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

Q: find a vector normal to the plane with the given equation. x − z = 0

A: Given: Plane: x-z=0 To Find: A vector normal to the given plane

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 velocity and acceleration vectors in terms ofur and uθ . r = 1/θ and dθ/dt = t2

A: Given Data The position vector is r=1/θ. The change in angle vector is dθ/dt=t2=2t.   Integrate the…

Q: 4. For any time t 2 0, if the position of a particle in the xy-plane is given by x = r² +1 and y=…

A:

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

A: Given:

Q: find the velocity and acceleration vectors in terms ofur and uθ .1. r =θ and dθ/dt = 2

A: Given, r=θ and dθdt=2   Find Velocity and acceleration vectors in terms of ur and uθ:

Q: Find the velocity and acceleration vectors in terms of u, and ug- de r= 5e a0 and = 1 dt v-Du, +Duo

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Q: Find the unit tangent vector for the vector function : r(t) = (t2 + 1,3 t, t3> %3D (1+4t2+9t)3…

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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: 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: Let f (x, y) = x 4y-2 and P = (2, 1). Find the unit vector that points in the direction of maximum…

A: Concept: The Unit vector is a quantity which has a magnitude as 1and as well as direction, it is…

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

A:

Q: Find the derivative of the vector function r(t)=ta×(b+tc) where a=⟨−4,−3,5⟩ b=⟨−1,2,5⟩ and…

A: Solved below

Q: Find the velocity and acceleration vectors in terms of u, and ug- de r=a cos 20 and == 5t, where a…

A:

Q: What is the directional derivative of the function f(x, y, z) = 2xy + z² at the point (1, –1,3) in…

A: The Directional Derivative: Let the function f(x, y) be the height of a mountain range at each point…

Q: Determine the rate of change at (0, 2) of the function 1 h (x, y) V1+x² + 2y² in the direction of…

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Q: Find the tangential and normal components of the acceleration vector. r(t) = 5(3t − t3) i + 15t2 j…

A:

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: Again just working on examples for exam, would like to see how you solve this to see if it is the…

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Q: Find the velocity and acceleration vectors in terms of u, and ug- do r= a(7 - sin 0) and =7, where a…

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Q: Determine if the vector filed is conservative and if so find the potential function F (x, y) = 12xyi…

A:

Q: The vector equation for the curve of intersection of the surfaces x = y² and z = y in terms of the…

A:

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 the acceleration vector for the position vector r(t) = (sin(11t), 4tº, e -2t). x component = y…

A: We need to find acceleration vector.

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

A:

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 a unit vector in the direction in which f(x, y) = 6 cos(x – 5y) decreases most rapidly at P and…

A: Given, fx,y=6cosx-5y Find the unit vector and rate of change of f at P.

Q: For time t > 0, the position of a particle moving in the xy-plane is given by the vector (, et).…

A: Position of particle = (1/t, e3t) Velocity = derivative of position of particle = (-1/t2 , 3e3t)

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

A:

Q: find the velocity and acceleration vectors in terms ofur and uθ . r = a(1 - cos θ) and dθ/dt = 3

A: Velocity is defined as the rate of displacement. Acceleration is known as the rate of change in…

Q: The position of a particle moving in the xy-plane is given by the vector (4t, y(2t)), where y is a…

A:

Q: Find a vector parallel to the plane 2x - y - z = 4 and orthogonal to i + j + k

A: Given:A plane 2x - y - z = 4 orthogonal to i + j + k

Q: 2. For a non-zero vector ü(t), show that 1 dü dt u| dt dû dt where û is the unit vector in the…

A: Let u→ be the vector and |u |→ is the magnitude of u.→ unit vector u⏜ is given by:  u^=u→|u→|…

Q: Find the directional derivative of o = x2 + 2xyz – yz? at the point (1, 1, 2) in the direction of…

A:

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: A body is spiraling upward due to rapidly rising air on a path similar to that of a helix and having…

A: Consider the position vector.

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

A:

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…

A:

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

A:

Q: The directional derivative of f(x, y, z) = x? + y? + 4xz at Po(1,-2,2) in the direction of the…

A:

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

A:

Q: What is the directional derivative of f(x, y) = 4xy+ y cos x at the point (0, 1) in the direction of…

A:

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

A:

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

A:

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.