The position of a particle moving in the xy-plane is given by the vector (4t, y(2t)), where y is a twice-differentiable function of t At time t ,what is the acceleration vector of the particle? (3, 2y" (1)) (6, 4y" (1)) B (12, 2y"(1)) (12, 4y"(1))

Q: 4. Find the directional derivative of f in the direction of vector v at point (1,3) such that v =…

A:

Q: Consider the curve y = 10 + 4x − x^(2) at (x, y) = (3, 13). Find a vector, v, that has length 4 and…

A: Given the curve y=10+4x-x2 at (x,y)=(3,13).

Q: 6. Find the unit vector for which the directional derivative Duf(x,y) of f(x,y) = %3D 3x2 + 4y2 at…

A:

Q: 2. Suppose that f (1,2)= 3 and that the directional derivative of fat point (1,2) in the direction…

A: Given that f1,2=3 and the directional derivative of f at point (1,2) in the direction of the vector…

Q: Find the directional derivative of f(x, y, z) = z3 – x²y at the point (5, -2, -2) in the direction…

A:

Q: Find a vector which is tangent to the curve of intersection of the surfaces z = x² – y? and xyz + 30…

A: We will find out the required tangent vector.

Q: An object is moving in the xy-plane along a path whose curvature at time t is given by the function…

A:

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3x sin(zy)…

A: The maximum rate of change of a function f(x, y) at (a, b) occurs in the direction ∇f(a, b)  where…

Q: 2. Suppose that f (1,2) = 3 and that the directional derivative of ƒat point (1,2) in the direction…

A:

Q: Find a vector equation of the normal line (the line orthogonal to the surface) for the surface…

A:

Q: Explain why the family of vector-valued functions that are the antiderivatives of a vector-valued…

A: The family of vector-valued functions that are antiderivatives of a vector-valued function will…

Q: Calculate the instantaneous rate of change of g at the point (4, 1,2) in the direction of the vector…

A: Instantaneous rate of change of a function g in the direction of a vector v is  =∇g.vv Maximum rate…

Q: Find the increase rate of the scalar V at point P from origin to the point P(2,6; 9,8 ; 9,5) where…

A: According to question given that The origin to the point P(2,6 ;9,8 ; 9,5) where V=3, 3xy+ 2, 6xyz

Q: Find the maximum rate of change of f(x, y, z) = x + y/z at the point (-3, -1, 3) and the direction…

A: As per honor code, we are entitled to solve only one question at a time so I am providing the same.…

Q: Find the velocity vector in terms of u, and ue- T=2 cos 2t and 0= 4t %3D O A. v= (4 sin 2t)u, + (8…

A:

Q: The divergence of the vector G=i+siny j + 3k is :- -8y x3 + siny -8y x3 + cosy Option 1 Option 3…

A:

Q: Find the maximum rate of change of f(x,y, z) = r + y/z at the point (-1, -3, 5) and the direction in…

A:

Q: 1. Find a vector which is tangent to the curve of intersection of the surfaces z = x2 – y? and xyz +…

A:

Q: Prove that the vector given by (sin ysinh x + cos ycosh x) i + (cos y cosh x- sin ysinh x) j is a…

A:

Q: Consider a closed rectangular box with dimensions xx  ft by  yy  ft by zz ft. If xx  is increasing…

A: Proceed as shown

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) : 5x sin(xy)…

A:

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A:

Q: Suppose ƒ is differentiable at (9, 9), ∇ƒ(9, 9) = ⟨3, 1⟩, and w = (1, -1). Compute the directional…

A: Given that ∇ƒ(9, 9) = ⟨3, 1⟩. Note that w = (1, -1) is not a unit vector. Its unit vector along same…

Q: 5. Compute the directional derivative and gradient of f(x, y, z) = 4x – y²e3xz at (2, – 1, 0) in the…

A: Gradient of vector function For a given vector f(x, y, z) the gradient vector denoted by ∇(f) is […

Q: an object is moving in 3-dimensional space with velocity vector v(t)=(sin(t),t,t^2) starting at…

A: Consider the given velocity vector: vt=sint,t,t2 Find the position vector: Integrate velocity vector…

Q: The diagram shows a small block B, of mass 0.2kg, and a particle P, of mass 0.5kg, which are…

A:

Q: Find the maximum rate of change of f(x, y) = ln(x² + y²) at the point (3, 5) and the direction in…

A: Here is the solution of the given problem. Unit Direction:

Q: It is known that the acceleration vector for a particle is given by A(t) = 4j + 2tk. Determine the…

A: We need to determine vector equation of curve traced.

Q: Find the direction in which the maximum rate of change occurs for the function f(z,9)2zsin(ay) at…

A:

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: The given function is: f(x,y)=8yx

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: The objective is to find the maximum rate of change of f at the given point and the direction in…

Q: In what direction from the point (1,-1) is the instantaneous rate of change of 22 f(x,y) = 3x* –…

A:

Q: Find the maximum rate of change of f(x, y) Maximum rate of change: = In(x² + y?) at the point (3, 1)…

A:

Q: 3. At point (1,0,3) on the surface f(x,y) = 2x^2 + 3 y^2+ z^2-11, the directional derivative in the…

A:

Q: Find the two-unit vectors that are parallel to the tangent line to the curve y =x2sin(x) at the…

A:

Q: 2. If a particle moves in the xy-plane so that at any time t > 0, its position vector is (In(r² +…

A: Solution-

Q: Find a vector equation for the tangent line to the curve of intersection of the cylinders x2+y2=25…

A:

Q: If f(x,y) = ln(xy) + x^2y^2, how do I calculate the second directional derivative of f in the…

A:

Q: Find the maximum rate of change of f(x, y) = ln(x² + y²) at the point (5, 2) and the direction in…

A: As per bartleby guidelines, for more than one questions only 1st one is to be answered. Please…

Q: (a) What is the maximum directional derivative of g(x, y) = y²e2¤ at (2, – 1) and in the direction…

A:

Q: Find the maximum rate of change of f(x, y) = In(x² + y²) at the point (1, -4) and the direction in…

A: Here, the given function is: f(x,y)=ln(x2+y2)

Q: Find the directional derivative of the function: f(x, y) = ez² + 4y at the point (0, 0) in the…

A:

Q: Find a vector normal to the cylinder x2 + z2 = 8 at (2, 0, 2) by finding the gradient of the…

A:

Q: Find a nonzero vector normal to the plane z − 5(x − 1) = −2(3 — y). - -

A:

Q: Find a vector tangent to the curve of intersection of the two cyclinders x2 +y? = 200 and y? + z2 =…

A:

Q: 3 If f(x, y) = x³ + y² − 1, then the directional - derivative at the point (-1,2) in the direction…

A: A detailed solution is given below.

Q: Find the maximum rate of change of f(x, y) = In(x² + y²) at the point (3, 5) and the direction in…

A: This is a problem related to the derivative of the function. For calculating the maximum rate of…

Q: Find the direotional derivative of the scalar function f-x'+ y' +2z', at the given point (1,1,2), in…

A: Explanation of the answer is as follows

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A:

Q: nit vector that is parallel to the

A: Here have to find the unit vector that is parallel to the line tangent to the parabola y = x2 at the…

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.