6. A particle moves so that its position vector is given by i =sin 5tî – cos 5tj , where t is the time. Find the angle between the velocity V of the particle and the position vector i.

Q: (9.) r(t) = (1, cos t, 2 sin t)

A: As per your query the solution of question no 9 is given the next step.

Q: r(t) = (sin 7t, t, cos t)

A: The vector equation is r(t)=sinπt, t, cosπt. Here, x=sinπt, y=t, z=cosπt Then x=sinπy, and z=cosπy…

Q: (a) Find the position vector of a particle that has the given acceleration and the specified initial…

A: Solve the following

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

A:

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

A:

Q: The position vector for a particle moving on a helix is  c(t) = (2 cos(t), 4 sin(t), t2).   Find a…

A: The position vector of the particle moving on a helix is given as follows.

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

A: As per given by the question, there are given: a→t=6t, 5sint, cos6tv→0=4, 3, 5r→0=3, -4, -4 Now, For…

Q: 1. Suppose that r(t) = (3 cos(3t) t,3 sin(3t), 5t). %3D a. Determine the velocity, the acceleration…

A: For a position vector r(t), the velocity vector of the r(t)  is given by the first derivative of the…

Q: Q2:- A/ Given a position vector: R (t)= 3 cos ti+3 sin tj+ t2 k find 1- The velocity vector and…

A:

Q: The position vector of a particle moving along a helix is c(t) = (cos(t), sin(t), t²). (a) Find the…

A:

Q: Given that the acceleration vector is a (t) = (-16 cos(-4t), – 16 sin(-4t), –t), the initial…

A:

Q: 3. Consider the following helix with vector equation 7 (t) = 2 cos (t) 7 (t) 7 + tỉ + 2 sin (a)…

A:

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

A:

Q: At time to, a moving particle has the velocity vector v = 7i and the acceleration vector a = 7i +…

A:

Q: 2. Suppose that a motion described by the vector valued function (i.e. position function) r(t) has…

A:

Q: 1. Suppose that r(t) = (3 cos(3t) t,3 sin(3t), 5t). a. Determine the velocity, the acceleration and…

A: For velocity vector diffrenciate displacement vector. And for acceleration vector diffrenciate…

Q: The motion of a point on the circumference of a rolling wheel of radius 3 feet is described by the…

A:

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

A:

Q: Suppose r(t) = cos(nt) i + sin(t) j+ 3tk represents the position of a particle on a helix, where z…

A: Given the vector

Q: 5. Find the parametric equations of the line tangent to the curve C defined by the vector equation…

A: To find the parametric equation of the given tangent to the curve. The vector equation of the curve…

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

A:

Q: The position of a particle is defined by the vector r(t)=⟨sint,cos2t⟩. Find the maximum speed of the…

A: r(t) = ⟨sint,cos2t⟩ Hence, v(t) = ⟨cost,-2sin2t⟩

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

A: We will use integration to go toward position fro acceleration

Q: A particle's position vector is given by: F(t) = R(1+ cos(wot + q cos wot))& + R sin(wnt + q cos…

A:

Q: Suppose r(t) = cos(rt) i + sin(nt) j + 5tk represents the position of a particle on a helix, where z…

A:

Q: 4. Determine the directional derivatives of $(x, y) = tan"2+3 sin ). at the point (1,1) in the…

A:

Q: Find a vector equation for the tangent line to the curve 7(t) = (5 cos(6t)) i + (5 sin(6t)) j+…

A: Given the vector function, r(t), we call r′(t) the tangent vector provided it exists and provided…

Q: 2. Suppose that the position of a particle is r(t) = (cos(nt), ² sin(nt), t), 0≤t≤ 2n. A. Calculate…

A: Understanding of derivative while finding velocity and acceleration from position vector is…

Q: 6. Find the work done by the force F = 31 – 5j in moving an object from the point (2, 2) to the…

A: Given that the force F=3i-5j moving from the point (2,2) to the point (7,-13). We need to find the…

Q: The position vector of a moving point is given as :R(t)=(cos t)i+(sint) j+(t) k ; the distance…

A:

Q: 10. A particle moves in the xy-plane so that the position of the particle is given by x(1) =1+cos t…

A:

Q: Next Consider the two vector-valued functions given by r(t) = (t+1, cos 1+t w(+) = (*, sin() *) . a.…

A: (a) The two vector valued functions intersect if r(a) = w(b) for some t = a and s = b.…

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

A:

Q: Suppose 7(t) = cos(nt) i + sin(at) j+ 3tk represents the position of a particle on a helix, where z…

A:

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

A: We have acceleration, initial velocity, and initial position, and if we integrate acceleration with…

Q: A particle moves through 3-space in such a way that its acceleration is a(t) = 8sin 2ti +8 cos…

A:

Q: Find the tangent, normal, and binormal vector functions for the following three curves:   1:…

A: We have to find the tangent vector, normal vector and bionomial vector function

Q: Let r(t) = (sin 2t ,3t, cos 2t), -n SIST, a) Is speed always constant? b) Show that the velocity and…

A:

Q: Given that r (t) = (5t cos 2t) j- (5t sin 2t) k, is the position vector of a moving particle, find…

A:

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

A:

Q: Find a vector equation for the tangent line to the curve 7(t) = (5 cos(6t)) i + (5 sin(6t)) j +…

A:

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

A:

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

A:

Q: Q3) the position vector of a point is given by: R(t) = cos³t i+ sin³ t j, Find: 1. Coordinates of…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: A particle moves so that its position vector at time t is given by r= et cos ti + e sin tj. Show…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Let r(t) = (sin(2t), 3t, cos(2t)), t E [-T, "] be the position vector of a particle at time t. (a)…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: A particle moves so that its position vector at time t is given by r = e cos ti + e sin tj. Show…

A:

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

A: Topic :- Calculus

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.