Hello there. To solve this question, we'll have to remember some properties about finding values of expressions.
We need to plot two points in the line to show the approximate positions where Andrea and Larry should tape their cards.
The cards contains a number for each of them.
For Andrea, the number is:
[tex]2\pi[/tex]
To find where Andrea should tape her card, in this case we need to know an approximation for the number pi.
Using 3.141 as an approximation, we have that she should tape her card at:
[tex]2\cdot3.141=6.282\approx6.3[/tex]
For Larry, the number is:
[tex]\sqrt[]{17}[/tex]
In the case of Larry, we can use another idea to find the approximate value.
Remember that for positive numbers, the root of a number is an injective function. It means that for valeus a and b, with a < b, it is true that:
[tex]\sqrt[]{a}<\sqrt[]{b}[/tex]
Knowing:
[tex]16<17<25[/tex]
Taking the square root on both sides of the inequality, we have:
[tex]4<\sqrt[]{17}<5[/tex]
In fact, the approximate value of this square root is 4.12, therefore Larry should tape his card at:
[tex]4.1[/tex]
