Question

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.

z = 10 when x = 5, y = -2 and w = 3; x = 8, y = 6 and w = -12

Answer 1

The equation is\[zw=xy\]

Answer 2

Suppose we keep the right side constant. If you increase \(z\), then \(w\) must decrease so that \(xy\) remains constant. That's what it means for \(z\) and \(w\) to vary inversely.

Now suppose we keep \(w\) and \(x\) constant. If \(z\) increases, then \(y\) must also increase. That's what it means for \(z\) and \(y\) to vary jointly.

Answer 3

explain

Answer 4

Erm, what? I just did

Answer 5

can you explain it a different way

Answer 6

Well, the only other way I can think to explain the concept of joint/inverse variation is with a slightly more concrete example.

Let's take an equation that we know is true: \(2\cdot\dfrac{1}{2}=4\cdot\dfrac{1}{4}\).

Obviously, both sides are equal to 1, agreed?

Answer 7

yes

Answer 8

designer dolls, inc found that the number of dolls sold, n, varies directly as their advertising budget, a, and inversely as the price of each doll, p. designer dolls, inc. sold 12,000 dolls when $50,000 was spent on advertising and the price of the doll was set at $50. determine te number of dolls sold when the amount spent on advertising is increased to $65,000.

a. 15,600
b. 1,300
c. 2,880
d. 15,120

Answer 9

Okay, so we can write this as just
\[2\cdot\frac{1}{2}=1\]
We want to change the two factors on the left side while still keeping equality. To do that, say we make the fraction smaller, maybe drop it to \(\dfrac{1}{4}\). To maintain the equality, we have to change the 2 to a 4 (we make it bigger).
\[\color{red}{2}\cdot\color{blue}{\frac{1}{2}}=\color{red}{4}\cdot\color{blue}{\frac{1}{4}}=1\]
Red means increase, blue means decrease.

Answer 10

never mind

Answer 11

Uh, you can't just derail the question with another question. Either you want help or you want an answer, and I'm only willing to give one.