The statement "<span>The rate of change of y with respect to x is inversely proportional to y^4" can be written mathematically as dy/dx = k/y^4
To solve the differential equation, we use variable saparable method.
y^4 dy = kdx
Integrating both sides gives,
y^5 / 5 = kx + A
y^5 = 5kx + 5A = Bx + C; where B = 5k and C = 5A
![y= \sqrt[5]{Bx+C}](https://tex.z-dn.net/?f=y%3D%20%5Csqrt%5B5%5D%7BBx%2BC%7D%20)
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Define rates at which the individuals paint.
Bill: x = 1/8 signs/h
Bob: y = (2 signs)/(8 h) = 1/4 signs/h
Barry: z = (4/3 signs)/(8 h) = 1/6 signs/h
The job is to paint 2 signs, working together.
In the first 3 hours, the amount painted is
(x+y+z signs/h)*(3 h) = (1/8 + 1/4 + 1/6)*3 = 13/8 signs
Remaining: 2 - 13/8 = 3/8 signs
Barry quits.
In the next 1/2 hour (30 minutes), the amount painted is
(x + y signs/h)*(0.5 h) = (1/8 + 1/4)*0.5 = 3/16 signs
Remaining: 3/8 - 3/16 = 3/16 signs
Now Bob quits.
The time for Bill to finish the job is
(3/16 signs)/(1/8 signs/h) = 3/2 h
Answer: Bill finishes the job in 1.5 hours (or 1 hour, 30 minutes)
Answer:
10 eggs
Step-by-step explanation:
5 cartons multiplied by 12 eggs each equals 60 eggs in total.
Therefore 5/6 would be equal to 50/60 since we multiply the denominator and numerator by 10
As a result 10 of the eggs are not brown
If Sajid’s scale is 1:32, the ratio of the length of his model and the lorry is, of course, 1/32. Meaning that the lorry is (32*45)cm long. So, it is 1440 cm. If Chitra’s model uses the scale 1:72, every 72 cm of length of the lorry is 1 cm on the model, meaning that the length of his model is (1440/72) cm= 20 cm
Answer:
The expected number of days until the prisoner reaches freedom is 2.8.
Step-by-step explanation:
Door 1: 0.3 probability of being selected. Leads to his cell after two days' travel.
Door 2: 0.5 probability of being selected. Leads to his cell after four days' travel.
Door 3: 0.2 probability of being selected. Leads to his cell after one day of travel.
What is the expected number of days until the prisoner reaches freedom?
We multiply the probability of each door being used by the time that it leads to the cell. So
E = 0.3*2 + 0.5*4 + 0.2*1 = 2.8
The expected number of days until the prisoner reaches freedom is 2.8.
