Based on function transformations, the graph of y= cos(2θ), is the same as the graph of <span>y= cos(θ), with a component B of 2, in which case, it means the period is the only thing that differs
well the period for this function will then be </span>
so, the graph of is, the same as y= cos(θ), just shrunk by half horizontally
Answer:
Step-by-step explanation:
Volume of tank is 3000L.
Mass of salt is 15kg
Input rate of water is 30L/min
dV/dt=30L/min
Let y(t) be the amount of salt at any time
Then,
dy/dt = input rate - output rate.
The input rate is zero since only water is added and not salt solution
Now, output rate.
Concentrate on of the salt in the tank at any time (t) is given as
Since it holds initially holds 3000L of brine then the mass to volume rate is y(t)/3000
dy/dt= dV/dt × dM/dV
dy/dt=30×y/3000
dy/dt=y/100
Applying variable separation to solve the ODE
1/y dy=0.01dt
Integrate both side
∫ 1/y dy = ∫ 0.01dt
In(y)= 0.01t + A, .A is constant
Take exponential of both side
y=exp(0.01t+A)
y=exp(0.01t)exp(A)
exp(A) is another constant let say C
y(t)=Cexp(0.01t)
The initial condition given
At t=0 y=15kg
15=Cexp(0)
Therefore, C=15
Then, the solution becomes
y(t) = 15exp(0.01t)
At any time that is the mass.
Term: 3 4 5
Value 20 .. 5
20 20r 20r^2
So 20r^2 = 5
r^2 = 1/4
r = 1/2
Answer:
125 is the value of the question
Vertical angles are congruent due to the fact that they intersect. If they did not, they would in fact be parallel. (last section)