Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve. r(t) = (2 cos ³t) j+ (2 sin ³t) k, Osts

Q: A disk rotates about an axis through its center. Point A is located on its rim and point B is…

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Q: Consider the curve parametrized by a = e-sin(0) and y = ecos(8) for 0 ≤ 0 < 2π. At what points (x,…

A: The parametrized curve x=e-sinθ and y=ecosθ for 0≤θ&lt;2π.

Q: cos t + sin t *(a) g(t) = cost * sin t Cost

A: The unit tangent vector t is  (dr/dt)/|dr/dt| . Here r(t) =g(t)

Q: The tangent plane at the point ,4 is z= 2'24 (Type an exact answer, using radicals as needed.)

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Q: The angle between tangent and the radius vector of the curve r 5(1- sin@) at 0= is %3D

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Q: Find the lengths of the curves 1.The curve r = cos^3 (u/3), 0&lt;= u&lt;= pai/4 2. The curve r =…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: Find the length of the curve x = cos t, y= sin t, 0 <IST. 4/2 4 IT 2/2 IT 2 2

A: Given that: x=cos2t, y=sin2t, 0≤t≤π

Q: 21. For the curve 7(t) = sin ti + cos tj, find 7 '(t) and sketch the position vector 7(÷) and the…

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Q: Find the tangent plane to the equation 3y cos(4x – 2y) at the point (2,4,12) Z =

A: Z=3ycos(4x-2y)  Point= (2,4,12)

Q: A crate of weight 60 kg is being pulled along a level floor by a force F that is at an angle e with…

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Q: Find the equation of the tangent line to the parametric curve x = θ+cosθ, y=1+sinθ; θ = π/6

A: We have to find equation of tangent line to the parametric curve at θ=π6 where parametric curve is:…

Q: Find the length of the curve. r(t) = (3t, 3 cos(t), 3 sin(t)), -3 sts 3 %3D

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Q: For the following parameterized curve, find the unit tangent vector. r(t) = (6 sin (t),6 cos (t),7…

A: Given that        the parameterized curve            r(t) = &lt; 6sin(t), 6cos(t), 7cos(t)&gt;  Here…

Q: A curve is parametrized by the given equations. Find the equation of the tangent line to the curve…

A: Equation of the tangent line

Q: Find the length of the curve r(t) = (cos 3t, sin 3t, 2t3/2),0 sts 3. %3D

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Q: For the curve C given by r(t) =, find: (a) the unit tangent vector to the curve C at the point (0,…

A: For the given curve C is, r(t)=&lt;5t, 2cost, 2sint&gt; a)  At the point (0,2,0) so,…

Q: If an object of weight W is dragged along a horizontal plane by a force acting along a rope attached…

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Q: The following figure shows a single-stage gear train. Gear trains are used in many products, such as…

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Q: Solve the problem by using Laplace Trons form +y= Sin 2€ %3D yo) = 0

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Q: Find the angle between the radius vector to the curve r = 2a sin 3u and its tangent when u = pai/6.

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Q: Find the angle between the radius vector to the curve r = 2a sin 30 and its tangent when 0 = /6.

A: The given curve is r and differentiate with respect to theta:

Q: Find the length of the curve The curve r = (1 + sin 2u)^1/2 , 0 … u … pi(2^(1/2))

A: We have been given the curve  r=1+sin2u where 0&lt;u&lt;π

Q: consider the motion of a point (or particle) on the circumference of a rolling circle. As the circle…

A: Given, the position of the particle is  r(t) =b(ωt-sinωt)i^+b(1-cosωt)j^ The velocity vector is…

Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

A: Let r(t) be a curve, the derivative r'(t) is a vector tangent to the curve. The equation of the line…

Q: Find parametric equations for the tangent line at the point (cos(), sin(5 ), ) on the curve a = cos…

A: Here, the given parametric equation of the curver(t)=(x,y,z) where x=cos t, y=sin t, z=t. To find…

Q: Find an equation of the plane tangent to the following surface at the given point. 13 cos (xyz) =- 2…

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Q: Consider a tall building located on the Earth's equator. As the Earth rotates, a person on the top…

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Q: V. The tangent line at the point (t, y) = (- to 4'2 1 Then, the curve y = cos t is y = bt - - - a a…

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Q: Find an equation of the tangent(s) to the curve with paramnetric equations ¤ = 1+ VE, y = e" at the…

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Q: The equation of the tangent plane to the surfice. -yeV + = 0 at the point (0,1,1) is ar + by + cz =…

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Q: Find the length of the curve r = 4 – 4 sin 0

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Q: Find the length of the curve 7 (t) = (4 cos(5t), 4 sin(5t), 5t) for – 3 < t < 9 Give your answer to…

A: Given: r→t =4cos(5t), 4sin(5t), 5t  for -3≤t≤9

Q: The equation of the tangent plane to the surfae ye+ = 0 at the point (0,-1, 1) is az+by+cz = Which…

A: Given yexy+z2 = 0    point (0 , -1 , 1)Let f = yexy+z2dfdx= yexy.y ⇒dfdy(0 , -1 , 1)=1dfdy= yexy.x…

Q: Find parametric equations for the tangent line to the curve of intersection of the cylinders x? +² =…

A: Here finds the parametric equation for the tangent line to the curve of intersection.   where the…

Q: A curve has parametric equations x = 2 sin t ,y = cos (2t) + 2 sin t for −π/2≤ t ≤−π/2 . Find out…

A: Given : parametric equations x = 2 sin t , y = cos (2t) + 2 sin t for −π/2 ≤ t ≤ π/2     Note :…

Q: Consider the following. x = sin(3t), y = -cos(3t), z = 6t; (0, 1, 2n) Find the equation of the…

A: Given :- The given curve x = sin 3t ,  y =-cos 3t  , z =6t   ;  0,1,2π To determine :- The equation…

Q: Find the exact length of the curve. x = 9 cos(t) − cos(9t), y = 9 sin(t) − sin(9t), 0 ≤ t ≤ pi

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Q: The length of the curve determined by equations x = 8 cos t + 8t sin t and y = 8 sin t – 8t cos t…

A: Given: x=8cost+8tsinty=8sint-8tcost0≤t≤π2

Q: Calculate the length of the curve γ (t) = (cos(2t), sin(2t)) t ∈ [0, π].

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Q: Find the cosine of the angle between the curves (cost, -sin(t)/5, sint) and (cos(nt/3), sin(nt/3),…

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Q: cos(t),2 sin(t) >, find:  (a) the unit tangent vector to the curve C at the point (0,2,0) (leave…

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Q: We start by finding the tangent vector to the curve. For r(t) = (10t, 3 cos(t), 3 sin(t)), we have…

A: Given rt=10t ,3cost ,3sint

Q: Find parametric equations for the tangent line to the curve of intersection of the cylinders x2 +?…

A: Given      x2 + z2 = 25 and y2 + z2 = 25 at the point (3,-3,4) Let    f(x,y,z) = x2 + z2 - 25  and…

Q: A curve in space is given by C = { (r, y, z) = cos(nt) ', In(10 – t²), ² + 4 for t € (0, v10) Give…

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Q: Show that the curve x = 3 cos(t), y = 2 sin(t) cos(t) has two tangents at (0, 0) and find their…

A: on solving this we get

Q: Find the length of the curve #(t) = et cos(t), y = e* sin(t) for 0 <t < 5. %3D %3D Give an exact…

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Q: Find an equation for the circle of curvature of the curve r(t) = t i + (sin t)j at the point (pai/2,…

A: The parameterized curve are x = t, y = sin t.The derivatives are,

Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.