Dy/dx = (ycos(x))/(1 + y²)
(1 + y²)/y dy = cos(x) dx
(1/y + y) dy = cos(x) dx
Integrating:
ln(y) + y²/2 = sin(x) + c
ln(1) + 1/2 = sin(0) + c
c = 1/2
Thus,
ln(y) + y²/2 = sin(x) + 1/2
Answer:
Blank 1: 40
Blank 2: 10
Step-by-step explanation:
You can start by representing the speed of the water as x and the speed of the dolphin as y, and writing an equation.
y+x=50
y-x=30
Adding these two equations together, you get:
2y=80
y=40 for the speed of the dolphin in still water. Now, you an use one of the previous equations to find the speed of the current.
40-x=30
x=10
Hope this helps!
Answer:
5 and 0 between 250 and 300
Answer:
Step-by-step explanation:
<u>The volume is the product of three dimensions, so the ratio of volumes is the cube of the scale factor:</u>
- k = 8/11
- k³ = (8/11)³ = 512 / 1331
Answer: 5 games
Step-by-step explanation: A .500 record means that the soccer team won half of their games ( that's how I interpret it). Since they are going to play 30 games, they need to win half of 30 or 15 games to have that record. 15-10 = 5. So, they need to win 5 more games to have a .500 record.
