What is the answer to solvefor h,V= 1/(3pir^2h) ?

The answer to solvefor h,V= 1/(3pir^2h) is h=-1/(3pr^2V)i

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Solve for h V=1/3pir^2h

solve for

h, V = \frac{1}{3 p i r ^{2} h}

h = - \frac{1}{3 p r ^{2} V} i

Solution steps

V = \frac{1}{3 p i r ^{2} h}

Substitute

h = x + y i

V = \frac{1}{3 p i r ^{2} ( x + y i )}

Multiply both sides by

3 p i r^{2} (x + y i)

V \cdot 3 p i r^{2} (x + y i) = \frac{1}{3 p i r ^{2} ( x + y i )} \cdot 3 p i r^{2} (x + y i)

Simplify

- 3 p r^{2} V y + 3 i p r^{2} V x = 1

Rewrite

1

in standard complex form:

1 + 0 i

- 3 p r^{2} V y + 3 i p r^{2} V x = 1 + 0 i

Complex numbers can be equal only if their real and imaginary parts are equalRewrite as system of equations:

[- 3 p r^{2} V y = 1 3 p r^{2} V x = 0]

[- 3 p r^{2} V y = 1 3 p r^{2} V x = 0] : x = 0, y = - \frac{1}{3 p r ^{2} V}, V \neq = 0

Substitute back

h = x + y i

h = - \frac{1}{3 p r ^{2} V} i

x, 7 - x = 5

\frac{45}{35}

x, \frac{1}{2} = \frac{x}{4}

x, - 5 x = 15

27/9

What is the answer to solvefor h,V= 1/(3pir^2h) ?
The answer to solvefor h,V= 1/(3pir^2h) is h=-1/(3pr^2V)i