A heat-seeking particle is located at the point (2, 3) on a flat metal plate whose temperature at a point (x, y) is T(x, y) = 10 – 8x? - 2y? Find an equation for the trajectory of the particle if it moves continuously in the direction of maximum temperature increase.

Q: Find the gradient of the function f(x,y) = 4y - 9x at the point (9,3). Then sketch the gradient and…

A:

Q: Consider the curve in the xy-plane represented by the two equations below. The slope of the line…

A: Given: x=et……1y=te-t……2 where t≥0   To find: Slope of line tangent at x=3

Q: If f(x, y, z) = x² +y² – 4.xz, find the rate of change of f at P(3, 1, –2) in the direction from P…

A:

Q: ds The position of a particle at time t is given by s. Find the velocity dt 4 - 5st + 2t - 7t= 0

A:

Q: Suppose that the temperature in a given region is given by T(x,y)=200xy(1-x2-2y2). Suppose that you…

A:

Q: A particle moves along the curve y=x3-x. If vx = 2 ft/sec and ax= -3 ft/sec2 as the particle passes…

A:

Q: t^2 y^′′+aty^′+by=0, t>0 Define what type of equation is  mentioned above ?

A:

Q: 1. A particle moves along the x-axis according to the equation x-2+3F, where x is in m and is in…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: The position of a particle in the xy-plane at time t is r(t) = (t+2) i+ (t- + 3) j Find an equation…

A:

Q: Consider the curve defined by x2y + 3x + y2 = 38. a. Find dy/dx dy dx .   b. Find an equation of…

A:

Q: A point moves along a straight line (xy) so that its distance s(cm) from the point x at time t(sec)…

A:

Q: 2. Suppose that a particle is moving along the curve 4x? + 16y² = 32. When it reaches the point (2,…

A:

Q: 23. Find all points of inflection of the curve y=2r – 12r² + 10x+3. A) x=-1 and x= 1 B) x=-1 C) x=-1…

A: As per our guidelines we are supposed to answer only one asked question.kindly repost other…

Q: Cvaluate (xy) s ds where C is the curve y = x², for 0 < x < 2.

A:

Q: 2. Let f(r,y) = n: Find the maximum rate of change of f(r, y) at the point (4, 1) and the direction…

A: Given the given function is fx,y=xx-y and the point is 4,1. Apply formula for the maximum rate of…

Q: :a stream function is given by: Y=2x²y + (x+t)y2 Find the velocity equation for flu me = 1s?

A:

Q: Find the linearization of the function f(x, y) = /36 – læ² – 2y² at the point (3, -1). L(x, y) = Use…

A:

Q: 21. A particle follows the trajectory x(t) 4 t3 +2t, y(t) = 201 – 12 with t in seconds and distance…

A: The trajectory of particle is given as

Q: Find the maximum rate of change of the the function 80 f(x, y, z) = 1+g² + 2y? + 3z² %3D at the…

A:

Q: The tank in the form of a right-circular cone of radius 11 feet and height 15 feet standing on its…

A: Given: Let us consider the right-circular cone, Radius=11 feet Height=15 feet and circular hole of…

Q: %3D Find the equation of the tangent line at (1, 1) of 6x²y- ncos(y) = 7m y= -2nx +3T B y=2nx+3n C.…

A: Solving the problem by doing the derivative and then calculate the equation of tangent line.

Q: The temperature at a point (x, y, z) is given by T(x,y,z) = 200 e-x- 3y-9z) where T is measured in…

A:

Q: A) The position of a particle P(x, y) at time t is given by: (2t + 3)7 y +t . Find the distance it…

A:

Q: tiny, no bug lands on a piece of graph paper and walks along a path so that t minutes after it…

A: Increasing function

Q: Find the linear approximation to the equation f(r, y) = 4 ln(z – y) at the point (2,15,0), and use…

A: Given: fx,y=4lnx4-y We have to find the linear approximation in two variables.

Q: Find the direction in which the function g(x, y) = cos(xy) decreases fastest at the point (1, pi)

A:

Q: The terrain of a mountainous area can be described by the surface z = e*Y + x+ 2y + 2. Here z is…

A: For a function, y=f(x), the value of y is calculated by substituting the value of x in the function,…

Q: Find the coordinates of the point(s) at which the curve y = x-2/3 has gradient – 1/6. %3D -

A:

Q: 3c The gradient of the curve which passes through the point (2,12) is given by 5x + 7 dy dx Find the…

A: The solution is given as

Q: dy of the curve yln x + 5x² + y' = 13 at the point (1,2) dx b) Find

A:

Q: A particle leaves the origin with its initial velocity given by v=23.8i - 143 m/s, undergoing…

A: Topic = Algebra

Q: A heat-seeking particle has the property that at any point (x, y) in the plane, it moves in the…

A:

Q: Suppose that the temperature in a given region is given by T(x,y)=200xy(1-x2-2y2) . Suppose that you…

A: Given that,Temperature in a given region is given byTx, y=200xy1-x2-2y2You and your friend are at…

Q: A particle moves counterclockwise around the ellipse with equation 9x? + 16y² = 25. a) At what rate…

A:

Q: The temperature T in a square region of the (x, y) plane is given by the formula T(x, y) = 2 y – x +…

A: To find- the steepest descent in temperature.  The curve the ant should move is At=xt, yt. This…

Q: If a curve f(x) has dx dy = (y – 1)2(2+ x) and passes through the point (-1,2), then what is the…

A:

Q: A particle moves along a straight line with velocity function v(t) = 8sin (t)- 4cos(t) and its…

A: Just integrate the velocity function and find the value of integration constant with the given…

Q: A spring of constant k=8 N/m hanging from the ceiling is placed at its lower end with an object of…

A:

Q: Find the position of the particle at time t=4. Is the particle moving toward the origin or away from…

A: If the velocity function is given then by integration we will calculate the position of the particle…

Q: y(t) = eBook equation subject to the indicated initial conditions. y" + 8y' + 17y= 8(t - 4n), y(0) =…

A: We have to solve the given problem.

Q: 2. Find for the curve dx x²y3 – 2xy = 6x² + 2y³ + 1 -

A:

Q: Determine the linearization of y = 4 – 2x at (1, 2). Then use it to approximate the value of y when…

A: It is given that, y=4-2x2  at 1,2 we have to determine the linearization of function. Then use it to…

Q: termine the equation of the tangent line to the curve y=Vx at the point (1, A) x-4y+3=0 в) х+4у-3-0…

A: we have to find equation of tangent

Q: The temperature at the point (x, y) on a metal plate is modeled by T(x,y)=4e^−(x²+y)/2,x≥0,y≥0. (c)…

A: Given: The temperature at the point x,y on a metal plate is modeled by Tx,y=4e-x2+y2, x≥0, y≥0 To…

Q: Find the directions in which f(r, y) = (r+y-2)2+(3x- y- 6)?, increase and decrease most rapidly at…

A:

Q: A particle moves on a coordinate line with acceleration a = d2s/dt2 = 15√t - (3/√t), subject to the…

A: Given that, a=d2sdt2=15t-3t

Q: 4. What is the direction in which the function f(x, y) = yx² -- decreases most rapidly at the point…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the direction at which the function f (x, у, 2) %3 хIn(е' — хг) increases fastest at (-3,0,0)

A:

Q: Suppose that the temperature in a given region is given by T(x,y)=200xy(1−2x2−y2). Suppose that you…

A: We need to find instantaneous rate of change of temperature in a direction and multiply it by speed…