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1 answer:
First part
Determine 2 points that pass through x + 2y = 5
(i) If x = 1
x + 2y = 5
1 + 2y = 5
2y = 4
y = 2
(ii) If x = 3
x + 2y = 5
3 + 2y = 5
2y = 2
y = 1
Two points that pass through this line are (1,2) and (3,1)
Second part
Determine 2 points that pass through 3x = 15 - 6y
(i) If x = 1
3x = 15 - 6y
3(1) = 15 - 6y
3 = 15 - 6y
6y = 15 - 3
6y = 12
y = 2
(ii) If x = 3
3x = 15 - 6y
3(3) = 15 - 6y
9 = 15 - 6y
6y = 15 - 9
6y = 6
y = 1
Two points that pass through this line are (1,2) and (3,1)
BOTH OF THE LINE pass through the same two points, that means the lines are the same because they overlap. Look at the attachment.
Determine 2 points that pass through x + 2y = 5
(i) If x = 1
x + 2y = 5
1 + 2y = 5
2y = 4
y = 2
(ii) If x = 3
x + 2y = 5
3 + 2y = 5
2y = 2
y = 1
Two points that pass through this line are (1,2) and (3,1)
Second part
Determine 2 points that pass through 3x = 15 - 6y
(i) If x = 1
3x = 15 - 6y
3(1) = 15 - 6y
3 = 15 - 6y
6y = 15 - 3
6y = 12
y = 2
(ii) If x = 3
3x = 15 - 6y
3(3) = 15 - 6y
9 = 15 - 6y
6y = 15 - 9
6y = 6
y = 1
Two points that pass through this line are (1,2) and (3,1)
BOTH OF THE LINE pass through the same two points, that means the lines are the same because they overlap. Look at the attachment.
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The amount of oxygen in the flask through the intake tube illustrates proportions
The flask 99.35% will contain of oxygen after 5L have passed through the intake tube
<h3>How to calculate the percentage of oxygen?</h3>
To do this, we make use of the following representations
- P for the proportion of oxygen
- V for te volume of oxygen
- x for the proportion of oxygen in the flask after 5 L passed through
So. we have the following derivative
dP = dV - P * dV
Divide through by dV
dP/dV = 1 - P
Next, we set up the integral
Integrate both sides
Expand
-ln(|x - 1|) + ln(|0.04 - 1|) = 5
Evaluate the difference
-ln(|x - 1|) + ln(|-0.96|) = 5
Express as a fraction
ln(0.96/|x - 1|) = 5
Express both sides as exponents with a base of 2
e^ln(0.96/|x - 1|) = e^5
Solve for x
x = 1 - 0.96/e^5
Evaluate the difference
x = 0.9935
Express as percentage
x = 99.35%
Hence, the flask 99.35% will contain of oxygen after 5L have passed through the intake tube
Read more about proportions at:
Answer:
Step-by-step explanation:
