Find the positive t when the vector r(t) = (4t, 4t, 5t2 – 6) is perpendicular to r' (t). t =

Q: Find the unit tangent vector at the indicated point of the vector function r(t)=e^(18t) cos t…

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Q: Find the positive t when the vector r(t) = (4t, 4ť, 5t² – 6) is perpendicular to r' (t). -

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Q: Find a vector normal to the plane with the given equation. 3(x – 5) – 5(y – 1) + 10z = 0 n =

A: Consider the equation of the plane passing through a general point Po and with normal vector n.

Q: find the vector function r(t) given r'(t) and the initial condition

A: Solution: The objective is to find the vector function r(t)

Q: Find the tangential component aT of the acceleration vector of a particle moving in the plane with…

A: Application of derivative is used for solving the problem.

Q: Find the derivative of the vector function r(t)=ta×(b+tc), where a=⟨3,−2,−3⟩, b=⟨1,3,−2⟩, and…

A: To find the derivative of the vector function, rt=ta×b+tcWhere, a=3, -2, -3, b=1, 3, -2, and, c=-2,…

Q: I can't find the tangential component of the acceleration

A: The given position vector is,

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: Answer is mentioned below

Q: 4. Let r(t) = (t)i + (t-16t²) ; be the position of a particle in a plane at time t. Find the angle…

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Q: Given the vector function r(t) = (+1, 1-2t², 8t-4), find the are length of this curve on the…

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Q: how would I find the domain of the vector function r(t)=cos(t)i+ln(t)j+1/(t-4)k?

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Q: Sketch the curve represented by the vector-valued function                              r(t) = (t +…

A: Given: The vector-valued function  r(t) = (t + 1)i + (3t − 1)j + 2tk and it gives the orientation of…

Q: Draw the graph of the vector-valued functions (a) for the plane curve, r(t) = 2cost³i + 3sint³j, 0<t…

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Q: find the dot product of a vector function with itself. r(t) is a curve and the magnitude of r(t)=pi…

A: Let  u = a i^ +b j^ be a vector functionthe dot product of u with itself is given byu·u = a i^ +b…

Q: A particle moves in the x – y plane with velocity v=(1-t)î +(4– 2t + t² )j where t is the time and i…

A: As per our guidelines we are supposed to answer only first three subparts of question at a time.…

Q: Find the Tangent vector, the Normal vector, and the Binormal vector (T, N and B) for the curve F(t)…

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Q: -2 -1

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Q: Find the derivative of the vector function r(t) = In(13 – t²)i+ y13+tj– 9e 3 k r'(t) = {

A: The given vector function is                                   r(t)=ln13-t2i+13+tj-9e-3tk

Q: Find the tangential and normal components of the acceleration vector for the curve F(t) = (t²,…

A: Here we have to find the tangential and normal components of the acceleration vector for the curve…

Q: Find the velocity and acceleration vectors in terms of u, and ug. de r= a sin 60 and 4t, where a is…

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Q: Find a vector normal to the plane with the given equation.3(x − 4) − 8(y − 1) + 11z = 0

A: Consider the equation of the plane: 3x-4-8y-1+11z=0.   If equation of the plane has the form:…

Q: Find a vector function that represents the curve of intersection of the paraboloid z = 2a² + 2y² and…

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Q: b. Find the directional derivative of the function f(r, y, z) = re" + ye + ze" at the point (1, 1,…

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Q: nd the increase rate of the scalar V at point P from origin to the point P(12 , 1,11 here V=…

A: As gradient of a scalar function gives the magnitude and direction of rate of change.

Q: Find the directional derivative of the function f(x, y,z) =x-y+2z at the point P(1,2,3) in the…

A: Note:- Let a function f(x, y, z), then Direction Derivative of the function f at point P in…

Q: Find dr Ct) for the vector functions. dt r(t) = (1-2t)it Ct cos t)j -t %3D

A: To find dr(t)/dt

Q: Differentiate the vector-valued function r(t)=⟨sin(t2),4t2−t⟩.

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Q: Find the derivative of the vector function r(t) = In(10 – t) i+ v10+tj+ 8e-8* k r'(t) = (

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Q: h (r, s, t) = ln (3r + 6s + 9t), (1, 1, 1), v = 4i+ 12j + 6k

A: We have hr,s,t=ln3r+6s+9t at 1,1,1 in the direction of v=4i+12j+6k

Q: Find the directional derivative of the function at the given point in the direction of the vector…

A: This is a problem of Vector Calculus.

Q: Q1:(A) What is the angle between the normal vectors to the curve F (1) = (2x² + x + 1)i + (+1)j +rk…

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

A: First solve the given equations for finding the values in terms of x

Q: Find a vector equation of the line tangent to the graph of r(f) at the point Po on the curve. r(1) =…

A: Find the derivative of the function r(t) to find the equation tangent to the graph of the function.…

Q: Find the derivative, r'(t), of the vector function. r(t) = (e-t, 6t – t3, In(t))

A: Solution-  Given vector function  r(t) = (e-t, 6t-t3, ln (t)) We have to differentiate these…

Q: Let r(t) = (e²t, e−³,5t) Calculate the velocity vector and the acceleration vector at t = 0.

A: r(t) = ( e2t , e-3t , 5t ) given  find velocity vector and acceleration vector    velocity vector…

Q: Find the tangential and normal components of the acceleration vector. r(t) = (9 + t)i + (t2 – 2t)j…

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Q: The unit vector tangent to the curve r(t) = (1,41*,3r*) is (a) (0,4/5,3/5). (b) (0,81,6t)

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Q: Determine the tangential (a,) and the normal (aN) components of acceleration of the vector function…

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Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

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Q: (b) Find the directional derivative of the function f(x,y,z) = xy sin z at the point (1,2, %3D T2)…

A: Solution:

Q: For t > 0, a particle moves in the xy-plane with position vector (x (t), y (t)), where x (t) = te-t…

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Q: Find the derivative, r'(t), of the vector function. r(t) = (e-t, 4t - t, In(t) r'(t)

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

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Q: time ?

A: Uploaded question :   The rocket is launched at time t = 0 with r (0)=2i-6j+4k. If the initial…

Q: The position vector in the xy plane is [t2,sin(t)].  What is the distance traveled by the particle…

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Q: Find the tangential and normal components of the acceleration vector. r(t) = 4(3tt³)i + 12t²j aT an…

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Q: Find the derivative of the vector function r(t) = ta x (b + tc), where a = (2,-2, 5), b (2,-5, 3),…

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Q: Find the directional derivative of the function f(x, y) = In(at + y) at the point (- 1, - 2) in the…

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Q: Find the tangent vector of r(t) = (t° , 3tª) at time t = 1. A) (3, 12) B) 15 C) (3, 7) D) 3t2 + 12t3

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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.