Make R2 the Subject of Formula R2 = 4π(R12 - R22) - Mathematics

Make R₂ the subject of formula R² = 4π(R₁² - R₂²)

Sum

R² = 4π(R₁² - R₂²)

⇒ R² = 4πR₁² - 4πR₂²

⇒ 4πR₂²= 4πR₁² - R²

⇒ R₂² = `(4pi"R"_1^2 - "R"^2)/(4pi)`

⇒ R₂ = `sqrt((4pi"R"_1^2 - "R"^2)/(4pi)`.

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Changing the Subject of a Formula

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Chapter 6: Changing the subject of a formula - Exercise 6.2

Chapter 6 Changing the subject of a formula
Exercise 6.2 | Q 12

Make R the subject of formula A = `"P"(1 + "R"/100)^"N"`

Make r₂ the subject of formula `(1)/"R" = (1)/"r"_1 + (1)/"r"_2`

Make y the subject of formula W = `"pq" + (1)/(2)"wy"^2`

If 3ax + 2b² = 3bx + 2a², then express x in terms of a and b. Also, express the result in the simplest form.

If b = `(2"a")/("a" - 2)`, and c = `(4"b" - 3)/(3"b" + 4)`, then express c in terms of a.

Make s the subject of the formula v² = u² + 2as. Find s when u = 3, a = 2 and v = 5.

Make a the subject of the formula S = `"n"/(2){2"a" + ("n" - 1)"d"}`. Find a when S = 50, n = 10 and d = 2.

Make m the subject of the formula x = `"my"/(14 - "mt")`. Find m, when x = 6, y = 10 and t = 3.

Make I the subject of the following M = `"L" /"F"(1/2"N" - "C") xx "I"`. Find I, If M = 44, L = 20, F = 15, N = 50 and C = 13.

If s = `"n"/(2)[2"a" + ("n" - 1)"d"]`, the n express d in terms of s, a and n. find d if n = 3, a = n + 1 and s = 18.