v/120=(699.84/v)^(1/2)

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Solution for v/120=(699.84/v)^(1/2) equation: 


D( v )

v = 0

699.84/v < 0

v = 0

v = 0

699.84/v < 0

699.84/v < 0

699.84*v^-1 < 0

699.84*v^-1 < 0 // : 699.84

v^-1 < 0/699.84

v^-1 < 0

1/(v^1) < 0

v <> 0

1/(v^1) < 0 // * v^2

(v^2)/(v^1) < 0

v^1 < 0

v < 0

v in (-oo:0)

v in (0:+oo)

v/120 = (699.84/v)^(1/2) // - (699.84/v)^(1/2)

v/120-(699.84/v)^(1/2) = 0

1/120*v-699.84^(1/2)*v^(-1/2) = 0

t_1 = v^(1/2)

1/120*t_1^2-699.84^(1/2)*t_1^-1 = 0

t_1^-1*(1/120*t_1^3-699.84^(1/2)) = 0

1/120*t_1^3 = 699.84^(1/2) // : 1/120

t_1^3 = 120*699.84^(1/2)

t_1^3 = 120*699.84^(1/2) // ^ 1/3

t_1 = 2*15^(1/3)*699.84^(1/6)

1/t_1 = 0

1*t_1^-1 = 0 // : 1

t_1^-1 = 0

t_1 należy do O

t_1 = 2*15^(1/3)*699.84^(1/6)

v^(1/2)-(2*15^(1/3)*699.84^(1/6)) = 0

v^(1/2)-2*699.84^(1/6)*15^(1/3) = 0

1*v^(1/2) = -(-2*699.84^(1/6)*15^(1/3)) // : 1

v^(1/2) = 2*699.84^(1/6)*15^(1/3)

v^(1/2) = 2*699.84^(1/6)*15^(1/3) // ^ 2

v = 4*699.84^(1/3)*15^(2/3)

v = 4*699.84^(1/3)*15^(2/3)

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