Suppose that z varies jointly as u and v and inversely as w, and that z=.8 and when u=8, v=6, w=5. How do you find z when u=3, v=10 and w=5?

Question

Jace Anderson · Accepted Answer

undefined To find z when u=3, v=10, and w=5, we can use the concept of joint variation and inverse variation.

Since z varies jointly as u and v, we can write the equation as z = k * u * v, where k is the constant of variation.

Since z varies inversely as w, we can write the equation as z = k / w.

To find the value of k, we can use the given information when u=8, v=6, and w=5.

Plugging these values into the equation z = k * u * v, we get 0.8 = k * 8 * 6.

Simplifying this equation, we find k = 0.8 / (8 * 6) = 0.0167.

Now, we can use this value of k to find z when u=3, v=10, and w=5.

Using the equation z = k * u * v, we get z = 0.0167 * 3 * 10 = 0.501.

Therefore, when u=3, v=10, and w=5, z is approximately equal to 0.501.

Isaiah Anthony · Answer

#z=4/5# #"the initial statement is "zprop(uv)/w# #"to convert to an equation multiply by k the constant"# #"of variation"# #rArrz=(kuv)/w# #"to find k use the given condition"# #z=0.8" when "u=8,v=6,w=5# #z=(kuv)/w# #rArrk=(wz)/(uv)=(5xx0.8)/(3xx10)=0.8/6=8/60=2/15# #"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(z=(2uv)/(15w))color(white)(2/2)|)))# #"when "u=3,v=10" and "w=5# #rArrz=(2xx3xx10)/(15xx5)=60/75=4/5#