Whats the equation of variation where y varies jointly as x and z and inversely as the square of w and y=20 when x= -0.5, z =4, and w = 5?

Question

Whats the equation of variation where y varies jointly as x and z and inversely as the square of w and y=20 when x=  -0.5, z =4, and w = 5?

Isaiah Anthony · Accepted Answer

undefined The equation of variation is y = kxz/w^2. To find the value of k, substitute the given values into the equation: 20 = k(-0.5)(4)/(5^2). Simplifying this equation gives k = -400. Therefore, the equation of variation is y = -400xz/w^2.

Genesis Allen · Answer

#y=-(250xz)/w^2# #"the initial statement is "yprop(xz)/w^2# #"to convert to an equation multiply by k the constant"# #"of variation"# #rArry=kxx(xz)/w^2=(kxz)/w^2# #"to find k use the given condition"# #y=20" when "x=-0.5,z=4" and "w=5# #y=(kxz)/w^2rArrk=(yxxw^2)/(xz)=(20xx5^2)/(-0.5xx4)=-250# #"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=-(250xz)/w^2)color(white)(2/2)|)))#

Isaiah Anthony · Answer

undefined The equation of variation is $ y = k \cdot \frac{xz}{w^2} $, where $ k $ is a constant. Plugging in the given values, we get $ 20 = k \cdot \frac{(-0.5)(4)}{5^2} $. Solving for $ k $, we find $ k = -8 $. Therefore, the equation of variation is $ y = -8 \cdot \frac{xz}{w^2} $.