If the boat can travel 45 mph in still water and the current is 10 mph, down stream, or with the current, has the boat moving at 55. Upstream has the boat moving 35 mph. It took t time to go with the current and an hour longer, t + 1, to go against it. Going from point A to B and back to A again means that the trip there was the same distance as the trip back. So d is the same for both upstream and downstream. The equation for upstream is d = 35(t + 1) or d = 35t + 35; the equation for downstream is d = 55t. Since the distances are the same, the transitive property says that so are the rates and times; therefore, we can set those equal to one another. 35t + 35 = 55t. Solve for t. When we find that t = 7/4 (1 3/4 hours), we sub that in to solve for distance. 55(7/4) = 96 1/4 miles.
Answer:
There are 3 numbers greater than 7 on this spinner: 8, 9 and 10. Mariah wrote 4 instead of 3, which makes her probability higher.
She should have:
3/10(250) = 750/10 = 75
2/4 on the 0 to 1 and 5/4 on the 1 to 2
Answer:
D
Step-by-step explanation:
First take out a factor of 2:
2(1 - 25x^2)
Then factor the difference of squares:
2(1 -5x)(1+5x)
Answer:
Step-by-step explanation:
The large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved.
Volume = 500 gallons
Initial Amount of Salt, A(0)=50 pounds
Brine solution with concentration of 2 lb/gal is pumped into the tank at a rate of 3 gal/min
=(concentration of salt in inflow)(input rate of brine)
When the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min.
Concentration c(t) of the salt in the tank at time t
Concentration, 
=(concentration of salt in outflow)(output rate of brine)
Now, the rate of change of the amount of salt in the tank
We solve the resulting differential equation by separation of variables.
Taking the integral of both sides
Recall that when t=0, A(t)=50 (our initial condition)
