For the line through (–10, 2) with slope 10 find the parametrization of y(t) with given x(t) = – 10 + t. (Use symbolic notation and fractions where needed.)

Q: Find the orthogonal trajectories for the family of curves, sin? y C In x.

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Q: Find the point(s) of intersection of the line x = 1 – t, y = t, z =1– 2t - and the paraboloid z = 8…

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Q: Express the given parametrization in the form y f(x) by eliminating the parameter. - In(t), y = 5 +…

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Q: The tangent of the parabola x = y² + y + 1 at the point (1,0) is

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Q: (5xy --- 6x(2^

A: Given,        F=(5xy-6x2)i+(2y-4x)j and   y=x3 from the point (1, 1) to (2, 8).

Q: Find the parametrization of the line through (5, 9) with slope 12 for given x(t) = 5t. (Use symbolic…

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Q: Find the linear approximation at x = 0 to Write %3D 2- your answer in the form y = Ax + B. %3D

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Q: Find the plane thst passes through the equation of. the point P(6,0,-2) ¢ = 1+t, z=2 -t entains the…

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Q: Find a point on the curve y = x² that is closest to the point (18, 0). %3D AY y =2 (x, y) (18, 0)

A: Find a point on the curve y=x2 that is closest to the point  Here use distance formula…

Q: Find the orthogonal trajectories of the family of curves r² + y² = 2my where m is a constant.

A: As given equation of curve is: x2+y2=2my Differentiate it with respect to x:…

Q: The parametric equations of a curve are given by x = In (VE +1) and y = cosh-' (2t). dy when t = 1.…

A: Given x=lnt+1 and y=cosh−12t We have to find the dydx when t=1 We know that dydx=dydtdxdt.....1…

Q: Find the orthogonal trajectories of the families of r e, where a being a parameter. (0)

A: Orthogonal trajectories are another family of of curve which are perpendicular to the the original…

Q: Find the equation of the tangent plane to the paraboloid z = 2x2 +y? at the point (1,2,6). Select…

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Q: Find the tangent plane to the equation z = 2x – 3y + y at the point (1, 2, – 8). -

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Q: Find a parametrization for the curve described below. the line segment with endpoints (5 - 1) and…

A: Given point :( 5 , -1 ) (10 , -6 )

Q: Find the point on the ellipse x = 2 cos t, y = sin t, 0 <=t<= 2pai closest to the point (3/4,…

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Q: 9. Find the point (x, y) on the line y = 2x + 3 such that the distance from (x, y) to (1, 1) is as…

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Q: Find a parametrization c(t) of the line y = 5 − 2x such thatc(0) = (2, 1).

A: This question comes under the category of calculus and from the parametrization of the line here we…

Q: Find an equation of the parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the…

A: Given" Parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the line y = x − 1 at…

Q: Express the given parametrization in the form y = f(x) by eliminating the parameter. x = 5t + 2, y =…

A: Given

Q: Exercise 1.3.2 Give a paramatrization for the curve curve y = x³ + ()x-¹, then deduce the length of…

A: Given curve is  y=16x3+12x-1

Q: Find the appropriate parametrization for the given piecewise smooth-curvein R^2, with the implied…

A: Here, a semi-circle is of radius 3.

Q: Find the exact length of the curve y = In(1 – x²), 0 Sx S

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Q: Find a parametrization for the line through the point (a, b) having slope m.

A: Given that slope = m , this can be written as <1,m> vector. And point= (a,b)

Q: Consider a particle moving rectilinearly according to x = 13 - 312 -45t m, where t is in sec. Draw…

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Q: Find the tangent plane to the equation z 5z° + 4y – y at the point (4, 2, – 66)

A: Given: z=-5x2+4y2-y      4,2,-66

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A: Follow the procedure given below.

Q: (a) Assume that traffic flows at a rate of 240 vehicles per hour on the stretch of road between…

A: The number of vehicles coming and leaving the signal is same in all the signals. That is, Total…

Q: The length of the curve y = Ey3/2 between x = 0 and X 1 is %3D

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Q: If the equation of the tangent plane to x2+y2-147z²=0 at (1,1,/2 / 147) is x+ay+Bz+y=0, then a+ß+y=

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Q: 2-g(%,y)%3D플-플 * at (VT ,1)

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Q: 2. Find an equation for the plane tangent to the surface 3x2 - 4xy+ z2 = 0 at the point (1, 1, 1).…

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Q: The surface of a hill above the xy-plane is described implicitly by 3x² + y² + (z + 1)² = 2, z ≥ 0.…

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Q: Find the orthogonal trajectories of the family of curves x² + Y? = R? %3D

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Q: ind an equation for the tangent plane of z = –2x²y – 3x² + y at the point (1, –1, –2).

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Q: Express x = In(3t), y = 5 – t in the form y = f(x) by eliminating the parameter. %3D y =

A: Given that x=ln(3t) and y= 5-t we need to write y=f(x) by eliminating the parameter  Now , x= ln(3t)…

Q: Let h(r,y) = r'e. Find its linearization at the point (1,0) and use this to approximate f(2,0). %3D

A: Given function is h(x,y)=x2ey we have to find linearization at point (1,0). then to approximate…

Q: Determine the orthogonal trajectories of the family of circles (equation below) that is tangent to…

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Q: Find the length of parametrized curve given by  x(t) = 6t2 + 12t, y(t) = -4t3- 12t2 - 9t where t…

A: Consider the parametric curve given by: x(t)=6t2+12t and y(t)=-4t3-12t2-9t for t from 0 to 1. The…

Q: Find the Võlumé of thé šólid generated by revolving the shaded region about the given axi About the…

A: Explanation: If we rotate the shaded region about the x-axis, we will get the cone shape. Height of…

Q: Find the equation of the tangent plane to the surface z = x² +y² + 1 at the point (1,1,3). Write the…

A: use the equation of tangent  plane for the given surface.

Q: Find the family of oblique trajectories that intersect the family of the paraboles y =cx at angle 0…

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Q: Find an equation of the parabola y = ax² + bx + c that passes through (0, 1) and is tangent to the…

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Q: Determine the linearization of f(x, y) = arctan(x² + y²) at

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Q: Find the orthogonal trajectories of the given family of curves y? = tcx 1-cx

A: The orthogonal trajectory is the family of curves that is perpendicular to the given curve. The…

Q: Find the parametrization of the line through (2, 8) with slope 11 for given x(t) = 41. (Use symbolic…

A: SOLUTION-

Q: Find the orthogonal trajectories of the family of curves r 5C sin 0, where C being parameter.

A: Follow the below steps to find the orthogonal trajectories. Differentiate the function with respect…

Q: FInd c and d so that the curve y = x3+ cx2+d will have a relative extrema at (2,5). Find other…

A: Maxima or minima: Let f(x) is any function. 1) Evaluate f'(x) = 0 for critical point. 2) Evaluate…

Q: 3. Find the equation of the plane tangent to the graph of f (x, y) = 3x + 4y – xy at the point (1,…

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Q: At which points does the curve r(t)=ti+(2t -t² )k intersect the paraboloid z = x² +y? ?

A: Given: r→t=ti^+2t-t2k^ and z=x2+y2

Q: Assuming that the equations define y as a differentiablefunction of x, use Theorem 8 to find the…

A: the equation we have  (x3-y4)6+ln(x2+y)=1

Q: Find an equation for the tangent plane to z = 9x? – 8y² at the point (1, 1, 1). - = 0.

A: Here we find the equation of tangent plane.