Answer: 6,000.
Step-by-step explanation:
Answer:
a. 
b. 
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:
Then, to find the amount of caffeine metabolized per hour, we need to differentiate the previous equation. Following the differentiation rules we get:
The rate is negative as it represents the amount of caffeine leaving the body at certain time.
ANSWER:
x = 10 / 3
y = 0
STEP-BY-STEP EXPLANATION:
We will be using simultaneous equations to solve this problem. Let's first establish the two equations which we will be using.
Equation No. 1 -
- 6x - 14y = - 20
Equation No. 2 -
- 3x - 7y = - 10
First, we will make ( x ) the subject in the first equation and simplify accordingly.
Equation No. 1 -
- 6x - 14y = - 20
- 6x = - 20 + 14y
x = ( - 20 + 14y ) / - 6
x = ( - 10 + 7y ) / - 3
From this, we will make ( y ) the subject in the second equation and substitute the value of ( x ) from the first equation into the second equation to solve for ( y ) accordingly.
Equation No. 2 -
- 3x - 7y = - 10
- 7y = - 10 + 3x
- 7y = - 10 + 3 [ ( - 10 + 7y ) / - 3 ]
- 7y = - 10 + [ ( - 30 + 21y ) / - 3 ]
- 7y = - 10 + ( 10 - 7y )
- 7y = - 7y
- 7y + 7y = 0
0y = 0
y = 0
Using this, we will substitute the value of ( y ) from the second equation into the first equation to solve for ( x ) accordingly.
x = ( - 10 + 7y ) / - 3
x = [ - 10 + 7 ( 0 ) ] / - 3
x = [ - 10 + 0 ] / - 3
x = - 10 / - 3
x = 10 / 3
Your answer is b. hope this helps :)
