Advertisements
Advertisements
Question
Make z the subject of the formula y = `(2z + 1)/(2z - 1)`. If x = `(y + 1)/(y - 1)`, express z in terms of x, and find its value when x = 34.
Advertisements
Solution
y = `(2z + 1)/(2z - 1)`
⇒(2z - 1) y = 2z + 1
⇒ 2zy - y = 2z + 1
⇒ 2zy - 2z = 1 + y
⇒ z(2y - 1) = 1 + y
⇒ z = `(1 + y)/(2y - 1)`
⇒ x = `(y + 1)/(y - 1)`
⇒ x = `(((2z + 1)/(2z - 1)) + 1)/(((2z + 1)/(2z - 1)) - 1)`
= `(2z + 1 + 2z - 1)/(2z + 1 - 2z + 1)`
= `(4z)/(2)`
= 2z
⇒ z = `x/(2)`
Substituting x = 34, we get
z = `(34)/(2)`
= 17.
APPEARS IN
RELATED QUESTIONS
The simple interest on a sum of money is the product of the sum of money, the number of years and the rate percentage. Write the formula to find the simple interest on Rs A for T years at R% per annum.
The area A of a circular ring is π times the difference between the squares of outer radius R and inner radius r. Make a formula for this statement.
Make R the subject of formula A = `"P"(1 + "R"/100)^"N"`
Make x the subject of formula `"a"x^2/"a"^2 + y^2/"b"^2` = 1
Make r2 the subject of formula `(1)/"R" = (1)/"r"_1 + (1)/"r"_2`
Make a the subject of formula x = `sqrt(("a" + "b")/("a" - "b")`
Make y the subject of formula W = `"pq" + (1)/(2)"wy"^2`
Make k the subject of formula T = `2pisqrt(("k"^2 + "h"^2)/"hg"`
Given: mx + ny = p and y = ax + b. Find x in terms of m, n, p, a and b.
The total energy E possess by a body of Mass 'm', moving with a velocity 'v' at a height 'h' is given by: E = `(1)/(2) "m" "u"^2 + "mgh"`. Make 'm' the subject of formula.
