I hope this helps you
there is a 5,12,13 triangle
x^2=5^2+12^2
x^2=25+144
x^2=169
x=13
Can you give me more info abt the problem plz so I can do the best I can to help
Answer:
a. ![A = C_{0}(1-x)^t\\x: percentage\ of \ caffeine\ metabolized\\](https://tex.z-dn.net/?f=A%20%3D%20C_%7B0%7D%281-x%29%5Et%5C%5Cx%3A%20percentage%5C%20of%20%5C%20caffeine%5C%20metabolized%5C%5C)
b. ![\frac{dA}{dt}= -11.25 \frac{mg}{h}](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdt%7D%3D%20-11.25%20%5Cfrac%7Bmg%7D%7Bh%7D)
Step-by-step explanation:
First, we need tot find a general expression for the amount of caffeine remaining in the body after certain time. As the problem states that every hour x percent of caffeine leaves the body, we must substract that percentage from the initial quantity of caffeine, by each hour passing. That expression would be:
![A= C_{0}(1-x)^t\\t: time \ in \ hours\\x: percentage \ of \ caffeine\ metabolized\\](https://tex.z-dn.net/?f=A%3D%20C_%7B0%7D%281-x%29%5Et%5C%5Ct%3A%20time%20%5C%20in%20%5C%20hours%5C%5Cx%3A%20percentage%20%5C%20of%20%5C%20caffeine%5C%20metabolized%5C%5C)
Then, to find the amount of caffeine metabolized per hour, we need to differentiate the previous equation. Following the differentiation rules we get:
![\frac{dA}{dt} =C_{0}(1-x)^t \ln (1-x)\\\frac{dA}{dt} =100*0.88\ln(0.88)\\\frac{dA}{dt} =-11.25 \frac{mg}{h}](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdt%7D%20%3DC_%7B0%7D%281-x%29%5Et%20%5Cln%20%281-x%29%5C%5C%5Cfrac%7BdA%7D%7Bdt%7D%20%3D100%2A0.88%5Cln%280.88%29%5C%5C%5Cfrac%7BdA%7D%7Bdt%7D%20%3D-11.25%20%5Cfrac%7Bmg%7D%7Bh%7D)
The rate is negative as it represents the amount of caffeine leaving the body at certain time.
Set up an algebraic equation to find the cost of each game.
5x+15=155.
x is the cost of each game multiplied by 5(total amount of games).
15 is the cost or the carrier.
155 is the total cost.
Now you solve:
5x+15=155,
5x=140,
x=28.
The cost of each game is $28.
Check: 5 (28)+15=155