Answer:
6
Step-by-step explanation:
The absolute value of a non-negative number is the same number.
Example: The absolute value of 4 is 4.
If a number is negative, its absolute value is the same number, without the negative sign.
Example: The absolute value of -3 is 3.
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:
The total percentage return is 26.19
Step-by-step explanation:
Given as :
The amount paid for three years = $ 2800
So, Total amount paid for three years = $ 2800 × 3 = $ 8400
The return amount after three years = $ 2200
The time period = 3 years
Let the percentage return = x %
So, According to question
x % of $ 8400 = $ 2200
Or, x % = 
Or, 
= 
∴ x = × 100
I.e x = 26.19
Hence The total percentage return is 26.19 Answer
