Question

apply

1. the formula (t = \frac{sqrt{h}}{4}) represents the time (t) in seconds that it takes an object to fall from a height of (h) feet. if a rock falls from 125 feet, estimate how long it will take the rock to hit the ground. estimate the square root to the nearest integer. locate the value on a number line.
2. the radius of a circle with area (a) can be approximated using the formula (r=sqrt{\frac{a}{3}}). estimate the radius of a wrestling mat circle with an area of 452 square feet. round to the nearest integer. locate the value on a number line.

Explanation:

Step1: Substitute $h = 125$ into the time - fall formula

Given $t=\frac{\sqrt{h}}{4}$, substituting $h = 125$ gives $t=\frac{\sqrt{125}}{4}$.

Step2: Estimate $\sqrt{125}$

We know that $11^2=121$ and $12^2 = 144$. Since $125$ is closer to $121$, $\sqrt{125}\approx11$.

Step3: Calculate the time $t$

$t=\frac{\sqrt{125}}{4}\approx\frac{11}{4}=2.75\approx3$ seconds.

Step4: For the circle - radius problem, substitute $A = 452$ into the radius formula

Given $r=\sqrt{\frac{A}{3}}$, substituting $A = 452$ gives $r=\sqrt{\frac{452}{3}}$. First, calculate $\frac{452}{3}\approx150.67$.

Step5: Estimate $\sqrt{150.67}$

We know that $12^2=144$ and $13^2 = 169$. Since $150.67$ is closer to $144$, $\sqrt{150.67}\approx12$.

Answer:

1. For the falling - rock problem, it takes about 3 seconds for the rock to hit the ground.
2. For the circle problem, the radius of the wrestling - mat circle is about 12 feet.