1,200 people have spinal injuries from falls.
Answer:
3:36 PM
Step-by-step explanation:
Let fraction (y) of the people that heard the rumor , the differential equation that is satisfied by the by y is,

Solving the differential equation,
![y(t) = \frac{y_{o}}{[y_{o} + (1 + y_{o})e^{-kt}]}](https://tex.z-dn.net/?f=y%28t%29%20%3D%20%5Cfrac%7By_%7Bo%7D%7D%7B%5By_%7Bo%7D%20%2B%20%281%20%2B%20y_%7Bo%7D%29e%5E%7B-kt%7D%5D%7D)
The total number of inhabitants of the town = 2000
The number of people that heard the rumor = 160
At 8 AM, let t = 0,

= 0.08
By noon, half of the town as heard the rumor.
Then,

Therefore,
![\frac{1}{2} = \frac{0.08}{[0.08 + (1 - 0.08)e^{-4k}]}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%3D%20%5Cfrac%7B0.08%7D%7B%5B0.08%20%2B%20%281%20-%200.08%29e%5E%7B-4k%7D%5D%7D)
![\frac{0.08}{[0.08 + 0.92e^{-4k}]} = \frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B0.08%7D%7B%5B0.08%20%2B%200.92e%5E%7B-4k%7D%5D%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D)




k ≈ 0.06106
Calculating time, t when y(t) = 90%
⇒ y(t) = 0.9
![\frac{0.08}{[0.08 + 0.92e^{-0.06106t}]} =0.9](https://tex.z-dn.net/?f=%5Cfrac%7B0.08%7D%7B%5B0.08%20%2B%200.92e%5E%7B-0.06106t%7D%5D%7D%20%3D0.9)





t = 7.59 hours
⇒ 7 hours 36 minutes
From 8 A.M. plus 7 hours 36 minutes = 3:36 PM
At 3:36 PM will 90% of the population have heard the rumor
The answer is 6 because 6 is a multiple of 3 and is half of 12 so he could buy 2 of them
Answer:
- B solving by factoring
- A the quadratic formula
Step-by-step explanation:
<h3>1.</h3>
The "zero product principle" or "zero product rule" tells you a product will be zero if and only if one or more of the factors is zero. This fact is used to solve quadratic equations by factoring.
Factoring the equation y = ax² +bx +c to the form y = a(x -r)(x -s) allows you to immediately identify the solutions of y=0 as x=r and x=s. These are the values of x that make the factors zero, hence making the product zero.
Finding the values of x that satisfy ax² +bx +c = 0 by rearranging it to the form a(x -r)(x -s) = 0 is called "solving by factoring."
<h3>2.</h3>
When the process of "completing the square" is applied to the standard-form quadratic y = ax² +bx +c, the result is a formula for the two solutions to y = 0:

This quadratic formula tells you the solutions based on the coefficients of the original equation, so <em>does not require rearranging</em> the equation in any way.