Answer:
DJ = 48
Step-by-step explanation:
In triangle CDE, point J is the centroid.
Length of median DH = 72
By the property of the centroid of a triangle,
"Centroid of a triangle divides the medians in the ratio of 2 : 1"
By this property, length of DJ = ![\frac{2}{(2+1)}(DH)](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B%282%2B1%29%7D%28DH%29)
= ![\frac{2}{3}(72)](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%2872%29)
= 48 units
Therefore, length of DJ = 48 units
Answer:
Illinois is 4 times larger than Hawaii
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.