Question

'L varies jointly as a and square root of b, and L = 72 when a = 8 and b = 9. Find L when a = 1/2 and b = 36? Y varies jointly as the cube of x and the square root of w, and Y = 128 when x = 2 and w = 16. Find Y when x = 1/2 and w = 64?

Answer 1

`L=9" and " y=4`

Explanation:

`"the initial statement is "Lpropasqrtb`

`"to convert to an equation multiply by k the constant"`
`"of variation"`

`rArrL=kasqrtb`

`"to find k use the given conditions"`

`L=72" when "a=8" and " b=9`

`L=kasqrtbrArrk=L/(asqrtb)=72/(8xxsqrt9)=72/24=3`

`" equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(L=3asqrtb)color(white)(2/2)|)))`

`"when "a=1/2" and "b=36"`

`L=3xx1/2xxsqrt36=3xx1/2xx6=9`

`color(blue)"-------------------------------------------------------"`

`"Similarly"`

`y=kx^3sqrtw`

`y=128" when "x=2" and "w=16`

`k=y/(x^3sqrtw)=128/(8xx4)=128/32=4`

`"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=4x^3sqrtw)color(white)(2/2)|)))`

`"when "x=1/2" and "w=64`

`y=4xx(1/2)^3xxsqrt64=4xx1/8xx8=4`