Could someone show me how to solve this joint variation problems?
Y varies jointly as x and y and inversely as w. Write the appropriate combined variation equation and find z for the given values of x, y and w. z=15 when x equals three, y equals four, and w equals nine, x equals 1.5 y equals 20.5 and w equals 5.4 (I don't know how to do a variation that is both joint and inverse).
Z varies jointly as x and y and inversely as w.. Write the appropriate combined variation equation and find z for the given values of x, y and w. y equals 120 when x equals eight and z equals 20; x equals 54 and z equals seven. (same problem as the last one).
If x1, y1 and x2, y2 satisfy xy=k, then x1y1 equals x2y2. 3,y and 18,6 (I am confused how x1y1=x2y2, yet the y values are differing). How do you find x or y for this?)
~Thanks for your help, Juliette
z=k(xy)/w
20=k(120*8)/20 find k
On the second part, (after the semicolon), y is not mentioned.
x1y1=k=x2y2 because xy=k for any x,y.
3y=18*6 solve for y.
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To solve joint variation problems, you need to use the concept that says a variable varies jointly as two or more other variables. In your first problem, you are given that Y varies jointly as x and y and inversely as w.
To write the combined variation equation, you start with the general form for joint variation:
Y = kxy/w
Where k is the constant of variation. Plugging in the given values of x, y, and w, you get:
15 = k * (3) * (4) / (9)
Now, solve for k:
k = (15 * 9) / (3 * 4) = 45/4 = 11.25
Now that you have the value of k, you can use it to find z for the second set of given values:
z = k * (1.5) * (20.5) / (5.4)
Simplify the equation:
z = (11.25) * (1.5) * (20.5) / (5.4)
Finally, calculate z:
z ≈ 112.5
So, z is approximately equal to 112.5.
For the second problem, you follow the same steps. The given information is that Z varies jointly as x and y and inversely as w. You need to find the combined variation equation and solve for z using the given values.
Please provide some time, I will be right back with the answer to this problem as well as the last one.