11. Solve for the value of x in the triangle shown below. Show your work! (1 point for equation, 1 point for answer)

Mathematics

1 answer:

Brut [27]3 years ago

7 0

3 inside angles need to = 180, since it is a right triangle, the bottom left angle = 80 so the other 2 angles need to equal 90 degrees

so you have:

(8x+2) + (9x+3) = 90

combine like terms to get:

17x+5 = 90

subtract 5 from both sides:

17x = 85

divide both sides by 17

x = 85/17 = 5

x = 5

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A cup of coffee contains about 100 mg of caffeine. Caffeine is metabolized and leaves the body at a continuous rate of about 12%

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Answer:

a. $A = C_{0}(1-x)^t\\x: percentage\ of \ caffeine\ metabolized\\$

b. $\frac{dA}{dt}= -11.25 \frac{mg}{h}$

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:

$A= C_{0}(1-x)^t\\t: time \ in \ hours\\x: percentage \ of \ caffeine\ metabolized\\$

Then, to find the amount of caffeine metabolized per hour, we need to differentiate the previous equation. Following the differentiation rules we get:

$\frac{dA}{dt} =C_{0}(1-x)^t \ln (1-x)\\\frac{dA}{dt} =100*0.88\ln(0.88)\\\frac{dA}{dt} =-11.25 \frac{mg}{h}$