The temperature at each point x y of a metal plate is given

Reference no: EM13371381

The temperature at each point (x, y) of a metal plate is given by

T(x,y) = 1 + x² + 3/2y²

The path of a heat-seeking particle on the plate is a curve r(t) = (x(t), y(t)) such that for each t, the velocity e(t) of the particle at time t is in the direction of the fastest increase of the temperature Tat r(t). Suppose that particle starts at the point (1,1) with speed |r'(1)| = 8 units.

(a) Determine the equation for 9(t) thus obtaining differential equations for the functions x(t) and y(t). What initial conditions do these functions satisfy at t = 0?

(b) Use part (a) to find explicitly the functions x(t) and y(t) and thus the path r(t).

Reference no: EM13371381

Questions Cloud

1 find the currents i1 and i2 for the following circuit : 1. find the currents i1 and i2 for the following circuit given the values shown in the table below. the operating

Keyboards microphones and mice have generally been used as : keyboards microphones and mice have generally been used as the standard input devices for most computer systems. the

Management theories are all about the application of those : management theories are all about the application of those theories to management problems such as scientific theory

1 the distribution of the weights of the packages received : 1. the distribution of the weights of the packages received by a parcel service is normal. nine packages are randomly

The temperature at each point x y of a metal plate is given : the temperature at each point x y of a metal plate is given bytxy 1 x2 32y2the path of a heat-seeking particle on

1 complete the partial code provided with this lab that : 1. complete the partial code provided with this lab that implements a simple group communication application using

1the driver of a truck loaded with 900 boxes of books will : 1the driver of a truck loaded with 900 boxes of books will be fined if the total weight of the boxes exceeds 36450

Problem 11 there is a formula for sample size n with given : problem 11. there is a formula for sample size n with given margin of error m and condence level c for population

In 1936 statistician and geneticist ra fisher reanalyzed : in 1936 statistician and geneticist r.a. fisher reanalyzed mendels famous pea data and using the chi-square statistic

User Account

All Pages