a function machine accepts inputs as ordered pairs. the components of the ordered pairs are natural number and the first component is the length of a rectangle and the second component is the width. The given machine computes the perimeter (the distance around the rectangle). Find the output for
(1,8)
(8,10)
(10,3)
(5,10)
Find an input that gives an output of 16
Thanks for the help, I have no clue.
you know the perimeter is 2(length+width)
So,
f(1,8) = 2(1+8) = 2(9) = 18
and so on for the others.
To produce an output of 16, all you need is two numbers that add up to 8.
To find the output for each ordered pair, we need to calculate the perimeter of the corresponding rectangle. The perimeter of a rectangle is calculated by adding twice the length and twice the width.
Let's compute the perimeter for each ordered pair:
1) (1,8)
Perimeter = 2 * length + 2 * width = 2 * 1 + 2 * 8 = 2 + 16 = 18
2) (8,10)
Perimeter = 2 * length + 2 * width = 2 * 8 + 2 * 10 = 16 + 20 = 36
3) (10,3)
Perimeter = 2 * length + 2 * width = 2 * 10 + 2 * 3 = 20 + 6 = 26
4) (5,10)
Perimeter = 2 * length + 2 * width = 2 * 5 + 2 * 10 = 10 + 20 = 30
Now, let's find an input that gives an output of 16.
To find an input with a perimeter of 16, we need to solve the equation:
2 * length + 2 * width = 16
Since the components of the ordered pair are natural numbers, you can try different combinations of length and width that satisfy the equation. Here are a few possible solutions:
- length = 2, width = 6: 2 * 2 + 2 * 6 = 4 + 12 = 16
- length = 3, width = 5: 2 * 3 + 2 * 5 = 6 + 10 = 16
- length = 4, width = 4: 2 * 4 + 2 * 4 = 8 + 8 = 16
There may be other combinations that satisfy the equation, so feel free to explore more possibilities until you find a suitable input.