1. Describe the vector that translates DEF to D'E'F'.

Q: Suppose you are climbing a hill whose shape is given by the equation z = 1000 −0.005x2 −0.01y2 where…

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Q: 6. Find the unit vectors that are parallel to the tangent line to the curve 2x3 at the point (2,…

A: The given curve is y=2x33 at the point 2,163. Calculate the unit vector that are parallel tot he…

Q: The three components of the derivative of the vector-valued function u are positive at t = t0.…

A: Given: The three components of the derivative of the vector-valued function u are positive at t =…

Q: Find the directional derivative of the function f(x, y) = 1+5x/ỹ at the point (5, 1) in the…

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Q: Find a non-zero vector B' which is perpendicular to A'= 2i'-3j'.

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Q: Find the derivative of the vector function r(t) = ta x (b + tc), where a = (-5, −1, −1), b = (−2,…

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Q: Find the approximation for the Green's function of the one-dimensional acoustic wave equation in the…

A: Given function is, cx=aebx Here, a>0 and it's constant here we have to see the effect of b so,…

Q: For z = e"v In(ry): - Find the gradient of z when r= and y = 2 - Find the directional derivative of…

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Q: Find the L^-1 iNVERSE LAPLACE i.) G(S) = 3s-2/2s^2-6s+6

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Q: Calculate the directional derivative in the direction of v at the given point. fx, v)- tan Cy). -(1,…

A: The partial derivatives of f(x,y) at the point (x,y)=(5,2)are:

Q: Suppose that over a certain region of space the electrical potential V is given by the following…

A: Given that, Vx,y,z=4x2-3xy+xyz Find Vx,Vy,Vz:  Vx=8x-3y+yzVy=-3x+xzVz=xy Gradient of V at P(6,6,5)…

Q: rative of the f he unit vecto p, then Ja + B|

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Q: 7. Find the equation for the 'unit tangent vector to the vector-valued function r=. く- I6 Sin(2t),…

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Q: Find unit vector tangent and normals to the are y=1/2 X3+1/2. Point(1,1)

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Q: 7. On a two-dimensional plane, sketch the vector |v>= such that it emanates from the coordinate…

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Q: Find y" by implicit differentiation. 5x3 + 4y3 = 9 У" - %3D

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Q: What do you mean by Vector Autoregressions?

A: Vector Autoregressions :  Vector Autoregression is the model used in stochastic process . It is an…

Q: Find the derivative, r'(t), of the vector function. r(t) at cos(2t)i + b sin5(t)j + c cos³ (t)k…

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Q: In R', evaluate the alternating 2-form 5 = -3 · dx ^ dy on the pair of vectors (a, b) If %3D a = (4,…

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Q: The temperature in °C on the surface of a metal plate is given by T(x, y) = 20-4x - y, where x and y…

A: The complete solutions are given below

Q: Differentiate, hcx) = In (x-Vr

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Q: Find the derivative of y with respect to x. 6x + 7 -1 6. y3-Cos %3D

A: dydx=?

Q: Subtracting the two equations, find a vector equation for the curve of intersection between y=…

A: Given: y=4x2+34z2y-1=3x2+12z2 , x>0

Q: Select the equations that define u as a function of w. A. 3w−4u = 8 B. 1/u + 1//w = w   C. u/w +…

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Q: Let  s(t)=2t^3- 21t^2 +72t in meters be the position of a particle moving on the coordinate line…

A: According to our guidelines, we can answer only the first three subparts of a problem, the rest can…

Q: Let r(t) =. Find the unit tangent vector T(t).

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.