Suppose a particle begins to move from the origin (1 = 0) following the curve in space r(t) = (5sint, 5 cost, 12t) Find the location of the particle on the curve at a distance 26z units along the curve from the origin in the direction of increasing t.

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Q: Find y' for y = vTy at the point (9,1).

A: Given: y=xy ⇒y=x12y12 ⇒y12=x12

Q: Find the orthogonal trajectories of the famil y of curves x'yxy=c where cis constant

A: Given:    x3y-xy3=c      Differentiating by using power rule we get…

Q: 2. A particle moves along the parabola y = x in the first quadrant in such a way that its…

A: Given: A particle moves along the parabola y = x2 in the first quadrant in such a way that its x -…

Q: (6) Find the orthogonal trajectories of the family of curves r 4C cos 0, where C being %3D…

A: We have to solve given problem:

Q: Find the orthogonal trajectories of the family of curve y = 3x+c,where c is an arbitrary constant.

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Q: (6) Find the orthogonal trajectories of the 3C cos 0, where C family of curves r being parameter.

A: Answer

Q: (6) Find the orthogonal trajectories of the family of curves r = 3C sin 0, where C being parameter.

A: Orthogonal trajectory curve of a family of curve is defined as a curve which intersects every member…

Q: Find the orthogonal trajectories of the family of curves x when 'a' is the parameter. +y Da

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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: .8 Estimate the error if cos t is approximated by 1 2 in the 4! integral cost? -- + - dt.

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Q: Find the orthogonal trajectories of the one parameter family of curves ex+e-y=c

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Q: A soft ball is thrown up vertically in the air at to = Os from an initial height of 15m and with an…

A: The formula for the motion of the object with variable velocity and constant acceleration is . Here,…

Q: Find the equation of the plane tangent to the graph of z + xyz = 33 at (1,2,3).

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Q: What is the isogonal trajectories family of curves x² - y² = a which intersects at an angle of ∅ =…

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Q: 2 35) Find a curve through the point (-4, 1) whose length integral, 1 s y s 2, is L = 1 +

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Q: Write the eguatoN: ation: vertical Asympto te at x- -1 d olible zero at X= 2 y intercept at (0,2

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Q: A stone, projected vertically upward with initial velocity 112ft/sec, moves according to s = 112t −…

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Q: ) A Cylinder tank of radius 4m and height 10m is initially filled with water. At the bottom of the…

A: Given that radius of a Cylinder tank is 4 meters and Height of tank is 10 meters. A hole is at the…

Q: 4. Find the equation of the tangent plane to the surface ew + In(xz) - evz = 0 at the point (1,0,…

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Q: Find the orthogonal trajectories to the family of curves: r=c- (in y -1).

A: Orthogonal trajectories can be find in the following way: (i) differentiate given family of curves,…

Q: Find the tangent plane to the graph of **yz +z'e* -y² = 5 at (1,3,2).

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Q: use taylors formula to find the cubic approximation to f(x,y)=sin(6x+y) near the origin

A: Given Function,fx, y = sin 6x + y

Q: Q2 (a) A miniature quadcopter flies in a curve line from one point to another. Suppose that the path…

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Q: (4) Find the orthogonal trajectories of the family of curves z +y 2C?, where C being %3D a…

A: Note:-    as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: 4. Find an equation for the tangent plane to the surface z = 3x + 5y + arctan in the point (0, 1,…

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Q: (4) Find the orthogonal trajectories of the family of curves z +y = 20C?, where C being %3D a…

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Q: 4. Find the equation of the tangent plane to the surface ey + In(xz) – evz = 0 at the point (1,0,…

A: Given:

Q: What is the moment of inertia of this area about the line y = -10 ?

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Q: 1.) If the ball IS Thrown. vertically upward with a veloorty of 15 m/s then ts height after t…

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

Q: What is the moment of inertia about the x-axis bounded by the curves y² = -16(x-4), the line 8x-15y…

A: here we have to find the moment of inertia about x axis so we can use integration to find this.

Q: 27. Find the length of the curve Vcos 2t dt y = from x = 0 to x = "/4.

A: The given curve is We know that by Second Fundamental theorem of calculus ,if F(x) is continuous on…

Q: 1. Tangent to the parabola z = x + 3y?, x = 1, at point (1,2, 13

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Q: Obtain the orthogonal trajectories of y=Cx^2 and compute for the positive value of y of the…

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Q: A plane area is bounded in the first quadrant by the curves y² = -16 (x-4), the line 8x-15y = 0, and…

A: Given the curve is y2=-16x-4 and the line 8x-15y=0 and x-axis. We have to find the moment of inertia…

Q: Find the orthogonal trajectories of the family of curves. (Use C for any needed constant.) y = 19k

A: The objective of the question is find the orthogonal trajectories of the family of the curves.

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

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Q: (6) Find the orthogonal trajectories of the family of curves r= 5C cos 8, where C being parameter.

A: we have to find the orthogonal trajectory for the given function

Q: 1. Find the orthogonal trajectories of the family of curve z + 3y = cy,where cis an arbitrary…

A: We will first find the differential equation of the of the given family of curves

Q: (6) Find the orthogonal trajectories of the family of curves r= 2C sin 0, where C being parameter.

A: See the detailed solution below.

Q: Once again, a particle travels at velocity t – 1 at time t. Divide the interval 0, 2 into 2k…

A: A particle travels at the velocity t-1 at time t.  We now divide the interval 0, 2 into 2k intervals…