More Math Help!?!?!?! please!?

Question

6. Draw a graph of a direct variation. Go to drawing tools and click on it. (Note: Your drawing tool icon may be different if not working in Microsoft Word.) This should give you a tool bar at the bottom of your screen. Choose AutoShapes, then Lines, then the straight line with two arrows on each end. Use it to draw on the graph shown below.







7. In a certain variation, z varies jointly as x and y, and inversely as w, and
z = 2 when x = 3, y = 6 and w = 10. Find z when x = 2, y = 3 and w = 5.






8. The amount of material needed to cover a ball varies directly with the square of the radius. It takes about 221.63 cm2 of material to cover a ball with a radius of 4.2 cm. What is the radius of a ball that needs 352.92 cm2 of material to cover it?






9. Explain in words how you can tell if a table of values (t-table) represents a direct variation.

Answer 1

Direct variation y = k*x, k is a constant
Inverse y= k/x, k is another constant.
Problems 7 and 8 deal with finding the constant for a complicated variation:
7. Direct Variation: z= k1 x y
Inverse z = k2/ w
So z = (k1/k2) (xy/w)
since k1/k2 is a constant, we can write
z = K(xy/w)
One z value is known 2 = K(1.8) , so K = 10/9
Then z = 10/9 (xy/w)
For other data:
z = 10/9 (6/5) = 4/3

8 is pretty similar except A = Kr^2, where A is the surface area of the ball.

Answer 2

Maybe it would be better if you asked "what does it mean for two variables to vary directly or inversely?"

Maybe if you learn about the topic, it'll be better than if we do all these problems. We'll try to help!