Answer:
y = 2cos5x-9/5sin5x
Step-by-step explanation:
Given the solution to the differential equation y'' + 25y = 0 to be
y = c1 cos(5x) + c2 sin(5x). In order to find the solution to the differential equation given the boundary conditions y(0) = 1, y'(π) = 9, we need to first get the constant c1 and c2 and substitute the values back into the original solution.
According to the boundary condition y(0) = 2, it means when x = 0, y = 2
On substituting;
2 = c1cos(5(0)) + c2sin(5(0))
2 = c1cos0+c2sin0
2 = c1 + 0
c1 = 2
Substituting the other boundary condition y'(π) = 9, to do that we need to first get the first differential of y(x) i.e y'(x). Given
y(x) = c1cos5x + c2sin5x
y'(x) = -5c1sin5x + 5c2cos5x
If y'(π) = 9, this means when x = π, y'(x) = 9
On substituting;
9 = -5c1sin5π + 5c2cos5π
9 = -5c1(0) + 5c2(-1)
9 = 0-5c2
-5c2 = 9
c2 = -9/5
Substituting c1 = 2 and c2 = -9/5 into the solution to the general differential equation
y = c1 cos(5x) + c2 sin(5x) will give
y = 2cos5x-9/5sin5x
The final expression gives the required solution to the differential equation.
Answer:
D
Step-by-step explanation:
8% in decimal form is written out as 0.08, so right away the answer is either C or D.
Then if you have "s" = 1875, you would get:
350 + (0.08 × 1875) = 500
That would mean any number greater than 1875 will give you a total more than 500.
Therefore the answer is D.
Answer:
3/4 or 0.75
Step-by-step explanation:
1. Cross multiply: (1/2) / (3/4)
2. 1 x 3 = 3 and 2 x 2 = 4
3. 3/4 or 0.75
Answer:
Step-by-step explanation:
Given
Required
The linear function of a competitor's website
On day 1, both websites have the same subscribers.
This implies that:
Substitute: 
This implies:
On day 34, both websites have the same subscribers.
This implies that:
Substitute: 
This implies:
To calculate the linear function of the competitor, we have:
Calculate slope (m)
The equation is then calculated as:
This gives:
Open bracket
<em></em><em> --- This represents the linear function of the competitor's website</em>
