I have a homework problem dealing with Inverse Variation which I don't get at all.
1. Copy and complete each table using the given equation.
a.|x | y | b. |x |y |
|0.2| | |1/4| |
| |3.2 | |1/2| |
| | 1 | | | 1 |
|4 | | | | 2 |
|2 | |
xy = 1.6 xy = 1/8
Thanks! I need all the help I can get!
The table did not print, sorry.
No problem! I can still help you understand how to complete the tables using the given equation for inverse variation. Inverse variation is a relationship between two variables where their product remains constant. The equation for inverse variation is typically expressed as:
y = k/x
where y and x are the variables, and k is the constant.
To complete the tables, we'll need to substitute the given values of x or y into the equation and solve for the missing values.
a. Given equation: y = k/x
| x | y |
|----|----|
| 0.2| |
| |3.2 |
| | 1 |
| 4 | |
| 2 | |
In the first row, we have an x-value of 0.2. Let's substitute this value into the equation:
y = k/0.2
To find k, we'll use the relationship between x and y given by the equation xy = 1.6. Substitute the x and y values from the first row:
0.2y = 1.6
Now we can solve for y:
y = 1.6/0.2
y = 8
So the first row of the table becomes:
| x | y |
|----|-----|
| 0.2| 8 |
To complete the rest of the table, you can use the same process. Substitute the given values of x or y into the equation, solve for the missing value using the given relationship xy = 1.6, and fill in the table.
Let's move on to part b:
| x | y |
|-----|-----|
| 1/4 | |
| | 1/2 |
| | 1 |
| 4 | |
| 2 | |
Again, we'll use the equation y = k/x and the given relationship xy = 1/8 to complete the table. Follow the same steps as explained for part a to find the missing values.
I hope this helps you understand how to complete the tables for inverse variation! Let me know if you have any more questions.