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 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.
Apple cost x rupees per dozen and mangoes cost y rupees per score. Write a formula to find the total cost C in rupees of 20 apples and 30 mangoes.
Make R the subject of formula A = `"P"(1 + "R"/100)^"N"`
Make L the subject of formula T = `2pisqrt("L"/"G")`
Make r2 the subject of formula `(1)/"R" = (1)/"r"_1 + (1)/"r"_2`
Make x the subject of the formula a = `1 - (2"b")/("cx" - "b")`. Find x, when a = 5, b = 12 and
Make y the subject of the formula `x/"a" + y/"b" `= 1. Find y, when a = 2, b = 8 and x = 5.
Make f the subject of the formula D = `sqrt((("f" + "p")/("f" - "p"))`. Find f, when D = 13 and P = 21.
Make c the subject of the formula a = b(1 + ct). Find c, when a = 1100, b = 100 and t = 4.
"The volume of a cone V is equal to the product of one third of π and square of radius r of the base and the height h". Express this statement as a formula. Make r the subject formula. Find r, when V = 1232cm3, π = `(22)/(7)`, h = 24cm.
