'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?

1 Answer
Jul 24, 2017

Answer:

#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#