Proportions: Direct and inverse variations

Question

1)PV=k with constant k

P and V vary directly or inversely

 

2) D=rt with constant r

D and t vary directly or inversely

 

3) C=2*pi symbol* r (2*pi symbol* is constant)

C and r vary directly or inversely

 

4) E=mc^2 with constant of c^2

E and m vary directly or inversely 

 

5) F= k/d^2 with constant k

F and d^2 vary directly or inversely 

 

6) F=ma with constant a

F and m vary directly or inversely 

Answer 1

If something varies directly, it means that as the first variable increases, the second variable also increases.  If the first variable decreases, then the second variable decreases.

 

If something varies inversely, it means that as the first variable increases, the second variable decreases.  If the first variable decreases, then the second variable increases.

 

So, for your first problem, PV=k.  For k to remain the same number, if P were to increase, then V would need to decrease.  For example, if k=6, and your problem was PV=6, we could start with P=1, and V=6.  This gives us 1(6) = 6.  But if I change the value of P to 2, we are forced to change the value of V to 3.  As P increased, V decreased.  P and V vary inversely.

 

For your second problem, D=rt.  For r to remain the same number, D and t would need to increase and decrease together.  Let's make r=6 again.  We could make D=18, and t=3 to begin with.  This gives us 18=(6)3.  If I change the value of D to 12, then to make the equation true without changing the value of r, I would need to change the value of t to 2.  If I changed the value of D to 24, I would have to change the value of t to 4.  As D increases, t increases.  As D decreases, t decreases.  D and t vary directly.

 

I'll leave the rest for you to work on for now, and just comment if you still need help.