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(20p) The temperature function T(x,y) is defined as T(x,y) = cos(-) at a specified location. Here...
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...
Let T(x,y) denote the temperature at location (x,y). You are given the following information. • The...
Let T(x,y) denote the temperature at location (x,y). You are given the following information. • The rate of change of T at the point A(1,2) in the direction ~ w = ˆ i + ˆ j is √8. • The rate of change of T at the point A(1,2) in the direction ~ v = 4ˆ i −3ˆ j is 6. • The temperature at A(1,2) is 20. (a) From the point A(1,2), in which direction would you head to...
Consider the following function 6 f(x, y,z)=z - x? cos(my) + xy? (i) Find the gradient...
Consider the following function 6 f(x, y,z)=z - x? cos(my) + xy? (i) Find the gradient of the function f(x, y, z) at the point P,(2,-1,-7). (ii) Find the directional derivative of f(x, y, z) at P,(2,-1,-7) along the direction of the vector ū = 2î+j+2k. (iii) Find the equation of the tangent plane to the surface given below at the point P,(2,-1, -7). 6 :- xcos(ty) + = 0 xy
Let f(x, y, z) = xeyz – cos(x2 – y2 + 22) a) Find the directional...
Let f(x, y, z) = xeyz – cos(x2 – y2 + 22) a) Find the directional derivative of f at the point (0,0,0) toward the point (1,2,0). b) Find the maximum rate of change of f at point (0,0,0). In which direction does the max rate of change at (0,0,0) does occur? (two questions here!)
Pt 3. The temperature (in C) at the point (r, y) (r and y are measured in em) is T(r.y). A bug cr...
pt 3. The temperature (in C) at the point (r, y) (r and y are measured in em) is T(r.y). A bug crawls along a path (see the picture below) from left to right toward the point P V T(P) (a) Find the directional derivative of the temperature at the point P in the direction of the bug's travel if the angle between this direction and VT(P) (the gradient of T at P) is r/3 and /VT(P)I-5 (b) At the...
Please solve the question clearly so I can read your handwriting. Thanks, Consider the function representing...
Please solve the question clearly so I can read your
handwriting. Thanks,
Consider the function representing the temperature field
T(x,y,z) = 2e22 cos TX – 10y Find the following: (i) the direction in which the temperature T is increasing most rapidly at point P(-1,1,0) and the magnitude of the rate of increase; (ii) the unit vector normal to the level surface T(x, y, z) = -12 at point P(-1,1,0); (iii) the rate of change of the temperature T at point...
A ship moves in space along the trajectory: rt,t,t]. The air pressure in this medium is given by ...
A ship moves in space along the trajectory: rt,t,t]. The air pressure in this medium is given by P(x,y,z)-e (cos(x ty)+1) a) Calculate the velocity vector of this trajectory b) Calculate the derivative of P in the direction of displacement of the trajectory r (t) at point P: (1,1,1) c) In which direction does the pressure at the point P: (1,1,1) increase fastest? d) What is the maximum rate of change of pressure in P (1, 1,1)?
A ship moves...
The function y(x, t) = (18.0 cm) cos(TX-27mt), with x in meters and t in seconds,...
The function y(x, t) = (18.0 cm) cos(TX-27mt), with x in meters and t in seconds, describes a wave on a taut string, what is the transverse speed for a point on the string at an instant when that point has the displacement y = +15.0 cm?
,Two random processes are defined by Y(t)-X(t) cos(wot) where X(t) and Y(t) are jointly wSs. a) I...
,Two random processes are defined by Y(t)-X(t) cos(wot) where X(t) and Y(t) are jointly wSs. a) If θ is a constant (non-random), is there any value of θ that will make Yl(t) and Y(t) orthogonal? b) if θ is a uniform r.v., statistically independent of x(t) and Y(t), are there any conditions on θ that will make Yı(t) and Y2(t) orthogonal?
,Two random processes are defined by Y(t)-X(t) cos(wot) where X(t) and Y(t) are jointly wSs. a) If θ is...
6. The temperature at (x,y) is T(x,y) = 20 + 100%+++") degrees (in Celsius). A bug...
6. The temperature at (x,y) is T(x,y) = 20 + 100%+++") degrees (in Celsius). A bug carries a tiny thermometer along the path c(t) = (cos(t - 2), sin(t -- 2)) where t is in seconds. What is the initial rate of change of the temperature t = 0.6s?
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...
Consider the following function 6 f(x, y,z)=z - x? cos(my) + xy? (i) Find the gradient of the function f(x, y, z) at the point P,(2,-1,-7). (ii) Find the directional derivative of f(x, y, z) at P,(2,-1,-7) along the direction of the vector ū = 2î+j+2k. (iii) Find the equation of the tangent plane to the surface given below at the point P,(2,-1, -7). 6 :- xcos(ty) + = 0 xy
Let f(x, y, z) = xeyz – cos(x2 – y2 + 22) a) Find the directional derivative of f at the point (0,0,0) toward the point (1,2,0). b) Find the maximum rate of change of f at point (0,0,0). In which direction does the max rate of change at (0,0,0) does occur? (two questions here!)
pt 3. The temperature (in C) at the point (r, y) (r and y are measured in em) is T(r.y). A bug crawls along a path (see the picture below) from left to right toward the point P V T(P) (a) Find the directional derivative of the temperature at the point P in the direction of the bug's travel if the angle between this direction and VT(P) (the gradient of T at P) is r/3 and /VT(P)I-5 (b) At the...
Please solve the question clearly so I can read your
handwriting. Thanks,
Consider the function representing the temperature field
T(x,y,z) = 2e22 cos TX – 10y Find the following: (i) the direction in which the temperature T is increasing most rapidly at point P(-1,1,0) and the magnitude of the rate of increase; (ii) the unit vector normal to the level surface T(x, y, z) = -12 at point P(-1,1,0); (iii) the rate of change of the temperature T at point...
A ship moves in space along the trajectory: rt,t,t]. The air pressure in this medium is given by P(x,y,z)-e (cos(x ty)+1) a) Calculate the velocity vector of this trajectory b) Calculate the derivative of P in the direction of displacement of the trajectory r (t) at point P: (1,1,1) c) In which direction does the pressure at the point P: (1,1,1) increase fastest? d) What is the maximum rate of change of pressure in P (1, 1,1)?
A ship moves...
The function y(x, t) = (18.0 cm) cos(TX-27mt), with x in meters and t in seconds, describes a wave on a taut string, what is the transverse speed for a point on the string at an instant when that point has the displacement y = +15.0 cm?
,Two random processes are defined by Y(t)-X(t) cos(wot) where X(t) and Y(t) are jointly wSs. a) If θ is a constant (non-random), is there any value of θ that will make Yl(t) and Y(t) orthogonal? b) if θ is a uniform r.v., statistically independent of x(t) and Y(t), are there any conditions on θ that will make Yı(t) and Y2(t) orthogonal?
,Two random processes are defined by Y(t)-X(t) cos(wot) where X(t) and Y(t) are jointly wSs. a) If θ is...
6. The temperature at (x,y) is T(x,y) = 20 + 100%+++") degrees (in Celsius). A bug carries a tiny thermometer along the path c(t) = (cos(t - 2), sin(t -- 2)) where t is in seconds. What is the initial rate of change of the temperature t = 0.6s?
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