## 45 Reputation

11 years, 289 days

## Gerschorin's circles...

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

## EUREKA ! Archimedes's principle...

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.

## directional derivatives gradient...

Hello, kitonum 3735,

I checked your answer again, there is a mistake !

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

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

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