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An ant is crawling on a hot plate and z= T(x,y) gives the temperature on the...
The temperature at point (x,y) on a metal plate is T(x.y) 16x -16xy+4y.An ant on the...
The temperature at point (x,y) on a metal plate is T(x.y) 16x -16xy+4y.An ant on the plate walks around the The minimum temperature isdegrees. The maximum temperature isdegrees. are the highest and
Given z = 2(x,y),X = x(s,t),y = y(s,t), and zx(-1,1)= 3, zy(-1,1)= 2, xs(-1,1)= -1, x,(-1,1)=...
Given z = 2(x,y),X = x(s,t),y = y(s,t), and zx(-1,1)= 3, zy(-1,1)= 2, xs(-1,1)= -1, x,(-1,1)= 3, ys(-1,1)= 1, z (1,2)=5, z (1,2)=3, x(1,2)= -1, y(1,2)= 1, y,(-1,1)= 4, xs(1,2)=3, xx(1,2)= -2, x(-1,1)= 1, y(- 1,1)=2, 7(1,2)=7, vs(1,2)=2, a. compute ( cas ? )ats = 1,t =2, b. if we plot the surface Z as a function of 5 and t, then at the point (1,2) in the st-plane, how fast is Z changing in the direction (-1,1) in the...
The concentration of salt in a fluid at (x,y,z) is given by F(x,y,z) = x6 + y3 + x2z2 &n...
The concentration of salt in a fluid at (x,y,z) is given by F(x,y,z) = x6 + y3 + x2z2 mg/cm3. Suppose you are at the point (−1, 1, 1). (a) In which direction should you move if you want the concentration to increase the fastest? Give your answer as a vector. (b) You start to move in the direction you found in part (a) at a speed of 7 units/sec. How fast is the concentration changing? Give an exact answer.
PLEASE DO LETTER d.) PLEASE DO LETTER f.) The plane from e.) is 4(x-2)+6(y-1)+(z-1)=0 or 4x+6y+z=15...
PLEASE DO LETTER d.)
PLEASE DO LETTER f.)
The plane from e.) is 4(x-2)+6(y-1)+(z-1)=0 or 4x+6y+z=15
15. The temperature on an unevenly heated metal plate positioned in the first quadrant of the xy-plane is given by 25xy + 25 C(x, y) = 7 (x - 1)2 + (y - 1)2 +1° Assume that temperature is measured in degrees Celsius and that x and y are each measured in inches. (Note: At no point in the following questions should you expand...
true or false is zero. F 9. The plane tangent to the surface za the point (0,0, 3) is given by the equation 2x - 12y -z+3-0. 10. If f is a differentiable function and zf(x -y), then z +. T 11. If...
true or false
is zero. F 9. The plane tangent to the surface za the point (0,0, 3) is given by the equation 2x - 12y -z+3-0. 10. If f is a differentiable function and zf(x -y), then z +. T 11. If a unit vector u makes the angle of π/4 with the gradient ▽f(P), the directional derivative Duf(P) is equal to |Vf(P)I/2. F 12. There is a point on the hyperboloid 2 -y is parallel to the plane...
The concentration of salt in a fluid at (x,y,z) is given by F(x,y,z)=x^2+y^4+2x^2z^2 mg/cm3 You are at the point (1,1,...
The concentration of salt in a fluid at (x,y,z) is given by F(x,y,z)=x^2+y^4+2x^2z^2 mg/cm3 You are at the point (1,1,1). a. In which direction should you move if you want the concentration to increase the fastest? b. You start to move in the direction you found in part (a) at a speed of 4 cm/sec. How fast is the concentration changing?
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.
(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...
The concentration of salt in a fluid at (x,y,z) is given by F(x,y,z)=x^2+y^4+2x^2z^2 mg/cm3 You are at the point (1,1,1...
The concentration of salt in a fluid at (x,y,z) is given by F(x,y,z)=x^2+y^4+2x^2z^2 mg/cm3 You are at the point (1,1,1). a. In which direction should you move if you want the concentration to increase the fastest? I keep getting <5,2,8> for this answer and it says it is incorrect You start to move in the direction you found in part (a) at a speed of 4 cm/sec. How fast is the concentration changing?
If z = f(x,y), where f is differentiable, and x = g(t) y = hết) g(3)...
If z = f(x,y), where f is differentiable, and x = g(t) y = hết) g(3) = 2 h(3) = 7 g'(3) = 5 h'(3) = -4 fx(2,7) = 6 fy(2,7) = -8 Find dz/dt when t = 3.
The temperature at point (x,y) on a metal plate is T(x.y) 16x -16xy+4y.An ant on the plate walks around the The minimum temperature isdegrees. The maximum temperature isdegrees. are the highest and
Given z = 2(x,y),X = x(s,t),y = y(s,t), and zx(-1,1)= 3, zy(-1,1)= 2, xs(-1,1)= -1, x,(-1,1)= 3, ys(-1,1)= 1, z (1,2)=5, z (1,2)=3, x(1,2)= -1, y(1,2)= 1, y,(-1,1)= 4, xs(1,2)=3, xx(1,2)= -2, x(-1,1)= 1, y(- 1,1)=2, 7(1,2)=7, vs(1,2)=2, a. compute ( cas ? )ats = 1,t =2, b. if we plot the surface Z as a function of 5 and t, then at the point (1,2) in the st-plane, how fast is Z changing in the direction (-1,1) in the...
PLEASE DO LETTER d.)
PLEASE DO LETTER f.)
The plane from e.) is 4(x-2)+6(y-1)+(z-1)=0 or 4x+6y+z=15
15. The temperature on an unevenly heated metal plate positioned in the first quadrant of the xy-plane is given by 25xy + 25 C(x, y) = 7 (x - 1)2 + (y - 1)2 +1° Assume that temperature is measured in degrees Celsius and that x and y are each measured in inches. (Note: At no point in the following questions should you expand...
true or false
is zero. F 9. The plane tangent to the surface za the point (0,0, 3) is given by the equation 2x - 12y -z+3-0. 10. If f is a differentiable function and zf(x -y), then z +. T 11. If a unit vector u makes the angle of π/4 with the gradient ▽f(P), the directional derivative Duf(P) is equal to |Vf(P)I/2. F 12. There is a point on the hyperboloid 2 -y is parallel to the plane...
If z = f(x,y), where f is differentiable, and x = g(t) y = hết) g(3) = 2 h(3) = 7 g'(3) = 5 h'(3) = -4 fx(2,7) = 6 fy(2,7) = -8 Find dz/dt when t = 3.
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