Answer:
(c) 2.034 s; (d) 8.944 cm
Step-by-step explanation:
Velocity and acceleration
s = 8cos(t) + 4sin(t)
v = -8sin(t) + 4cos(t)
a = -8cos(t) + 4sin(t)
(c) Time to first equilibrium position
The equilibrium position is where the mass hangs before it is pulled downward, that is, at s = 0.
Set s = 0 and solve for t.
If n = 1,
t = -1.107 + π = 2.034 s
(d) Distance from equilibrium position
The mass will reach its maximum distance when v = 0, that is, when it is at the peak or trough of its oscillation.
Set v = 0 and solve for t.
If n = 0,
t = 0.4636
Then
s = 8cos(0.4636) + 4sin(0.4636) = 8×0.8944 + 4×0.4472 = 7.156 + 1.789 = 8.944 cm
The figure below shows the graphs of s and v vs t. They indicate that the mass first reaches its equilibrium position at 2.034 s, and the amplitude of its vibration is 8.944 cm.
notice above... we use the decimal format for the percentage, thus 20% is really just 20/100, 40% is 40/100 and so on.
so.. whatever "x" and "y" amounts are, we know they have to add up to 60 Liters, that is x+y = 60
and whatever the concentration amount of each is, it must add up to (60)(0.40), that is 0.20x+0.50y=(60)(0.40)
thus
solve for "x", to see how much of the 20% solution will be needed
what about "y"? well, y = 60 - x
I’m assuming “triple 4” is just 3 times 4.
Using the information from the problem, we can form an equation that reads,
3*4 + 7*7
Solve:
12 + 49 = 61
The answer is 61
K> 4.5 is a closed line and its greater than so it would go to the right so
D is the correct answer.
Step-by-step explanation:
Amount payed = 15 dollars
No of persons = 3
Amount of 1 person = 15 ÷ 3 = 5
Option C is the correct answer