Does anyone at least slightly understand direct and inverse variation? I get the basic idea, but I'm still a little confused, especially with inverse variation.

Question

What I'm having more trouble with is conversion using direct and inverse variation. Today, my teacher kept talking and talking and wouldn't explain things very well, and there was no time for questions. Does anyone know the answer to this question? For any of my questions, please tell me the answer and walk me through it, too, because that is exactly what my teacher didn't do.

#1: Given that 1 inch is 2.54 centimeters and 1 ounce is 28.35 grams, convert 16.2 in²ozˉˡ (that is to the power of negative 1) to centimeters and grams.

I think we did that one in class, but I'm kind of confused about how to get the answer.

#2: A molecule is traveling at a speed of 400 meters per second. What is its speed in miles per hour? Given: 30 centimeters = 1 foot, 3600 seconds = 1 hour.

Thank you so much! I appreciate any help, even if you can only answer one!

Answer 1

If one variable = constant times other variable, that is DIRECT
example y = 5 x
If one variable = constant OVER other varible, that is INVERSE
example y = 5 / x

Answer 2

For unit conversions I like to think about one thing / the same thing = 1

For example if I want to convert 4 feet to inches.
write
4 ft
now multiply that 4 ft by something that is inches over feet, but the same top and bottom so it does not change the basic quantity.
4 ft ( 12 in/ 1 ft)
the ft cancels and we are left with inches
4 * 12 = 48 inches
Now yours:
16.2 in^2/oz * (2.54 cm/1 in)(2.54 cm/1 in)(1 oz/28.35 g)
= 3.69 cm^2/g

Answer 3

A molecule is traveling at a speed of 400 meters per second. What is its speed in miles per hour? Given: 30 centimeters = 1 foot, 3600 seconds = 1 hour.

400 m/s * (100 cm/1m)(1 ft/30 cm)(1 mi/5280 ft)(3600 s/1h)