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3 years ago

I need help understanding this and help with the problems...

Mathematics

2 answers:

Pavel [41]3 years ago

7 0

1. 15+37=?

15=10+5 (given on the diagram)
37=30+7 (given on the diagram)
add digits to digits 5+7=12=10+2
add tens to tens 10+30+10=50
add tens and digits 50+2=52.

2. 22+49=?

22=20+2 (given on the diagram)
49=40+9 (given on the diagram)
add digits to digits 2+9=11=10+1
add tens to tens 20+40+10=70
add tens and digits 70+1=71.

3. 38+26=?

38=30+8 (given on the diagram)
26=20+6 (given on the diagram)
add digits to digits 8+6=14=10+4
add tens to tens 30+20+10=60
add tens and digits 60+4=64.

Answer: 1) 52; 2) 71; 3) 64.

Phoenix [80]3 years ago

4 0

Number 1 is 52 number 2 is 71 and number 3 is 64

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3 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:

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

The rate is negative as it represents the amount of caffeine leaving the body at certain time.

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3 years ago

What are the solutions of x^2+5x=2? Check all that apply

astraxan [27]

X^2+5x=2
you then solve by completing the square using the formula (b/2)^2 in order to create the new term. Solve for x by using this term to complete the square.
Your answer is then
x=-5/2+-√33/2

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