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Question
Make f the subject of the formula D = `sqrt((("f" + "p")/("f" - "p"))`. Find f, when D = 13 and P = 21.
Solution
D = `sqrt((("f" + "p")/("f" - "p"))`
squaring both sides, we get
⇒ D2 = `(("f" + "p")/("f" - "p"))`
⇒ D2(f - p) = (f + p)
⇒ D2f - D2p = f + p
⇒ D2f - f = p + D2p
⇒ f(D2 - 1) = p(D2 + 1)
⇒ f = `("p"("D"^2 + 1))/(("D"^2 - 1)`
Substituting the values of D = 13 and p = 21
f = `(21(13^&2 + 1))/((13^2 - 1)`
= `(21 xx 170)/(168)`
= 21.25.
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