Question

Make h the subject of the formula E = 1 -\pi \sqrt{x} (h -0.5/1 -h)

Answer 1

To make h subject of the formula, the other expressions in the equation is expressed to equal h as follows:

• h = (1 + E + 0.5π√x/)(π√x + 1 + E)

How can h in the equation, $E = 1-\pi \sqrt{x} (\frac {h-0.5}{1-h})$ be made subject of the formula?

The steps in making h subject of the formula in the given equation are as follows:

Step 1: Add $pi \sqrt{x} (\frac {h-0.5}{1-h})$ to both sides

$E + \pi \sqrt{x} (\frac {h-0.5}{1-h})= 1$

Step 2: subtract E from both sides

$\pi \sqrt{x} (\frac {h-0.5}{1-h}) = 1 + E$

Step 3: divide both sides by π√x

h - 0.5/1 - h = 1 + E/π√x

Step 4: cross multiply

(h - 0.5)(π√x) = (1 + E)(1 - h)

hπ√x -0.5π√x = 1 - h + E - hE

Step 5: collect like terms

hπ√x + h + hE = 1 + E + 0.5π√x

h(π√x + 1 + E) = 1 + E + 0.5π√x

Step 6: divide both sides by (π√x + 1 + E)

h = (1 + E + 0.5π√x/)(π√x + 1 + E)

In conclusion, in making h subject of the formula, the other expressions in the equation is expressed to equal h.

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