Solve this problem.

Mathematics

1 answer:

Katyanochek1 [597]3 years ago

3 0

Answer:

Let x = the width of the smaller rectangle.

The length of the smaller rectangle is 2x - 1.

Area is A = lw

So the area of the smaller rectangle is A = (x)(2x - 1) = 2x^2 - x

Step-by-step explanation:

hope it helped

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Solve for x please and quick please

alisha [4.7K]

Answer:

x = √149 km

Step-by-step explanation:

Pythagorean theorem

x^2 = 10^2 + 7^2

x^2 = 100 + 49

x^2 = 149

x = √149

4 0

2 years ago

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

Mamont248 [21]

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:

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