Let T(x,y)=6xy be the temperature at point (x,y). A snail craws so that its position after...

Question

Question

Let T(x,y)=6xy

be the temperature at point (x,y). A snail craws so that its position after t seconds is given by

x=1+t and y=2+13t

How fast is the temperature rising on the snail's path after 3 second?

math calculus

Answer 1

Answer #1

Tay = 6xy x=1tt, y= 2413 € After 3 second x= 143= 4 y= 2+13 43= 41 - du dt & dy =13 dt D 24 To find 1t=3 Tony = bny Te (x,y)

Answer 2

Similar Homework Help Questions

The temperature at a point (x, y) is T(x,y), measured in degrees Celsius. A bug crawls...

The temperature at a point (x, y) is T(x,y), measured in degrees Celsius. A bug crawls so that its position after t seconds is given by x = 4 + t, y = 8 where x and y are measured in centimeters. The temperature function satisfies Tx(5, 9) = 2 and Ty(5, 9) = 7. How fast is the temperature rising on the bug's path after 21 seconds? Step 1 We know that the rate of change of the temperature...
A snail moves from a location with position vector r1,x = 1.33 m and r1,y =...

A snail moves from a location with position vector r1,x = 1.33 m and r1,y = -2.79 m to another location, with position vector r2,x = 3.57 m and r2,y = -4.41 m. The trip takes 304 seconds for the snail to finish. What are the components and the magnitude of the snails average velocity, in meters per second? 1) v av,x = 2) v av,y = 3) |v av|
(a) The temperature T(x, y) at a point (x, y) on a plate is given by T(x, y) = 16 − x 2 − 2y 2 . ...

(a) The temperature T(x, y) at a point (x, y) on a plate is given by T(x, y) = 16 − x 2 − 2y 2 . i. What is the direction of greatest increase in temperature at the point P = (1, 3)? [3 marks] ii. What are the directions of zero change in temperature at the point P? [4 marks] iii. Find the path of greatest increase in temperature from the point P to the point of maximum...

An object is moving in the xy-plane and its position after t-seconds is r(t)-t 2, t2...

An object is moving in the xy-plane and its position after t-seconds is r(t)-t 2, t2 - 2t>. (a) Find the position of the object at time t-5. C 3 15 (b) At what time is the object at the point (O, 0)? t- (c) Does the object pass through the point (4, 28)? Yes 0 No (d) Find an equation in x and y whose graph is the path of the object.
Scoring (x, y) = 20x* +6xy +12 y, determine the stress components at point 1. Given...

Scoring (x, y) = 20x* +6xy +12 y, determine the stress components at point 1. Given the stress function a (2, 3) (15 points) page 1
4. A particle moves along the curve y = A12 so that its position is given...

4. A particle moves along the curve y = A12 so that its position is given by x = Bt. (a) Find the position vector of the particle in the form 式t) = x(t) + y(t) j (b) Calculate the speed u = of the particle along this path at an arbitrary instant t.

(8 points) The temperature at a point (x, y, z) is given by T(x, y, z)...

(8 points) The temperature at a point (x, y, z) is given by T(x, y, z) = 1300e-x-2y-2? where T is measured in °C and x, y, and z in meters. 1. Find the rate of change of the temperature at the point P(2, -1, 2) in the direction toward the point Q(3,-3,3). Answer: Dp S(2.-1, 2) = 2. In what direction does the temperature increase fastest at P? Answer: 3. Find the maximum rate of increase at P. Answer:
2. Let f(x,y) = 2x2 - 6xy + 3y2 be a function defined on xy-plane (a)...

2. Let f(x,y) = 2x2 - 6xy + 3y2 be a function defined on xy-plane (a) Find first and second partial derivatives of (b) Determine the local extreme points off (max., min., saddle points) if there are any. (c) Find the absolute max. and absolute min. values of f over the closed region bounded by the lines x= 1, y = 0, and y = x
A particle moves along a straight line so that its position after seconds is given by...

A particle moves along a straight line so that its position after seconds is given by where measures the distance from the starting point in inches. On which time intervals is the particle moving in a positive direction? Find each open interval where the function f ( x ) = x x 2 + 1 is concave upward. At what -value(s) does have an inflection point?

The temperature at a point (x, y, z) is given by T(x, y, z) = 100e?x2 ? 3y2 ? 7z2 where T is...

The temperature at a point(x, y, z)is given byT(x, y, z) = 100e?x^2 ? 3y^2 ? 7z^2where T is measured in °C andx, y, zin meters.(a) Find the rate of change of temperature at the point P(2, ?1, 2) in the direction towards the point(3, ?2, 3).(b) In which direction does the temperature increase fastest at P?(c) Find the maximum rate of increase at P.