Hi, Ruben Rostamian,

I first reward you to pay attention to my question.

However, you made a little mistake with your response : "just say A".

According to the name of procedure after Gerschorin, we need to write Gerschorin(A or F).

Anyhow, my question was not quite clear !

I got all the solutions on my worsheet, i.e. the Matrix & Plots ( circles ).

I attempted to copy all the worksheet and paste it on Mapleprimes, the results did not appear, no matrix, no plots.

So, I gave up and asked the mapleprimes community for some help...

Best wishes

Archimedes should have reported that the king had been cheated.Either the crown was hollow, or it was not made of of pure gold.

This is a question of buoyant forces and Archimedes's principle : B=  or B=M*g                        

The scale reading is a measure of one of the forces on the crown,and the crown is stationary.Therefore we categorize the crown as a particule in equilibrium. Sigma F= B+T2-Fg=0                                                                          

B = Fg-T2 = 7.84 N - 6.84 N = 1N , 

 crown = mcrown*g* water/B, i.e:  crown = ( 7.84 N )-*(1000 kg/m^3)/1 N =  7.84 * 10^3 kg/m^3                    

Actually the density of gold is 19.3 *10^3/m^3.

Hello, kitonum 3735,

I checked your answer again, there is a mistake !

The graph S of f,is an elliptic paraboloid ... 

Your gradioent is good.

The point P(1,2) and the vector Nabla f(1,2) are shown in the x-y plane.

The point on S corresponding to P is Q (1,2,4). If a (variable) point in the x-y plane moves through P 

in the direction of Nabla f(1,2) , the corresponding point on the graph moves along a curve C of steepest

ascent on the paraboloid.

Regards

Bernard LAPORTE 20