Find the area of a rhombus, whose diagonals are 10cm and 5.2cmstep by step

1 answer:

3 0

The area of a rhombus is p x q divided by 2.

p and q are both the diagonals of the shape.

In this case, we would do 10 x 5.2 divided by 2, which gives us 26, so your answer is 26 cm^2 (squared).

Hope this helps!

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Find the first, fourth, and eighth terms of the sequence. a(n)=-2 x 2^n-1

leonid [27]

Answer:

2, 16 and 256.

Step-by-step explanation:

Just substitute for n:-

first term ( when n = 1) = 2 * 2^(1-1)

= 2 * 1 = 2

4th term = 2 * 2^(4-1) = 16

8th term = 2* 2^(8-1) = 256

8 0

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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%

Mamont248 [21]

Answer:

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

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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:

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