Multiply the original DE by xy:
xy2(1+x2y4+1−−−−−−−√)dx+2x2ydy=0(1)
Let v=xy2, so that dv=y2dx+2xydy. Then (1) becomes
x(y2dx+2xydy)+xy2x2y4+1−−−−−−−√dxxdv+vv2+1−−−−−√dx=0=0
This final equation is easily recognized as separable:
dxxln|x|+CKxvKx2y2−1K2x4y4−2Kx2y2y2=−dvvv2+1−−−−−√=ln∣∣∣v2+1−−−−−√+1v∣∣∣=v2+1−−−−−√+1=x2y4+1−−−−−−−√=x2y4=2KK2x2−1integrate both sides
Answer:
The number of children's tickets sold was 27
Step-by-step explanation:
Let
x ----> the number of children's tickets sold
y ----> the number of adult's tickets sold
we know that
----> equation A
----> equation B
Solve the system by substitution
Substitute equation B in equation A

solve for x



therefore
The number of children's tickets sold was 27
Answer:
The probability is 
Step-by-step explanation:
From the question we are told that
The population proportion is 
The mean of the sampling distribution is 
The sample size is n = 600
Generally the standard deviation is mathematically represented as

=>
=>
Generally the probability that the proportion of airborne viruses in a sample of 600 viruses would differ from the population proportion by greater than 3% is mathematically represented as

=> 
Now add p to both side of the inequality
=> 
=> 
Now converting the probabilities to their respective standardized score
=>
=> 
=> ![P(|p-\^{p}| > 0.03) = 1 - [P(Z \le 2.88) - P(Z \le -2.88)]](https://tex.z-dn.net/?f=P%28%7Cp-%5C%5E%7Bp%7D%7C%20%3E%20%200.03%29%20%20%3D%20%20%201%20-%20%5BP%28Z%20%5Cle%202.88%29%20-%20P%28Z%20%5Cle%20-2.88%29%5D)
From the z-table

and

So
![P(|p-\^{p}| > 0.03) = 1 - [0.9980 - 0.0020]](https://tex.z-dn.net/?f=P%28%7Cp-%5C%5E%7Bp%7D%7C%20%3E%20%200.03%29%20%20%3D%20%20%201%20-%20%5B0.9980%20-%200.0020%5D)
=> 
Let x be the first jug, y the second jug.
From first statement, subtracting 1 from x, makes them equal:
x - 1 = y
From second statement, subtracting 2 from y, makes it half of x:
x/2 = y-2
Solve system with substitution:
x/2 = (x-1) -2
x/2 = x - 3
x- x/2 = 3
x/2 = 3
x = 6
y = x-1 = 6-1 = 5
Therefore the largest jug contains 6 liters.