Understanding the DuBois Formula: Solving for Height in Relation to Surface Area

[swears]

Ok, my teacher did this problem today, but there is 1 step I don't understand. If someone could explain to me how it's done, that'd be great.

Here's the problem:

Using the DuBois formula: S = 0.01W^(0.25) H^(.75)

Solve for H(Height) as a function of S (Surface Area) for people of fixed weight(W) 70

Answer:

S = 0.01(70)^(.25) H^(.75)

S = 100/70^(.25) = H^(.75)
//This is the step I don't understand. Where does the 100 come from and what happened to 0.01? Am I an idiot?

34.57 S = H^(.75)

34.57^(4/3) S^(4/3) = H

H = 112.6 S^(4/3)

 

[arildno]

Evidently, you don't understand it, since you are too sloppy about how you write stuff.

 

[AKG]

S = 100/70^(.25) = H^(.75)
//This is the step I don't understand. Where does the 100 come from and what happened to 0.01? Am I an idiot?

It should not be "S =" at the beginning, it should be "S x", i.e. "S times". The whole thing should be:

S = 0.01(70)^(.25) H^(.75)

S x 100/70^(.25) = H^(.75)

34.57 S = H^(.75)

34.57^(4/3) S^(4/3) = H

H = 112.6 S^(4/3)

 

[swears]

Evidently, you don't understand it, since you are too sloppy about how you write stuff.

Thanks for the support

 

[swears]

AGK, how did you swap S and H^(.75)

 

[Hootenanny]

$$S = 0.01(70^{0.25}) \cdot H^{0.75}$$

$$S = \frac{70^{0.25}}{100}\cdot H^{0.75}$$

$$\frac{S}{H^{0.75}} = \frac{70^{0.25}}{100}$$

$$\frac{1}{H^{0.75}} = \frac{70^{0.25}}{100S}$$

$$H^{0.75} = \frac{100S}{70^{0.25}}$$

$$H^{0.75} = S \times \frac{100}{70^{0.25}}$$

Does that make more sense now?

~H

 

[swears]

Yes, that makes more sense, thanks.

I'm not sure how you got the 1 in step 4 though.

 

[Hootenanny]

Yes, that makes more sense, thanks.

I'm not sure how you got the 1 in step 4 though.

From here;

$$\frac{{\color{red}S}}{H^{0.75}} = \frac{70^{0.25}}{100}$$

Just divide both sides 'S'

$$\frac{1}{H^{0.75}} = \frac{70^{0.25}}{100{\color{red}S}}$$

Do you see?

~H

 

[swears]

Yes, Thanks.