Respuesta :

You solve an expression for a variable if that variable sits alone on one side of the equation, and everything else is on the other side.

So, our goal is to leave [tex] h [/tex] alone on the right hand side, and move everything else to the left.

So, we start with

[tex] V = \dfrac{1}{3}s^2h [/tex]

We multiply both sides by 3:

[tex] 3V = s^2h[/tex]

We divide both sides by [tex] s^2 [/tex]

[tex] \dfrac{3V}{s^2} = h [/tex]

To compute the required height, simply plug in the values:

[tex] \dfrac{3\cdot 400}{10^2} = \dfrac{3\cdot 400}{100} = 3\cdot 4 = 12[/tex]

tramserran

Answer: [tex]\bold{h=\dfrac{3V}{s^2}, \qquad h=12}[/tex]

Step-by-step explanation:

Isolate the variable "h" by multiplying both sides by 3 and dividing both sides by s².

[tex]V=\dfrac{1}{3}s^2h[/tex]

[tex](3)V=(3)\dfrac{1}{3}s^2h\ \quad \rightarrow\ \quad 3V=s^2h[/tex]

[tex]\dfrac{3V}{s^2}=\dfrac{s^2h}{s^2}\ \quad \rightarrow \quad \dfrac{3V}{s^2}=h[/tex]


Next, substitute V = 400 and s = 10 to solve for h:

[tex]h=\dfrac{3(400)}{(10)^2}[/tex]

   [tex]=\dfrac{1200}{100}[/tex]

   [tex]= 12[/tex]

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