1.s varies directly as m

2.p varies inversely as n
3.j varies directly as q and inversely as the square of r
4.the pressure(p) of a gas is directly proportional to the temperature (t) and inversely proportional to its volume(v)
5.t varies directly as a and inversely as b
6.y varies directly as x and inversely as the square of z
7.z varies jointly as x and y
8.a varies jointly as b and c
9.y varies inversely as x

direct variation: a = kb

inverse: a = k/b

now plug in a few of your variables. For example,

#5. t = ka/b
#7. z = kxy
and so on

To solve the problems given, it's important to understand what it means for one variable to vary directly or inversely with another variable.

1. If a variable, like s, varies directly as another variable, like m, it means that as m increases or decreases, s will also increase or decrease by the same factor. This can be represented by the equation s = km, where k is a constant of proportionality.

2. If a variable, like p, varies inversely as another variable, like n, it means that as n increases, p will decrease, and as n decreases, p will increase. This can be represented by the equation p = k/n, where k is a constant of proportionality.

3. If a variable, like j, varies directly with one variable, like q, and inversely with the square of another variable, like r, it means that as q increases or decreases, j will increase or decrease, and as r increases, j will decrease by the square of the increase, and vice versa. This can be represented by the equation j = k(q/r^2), where k is a constant of proportionality.

4. If the pressure of a gas, p, is directly proportional to the temperature, t, and inversely proportional to the volume, v, it means that as t increases or decreases, p will increase or decrease by the same factor, and as v increases, p will decrease by the same factor, and vice versa. This can be represented by the equation p = k(t/v), where k is a constant of proportionality.

5. If a variable, like t, varies directly as one variable, like a, and inversely as another variable, like b, it means that as a increases or decreases, t will increase or decrease by the same factor, and as b increases, t will decrease, and vice versa. This can be represented by the equation t = ka/b, where k is a constant of proportionality.

6. If a variable, like y, varies directly with one variable, like x, and inversely with the square of another variable, like z, it means that as x increases or decreases, y will increase or decrease by the same factor, and as z increases, y will decrease by the square of the increase, and vice versa. This can be represented by the equation y = k(x/z^2), where k is a constant of proportionality.

7. If a variable, like z, varies jointly as two variables, like x and y, it means that as x or y increases or decreases, z will increase or decrease by the same factor. This can be represented by the equation z = kxy, where k is a constant of proportionality.

8. If a variable, like a, varies jointly as two variables, like b and c, it means that as b or c increases or decreases, a will increase or decrease by the same factor. This can be represented by the equation a = kbc, where k is a constant of proportionality.

9. If a variable, like y, varies inversely as another variable, like x, it means that as x increases or decreases, y will decrease or increase by the same factor. This can be represented by the equation y = k/x, where k is a constant of proportionality.