(b) You start to move in the direction you found in part (a) at a speed of 3 cm/sec. How fast is the concentration changing

Complete Question

The concentration of salt in a fluid at (x,y,z) is given by F(x,y,z)=x^2+y^4+2x^2z^2 mg/cm3 You are at the point (1,1,1).

a. In which direction should you move if you want the concentration to increase the fastest?

I keep getting <5,2,8> for this answer and it says it is incorrect

You start to move in the direction you found in part (a) at a speed of 4 cm/sec. How fast is the concentration changing?

a

b

Explanation:

From the question we are told that

  The equation is

differentiating with respect to x

differentiating with respect to y

differentiating with respect to z

Gnerally the rate of change of the salt concentration is mathematically represented as

=>  

At  the point (1,1,1)

=>

generally rate at which the concentration is changing is mathematically represented as

=>      

=>    

=>    

=>    

  1.the balanced   chemical equation is as below

cu +   2 ag(no)₃ → cu(no₃)₂   +2 ag

2.the   much silver   produced   is   50.9 g

step 1: find the   moles of cu

moles =   mass÷   molar mass

  from periodic table the molar mass of cu = 63.5 g/mol

moles is therefore = 15.00 g÷ 63.5 g/mol = 0.236   moles

step 2: use the mole ratio to determine the   moles of ag

from equation above   cu: ag   is 1: 2

therefore the moles of ag   =0.236   moles   x 2/1 =0.472   moles

step 3: find the mass   of ag

mass = moles x molar mass

from periodic table   the molar mass of ag =107.87 g/mol

mass   = 0.472   moles x 107.87 g/mol = 50.9 g

3.   the   much   silver   collected worth is   1.797 oz

  convert   50.9 g   to oz

that is   1 gram = 0.0353 oz

          50.9 grams =?   oz

by cross multiplication

={(50.9 grams x 0.0353 oz) / 1   gram}   =1.797 oz