Question

order the set of numbers from least to greatest. then graph the set on a number line. 3 1/2, 10/3, π, √13. the radius of a circle can be approximated using the expression √(a/π) where a represents the area. a circular kiddie swimming pool has an area of about 28 square feet. an inflatable full - size circular pool has an area of about 113 square feet. how much greater is the radius of the full - size pool than the radius of the kiddie pool? round to the nearest whole number. the time in seconds that it takes an object to fall d feet can be found using the expressions √(d/16). in an egg drop contest, clara successfully dropped her egg container from a height of 35 feet, while vladimir successfully dropped his egg container from a height of 23 feet. how much longer did it take claras egg to reach the floor than vladimirs egg? round to the nearest tenth. which number is greater, 3.14 or π? justify your answer.

Explanation:

Step1: Convert mixed - number to improper fraction

$3\frac{1}{2}=\frac{3\times2 + 1}{2}=\frac{7}{2}=3.5$

Step2: Calculate decimal value of fraction

$\frac{10}{3}=10\div3\approx3.33$

Step3: Recall value of $\pi$

$\pi\approx3.14$

Step4: Calculate square - root value

$\sqrt{13}\approx3.61$ (since $3.61\times3.61 = 12.9721$ and $3.62\times3.62=13.1044$)

Step5: Order the numbers

Comparing the values $3.14<3.33<3.5<3.61$, so $\pi<\frac{10}{3}<3\frac{1}{2}<\sqrt{13}$

Answer:

$\pi,\frac{10}{3},3\frac{1}{2},\sqrt{13}$