Question

Let vector F = (15a^2x + 5ay^2) i + (5z^3 − 12ay) j − (3z + 5x^2 + 5y^2) k .

(a) Find the values of a such that div F = 0
a =

(smaller value)
a =

(larger value)

(b) Find the value of a such that div F is a minimum
a =

Answer 1

can you help me out @dan815 please

Answer 2

@ganeshie8

Answer 3

\[\large \mathrm{div}\left( P\hat{i},~ Q\hat{j},~ R\hat{k}\right) = P_x + Q_y + R_z\]

Answer 4

find the divergece
set it equal to 0 and solve \(a\)

Answer 5

how would I find the minimum?

Answer 6

@ganeshie8

Answer 7

is the divergence 3(5a^2-4a-1)

Answer 8

whats the minimum value of a parabola ?

Answer 9

I got a=-1/5 and a=1

Answer 10

you don't need x intercepts

Answer 11

so how do i find the value of "a" such that divF is a minimum?

Answer 12

wolfram says minimum = -27/5

http://www.wolframalpha.com/input/?i=minimum+3%285a%5E2-4a-1%29+

Answer 13

Oh you want the value of \(a\) that minimizes the divergence

Answer 14

then just take average value of xintercepts

Answer 15

so 2/5?

Answer 16

Yep!

Answer 17

so is there a easy way to find that value?

Answer 18

or the best thing to use is wolframalpha? haha

Answer 19

https://www.khanacademy.org/math/algebra/quadratics/solving_graphing_quadratics/v/quadratic-functions-2

Answer 20

thanks :)