We know that integration power rule is  Integration of (xn) = xn+1/n+1.   Here i attached the…

Q: Consider the series -3+ 5" n=0 To determine if this series converges, you could use O Divergence…

A: To test the convergence of the series

Q: xdy- ydx 4. The exact differential what is the d 5. In the differential equation 2xydx+(y -x²ty =0,…

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Q: From Rogawski ET 2e section 10.2, exercise 34. Use the formula for the sum of a geometric series to…

A: topic - geometric series

Q: (26ー1) 不t8

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Q: 4. Evaluate: lim (x,y)→(3,2) x cOS TY

A: To evaluate the limit of the given function, substitute x=3 and y=2  in the given function.

Q: . Determination of integrating factors: 2y(x+y+2)dx+(y² – x² –4x –1)dy = 0 %3D

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Q: 15. What is the general solution of the exact differential equation (x + siny – cosy)dx + x(siny +…

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Q: d y' (-9 csc 3x cot 3x – 9 csc 3x) dx

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Q: Set up a double integral to find the volume of the solid region bounded by the graphs of the…

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Q: There is a 4 km long straight beach. At one end, there is a boat anchored at A, 3 km off the beach.…

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Q: Evaluate the iterated integral by converting to polar coordinates. (x2 + y2,3/2 dy dx dr de =

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Q: 16-2 Evaluate: lim +4 V12+-a dne O 2 12 3 14

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Q: 5. S cot³ (40) /csc(40) de

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Q: Find all values of x where tangent lines to y = x° and y = x' are parallel. (Give your answer in the…

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Q: xdx S- can be solved by either algebraic subsitution or integrataion by parts. x-1 А) True B) False

A: We know that algebraic substitution is method in this replace the veriable of integration by a…

Q: 2. Find the maximum value of the directional derivative, D f, of the function _2 f(x, y, z) = x´ +…

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Q: Solve for the derivative of t y =2 V3-z Previous

A: This is a basic differentiation problem

Q: Simplify Using type products 1. (-2x-3y+4B)2

A: This is a problem of simplifying the given expression based on the general formula.

Q: Find an equation of the plane through (1,8, 5) that is perpendicular to the line x – 2 = 3t, y + 3 =…

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Q: 4) Find the equation of the plane that passes through the point (6,0, 2) and contains the line x = 4…

A: The plane that passes through the point (6, 0, 2) and contains the line x = 4 − 2t, y = 3 + 5t, z =…