Given the position function F(t) = (1, 2t, 1²). a) Find the unit vectors B,T,and N. b) Find the curvature of 7(t). c) Find the tangential component of the acceleration vector.

Q: Find a formula for the curvature of the function P= nrt/v-nb - (an^2)/(v^2) ,where n, R, a, b,and T…

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Q: Find the arc length of the space curve given by the vector equation r(1) = (- 9t + 16) + (-9² +…

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Q: Find the acceleration vector for the position vector r(t) = (sin(5t), 6t", e "). x component = y…

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Q: Sketch the curve of the vector function r(t) = 3ti+ (3t + 1)j,-1<ts2, and indicate the orientation…

A: The given curve in vector form: r(t)=3ti+(3t+1)j The point of t is -1≤t≤2 To find the curve at the…

Q: Find the velocity and acceleration vectors in terms of u, and ue en r=6 sin t and 0= 9t

A: The velocity is given by            v = r' ur +rθ' uθandThe accerleration is given by        a =r"-r…

Q: Given the vector function: *(t) = (1+ sin (3t), tan (2t), t) Relate the vector functions to the…

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Q: Find curvature of the parametric curve r(t) = (t, t3 – t, 3) at t = 1. Show your work.

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Q: Find the tangential and normal components of acceleration for the position vector denoted by 7 = (t…

A: We have given position vector  t+29,2t,t2 Then, Tangential component of acceleration aT=r't.r''tr't…

Q: Show that along the plane curve x = #1(t)e, +2(t)e2 the curvature is 4.30. [(a)2(5)213/2 a0 + 3

A: The curvature K at a point of a curve defines the speed of rotation of the tangent of the curve at…

Q: A space curve is given by the vector function r(t) = (3t, t² + 6t, t³ ). Then the unit tangent…

A: GIVEN: r(t) = {3t, t2 + 6t, t3}

Q: Find the curvature of the plane curve with equation y (x, f (x)) on the curve, by using the…

A: We will find out the required value of curvature .

Q: 21. r(t) = t³ j + t² k %3D

A: Given  r(t)=t3j+t2k

Q: Let R be a vector function whose graph is smooth curve such that, R(2) =, R'(2) = , and R"(2) =…

A: Radius of curvature of teh function is given by formula, R = (1+y'(x)2)32y''(x)

Q: a) The position of point moving in space is given by R(t) = 3 tan t i + cott j +2 lnt k, find the…

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Q: 2. Calculate the curvature, unit binormal vector and torsion for r(t) (e'cost)i+(e'sint)j +5k

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Q: Consider the following curve 7(1) = (-2sin(e), –V5,2cos() (a) Find the unit tangent vector. (b) Find…

A: The formula to obtain the unit tangent vector for any curve r(t) is given by: The formula to find…

Q: Suppose that C has length 5. What is the value of F. dr if: (a) F(P) is normal to C at all points P…

A: Given: Length of C is 5. (a) F(P) is normal to C at all points P on C. ∫CF→·dr→=∫CFdrcos90°=0…

Q: The normal component of the acceleration vector for an object with position vector r(t) = (cos(t),…

A: To check the given statement for True/False.The normal component of the acceleration vector for an…

Q: If r(t) = , then unit tangent is a principal unit normal is a and its curvature is a vector scalar

A: Explained below

Q: Exercise 10. Show that the curvature of a planar curve which satisfies the equation y = f(r) is…

A: To Show- The curvature of a planar curve, which satisfies the equation y=fx is given by…

Q: 5. Sketch the vector-valued equations r(t)=2costi+3sintj. Then, find the curvature of the ellipse at…

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Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: The intersecting curve of two surfaces is given as follows:

Q: A curve has a vector equation r = ti+ 4 sin(t)j + 4 cos(t)k. Find the curvature, K.

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Q: Find the curvature of the curve r(t) (2t +9) i 10 j + (4 - 1t 4) k %3D 1 K = 21+12 1 + t2 1 к 21 +…

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Q: Calculate the velocity and acceleration vectors, and speed for r(t) = (cos(t), sin(3t), cos(3t))…

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Q: Give the length of a curve given parametrically by x = x(t), y = y(t), and z = z(t) for a ≤ t ≤ b in…

A: given parametrically by x = x(t), y = y(t), and z = z(t) for a ≤ t ≤ b in the vector form.

Q: Find a vector parametrization of the circle of radius 5 in the xy-plane, centered at the origin,…

A: Solution: Given, Circle having center at (0, 0) and radius is 5 and

Q: Find a vector function that represents the curve of intersection of the paraboloid z=7x^2+5y^2 and…

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Q: Show that if r(t) is perpendicular to the tangent vector r′(t) for all t, then the curve r(t) lies…

A: If r(t) is perpendicular to the tangent vector r′(t) for all t, then the curve r(t) lies on a sphere…

Q: Find the velocity and acceleration vectors in terms of u, and ue. r=7 sin 3t and 0= 9t 3Du, +ue V =…

A: Given To determine  the velocity and acceleration vectors

Q: In cylindrical coordinates, a particle has position vector F = rê, + ze = r cos(0)i +rsin(0)j + zk.…

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Q: Find the point on the graph of z = 3x2 + u? at which vector n (24, 2, –1) is normal to the tangent…

A: Gradient of the surface denote the normal direction.

Q: The divergence of a vector D for rectangular coordinate is equal to [1/p / dp (pDp)] + [1/p Dø/dø]+…

A: We have to find divergence in rectangular coordinate

Q: Show that if M" has constant sectional curvature C then Ricci and scalar curvature of M" are Ric =…

A: We know that from given data: If M has a constant sectional curvature C , k. The Uniqueness of this…

Q: The magnitude of the torque t developed by applying a force F at a point with position vector r at…

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Q: Given the points A(x=2, y=3, z=-1) and B(p = 4, 0 = -50°, z = 2), find a unit vector in cylindrical…

A: The given points are A=x=2, y=3, z=-1 and B=ρ=4, ϕ=-50°, z=2. The relation between cartesian and…

Q: Hiwi fined the curvature for each the Fllbwing vector function Pt) =(44,-t, 2f>

A: Curvature of the 3d-vector

Q: Given the parametric equation of a planar curve r(0) e C² , derive the following equation: dn dr =-k…

A: Given, The parametric equation of a planar curve rθ∈C2. To derive- dndθ=-kdrdθ where ndenotes the…

Q: Consider the helix r(t)=(cos(2t),sin(2t),−4t)r(t)=(cos⁡(2t),sin⁡(2t),−4t). Compute, at t=π6t: A.…

A: Given r(t)=cos2t , sin 2t   , -4t      ; t=π6

Q: Consider a particle moving on a circular path of radius b described by               r(t) = b cos…

A: Given position vector is rt=bcosωt+bsinωt.

Q: find the velocity and acceleration vectors in terms ofur and uθ . r = a(1 + sin t) and θ = 1 - e-t

A: The velocity and acceleration in terms of ur→ and uθ→ are given by: v→=r'ur→+r θ'uθ→a→=r''-r…

Q: The velocity of a particle is given in terms of the time t by v = sinti - 2cos(2t)j + t2k   where…

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Q: The magnitude of the torque t developed by applying a force F at a point with position vector r at…

A: First we have to complete the required step by using the correct expression for torque.

Q: Consider the plane curve parametrized by F(1) -i+ (In(com(1)J, Find curvature s(4).

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Q: Calculate the curvature of the vector function when t= -7: 7(t) = (1+ 2t, 7 – 3t, -8 + 5t)

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.