Step 1) Multiply the terms in parenthesis on the right side of the equation:
#1.50 = color(red)((2 xx 3.14))sqrt(0.480/k)#
#1.50 = 6.28sqrt(0.480/k)#
Step 2) divide each side of the equation by #color(red)(6.28)# to isolate the radical while keeping the equation balanced:
#1.50/color(red)(6.28) = (6.28sqrt(0.480/k))/color(red)(6.28)#
#1.50/6.28 = (color(red)(cancel(color(black)(6.28)))sqrt(0.480/k))/cancel(color(red)(6.28))#
#1.50/6.28 = sqrt(0.480/k)#
Step 3) Square both sides of the equation to eliminate the radical while keeping the equation balanced:
#(1.50/6.28)^2 = (sqrt(0.480/k))^2#
#2.25/39.4384 = 0.480/k#
Step 4) Multiply each side of the equation by #color(red)(k)# to move the #k# variable out of the denominator while keeping the equation balanced:
#2.25/39.4384 * color(red)(k) = 0.480/k * color(red)(k)#
#2.25/39.4384k = 0.480/color(red)(cancel(color(black)(k))) * cancel(color(red)(k))#
#2.25/39.4384k = 0.480#
Step 5) Multiply each side of the equation by #color(red)(39.4384)/color(blue)(2.25)# to solve for #k# while keeping the equation balanced:
#color(red)(39.4384)/color(blue)(2.25) * 2.25/39.4384k = color(red)(39.4384)/color(blue)(2.25) * 0.480#
#cancel(color(red)(39.4384))/cancel(color(blue)(2.25)) * color(blue)(cancel(color(black)(2.25)))/color(red)(cancel(color(black)(39.4384)))k = 18.930432/color(blue)(2.25)#
#k = 8.413525bar3#
