ds² = dt² – dz² – (1 + 2h(t − z))dx² − (1 – 2h(t – z))dy² - - how that this is a solution to the linearized empty space Einstein equations for n arbitrary function h. Show that the curve x=y=z=0 is a geodesic of the above metric.

Q: A curve Cis given by the parametric equations z = 2t –2 and y = (t- 2) where t > 0. 1. The curve has…

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Q: Find a set of parametric equations where 0 ≤ t ≤ 1 that models the line segment from (7,-8, 10) to…

A: Find a set of parametric equations where 0≤t≤1 that models the line segment from (7, -8, 10) to (-4,…

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Q: osen y

A: Is it sen y =x

Q: 2. True or False: If the parametric curve x = a(t), y = b(t) satisfies d'(5) = 0 and b' (5) = 1 then…

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Q: a) Find the directional derivative of S = In(2x +3y) at point (-1,1) in the direction ef 4i - 3i

A: The directional derivative of a function f(x, y) in the direction of the unit vector (a, b) is given…

Q: Suppose parametric equations for the line segment between (7, 4) and (0, 6) have the form: S#(t)…

A: Values of constants

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A: Given To find parametric equations for the tangent line to the curve with the given parametric…

Q: 1. x (0) = 0 + cos 0 y (0) = 1+ sin 0 given that

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Q: 4. Find the parametric equation of the tangent line to r(t) = 4costi – 3tj %3D at Po(2, –n)

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Q: Which is a parametric equation for the curve 25 = (x +7) + (y+ A. c(t) = (5 cos(t) – 5, 5 sin(t) –…

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Q: express the parametric curve in the form y = f (x) c(t) = (4t − 3, 10 − t)

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Q: 1. The parametric equations for the astroid below are x = sin' (t), y =- cos (1) on 0<t < 2a. a)…

A: Given, the parametric equation for the astroid below are  First need to find the stating point on…