laporte bernard

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These are questions asked by laporte bernard

Hello,

 

A flate metal plate lies on an xy plane such that the temperature T at (x,y) is given by T=10(x^2+y^2)^2 , where T is in degrees and x and y are in centimeters.

Find the instantaneous rate of change of T with respect to distance at (1,2) in the direction of

a) the x-axis

b) the y-axis

How to get the equations of circles A, B, C, such as circle A with center (1,1) is drawn in the first quadrant.

Circle B with radius 2 and circle C are placed so that each circle is tangent to the other 2 circles and the x-axis.

THe 3 circles are on the first quadrant.

1) do it with Maple

2) do it by hand

3) draw the figure

 

Regards

assuming the skier is projected at an angle theta with respect to the horizontal over a landing incline sloped with an arbitrary angle phi :

xf = (vi*cos(theta)*t=d*cos(phi)

yf=(vi*sin(theta)*t-1/2*g*t^2=-d*sin(phi)

 

By eliminating the time t between these two equations and using differentiation to maximize d in terms of theta,

we should arrive at the following equation for the angle theta that gives the maximum value of d :

 

theta = 45° -phi/2  (Answer from a text book)

 

How can I handle that problem about ski jump with MAPLE  ?

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