If w is jointly proportional to u and v, and w=2 when u=4 and v=6, what is w when u=3 and v=8?

Question

Eva Abramson · Accepted Answer

#w=2# #"the initial statement is "wpropuv# #"to convert to an equation multiply by k the constant"# #"of variation"# #rArrw=kuv# #"to find k use the given condition"# #w=2" when "u=4" and "v=6# #w=kuvrArrk=w/(uv)=2/24=1/12# #"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(w=1/12uv)color(white)(2/2)|)))# #"when "u=3" and "v=8" then"# #w=1/12xx3xx8=1/12xx24=2#

Eva Adamson · Answer

undefined If $ w $ is jointly proportional to $ u $ and $ v $, then $ w = k \cdot u \cdot v $, where $ k $ is the constant of proportionality. To find the value of $ k $, we can use the given values: $ w = 2 $ when $ u = 4 $ and $ v = 6 $. Substituting these values into the equation, we get $ 2 = k \cdot 4 \cdot 6 $. Solving for $ k $, we find $ k = \frac{1}{12} $.

Now that we have the value of $ k $, we can use it to find $ w $ when $ u = 3 $ and $ v = 8 $. Substituting these values into the equation $ w = k \cdot u \cdot v $, we get $ w = \frac{1}{12} \cdot 3 \cdot 8 $. Simplifying, we find $ w = 2 $. Therefore, when $ u = 3 $ and $ v = 8 $, $ w $ is equal to $ 2 $.