In a room, the temperature is given by T = f(x,t) degrees Celsius, where x is th

Q: In a room, the temperature is given by T = f(x,t) degrees Celsius, where x is th

1) a)t is constant , then T/x =2 x is constant ,then T/t =1.2 b)dT=(T/x)(x-3) +(T/t)(t -5) dT=2(x-3) + 1.2(t -5) dT=2x-6 + 1.2t -6 dT=2x + 1.2t -12 c)dT at (x,t) =(2.5,6) dT=2*2.5 + 1.2*6 -12 dT=5 + 7.2 -12 dT=0.2 warmer by 0.2oC

ID: 2861027 • Letter: I

Question

In a room, the temperature is given by T = f(x,t) degrees Celsius, where x is the distance from the heater (in meters) and t is the elapsed time (in minutes) since the heat has been turned on. A person standing 3 meters from the heater 5 minutes after it has been turned on observes the following: (1) The temperature is increasing by 1.2 degree C per minute, and (2) walking away from the heater, the temperature decreases by 2 degree C per meter as time is held constant. Find partial differentiate/partial differentiate x and partial differentiate T/partial differentiate t at (3,5). Find the differential dT at (3,5). Use dT to estimate how much warmer/cooler it is at (2.5,6). Your house lies on the surface z = f (x, y) = 2 (x/50)^2 - (y/50)^2 directly above the point (200,150) in the xy-plane. x, y and z are measured in meters. How high above the xy-plane do you live? What is the slope of your lawn when you look from your house directly toward the z-axis (that is, along the vector -200i - 150j)? Express the slope as an angle in degrees! When you wash your car in the driveway, on this surface above the point (200,150), which way does the water run off? (Give your answer as a two dimensional vector.) Suppose that temperature, in degrees Celsius, at any point (x, y, z) in 3-space is given by T(x, y, z) = 100e^-x^2-y^2-z^2+2x-6z-10, where x, y, and z are measured in kilometers. Find the rate of change of temperature at the point (1,1, 2) in the direction towards the point (2,0, -1). There is a point P = (a, b, c) such that at every point other than P, the temperature increases most rapidly in the direction towards P. Find P.

Explanation / Answer

a)t is constant , then T/x =2

x is constant ,then T/t =1.2

b)dT=(T/x)(x-3) +(T/t)(t -5)

dT=2(x-3) + 1.2(t -5)

dT=2x-6 + 1.2t -6

dT=2x + 1.2t -12

c)dT at (x,t) =(2.5,6)

dT=2*2.5 + 1.2*6 -12

dT=5 + 7.2 -12

dT=0.2

warmer by 0.2oC

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In a room, the temperature is given by T = f(x,t) degrees Celsius, where x is th

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