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.
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!
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
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
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)
I can help you with both of your conversion questions. Let's break down each question and go through the steps to find the answers.
#1: Given that 1 inch is 2.54 centimeters and 1 ounce is 28.35 grams, we need to convert 16.2 in²ozˉˡ (inch² per ounce) to centimeters and grams.
To convert 16.2 in²ozˉˡ to centimeters, we need to multiply it by the conversion factor:
1 inch = 2.54 centimeters
1 ounce = 28.35 grams
First, let's convert inches to centimeters. Since we have inches squared, we need to square the conversion factor as well:
16.2 in² * (2.54 centimeters / 1 inch)²
Square the conversion factor:
16.2 in² * (2.54 centimeters)² / (1 inch)²
Now calculate the result:
16.2 in² * (2.54)² centimeters² / (1)² inch²
= 16.2 * (2.54)² * (2.54)² centimeters²
= 16.2 * 6.4516 * 6.4516 centimeters²
= 665.7388184 centimeters²
Next, let's convert ounces to grams. Again, since we have ounces in the denominator, we need to take the reciprocal of the conversion factor:
16.2 in²ozˉˡ * (28.35 grams / 1 ounce)
Now calculate the result:
16.2 * 28.35 grams / 1 ounce
= 459.27 grams
Therefore, 16.2 in²ozˉˡ is equivalent to 665.7388184 centimeters² and 459.27 grams.
#2: To convert the molecule's speed from meters per second to miles per hour, we need to use the conversion factors:
30 centimeters = 1 foot
3600 seconds = 1 hour
First, let's convert meters to feet by multiplying by the conversion factor:
400 meters * (30 centimeters / 1 foot)
Now calculate the result:
400 * 30 centimeters
= 12,000 centimeters
Next, let's convert centimeters to feet by dividing by 12 (since there are 12 inches in a foot):
12,000 centimeters / 12 inches
= 1,000 inches
Further, we convert inches to feet:
1,000 inches / 12 inches
= 83.33 feet
Finally, let's convert the speed from feet per second to miles per hour:
Let's first convert seconds to hours using the conversion factor:
1 hour = 3600 seconds
400 meters per second * (1 hour / 3600 seconds)
Now calculate the result:
400 / 3600
= 0.1111 hours
Now, convert feet to miles:
83.33 feet * (1 mile / 5,280 feet)
Calculate the result:
83.33 / 5280
= 0.0157 miles
Therefore, the molecule's speed is approximately 0.0157 miles per hour.
I hope this helps! Let me know if you have any further questions.