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: 5
Step-by-step explanation:
47+ 16x-4 +12x-3 =180
28x +40 =180
28x = 140
X= 5
First, you need to find the zero of x+3, which is -3
then you multiply -3×1, which equals -3
the reason why I multiplied -3×1 is because the 1 is the coefficient of x^2 but we just don't see it because we don't need to.
once we get -3 we add that to the next coefficient (-5)
-3+-5=-8
we take the sum (-8) and multiply that to -3 (the zero of x+3)
we get 24, so we add -22+24=2
-22 Is the next coefficient to come and 2 is our remainder
the new equation is: x-8 remainder 2
Answer: C, 9 units
Step-by-step explanation:
(-4, -3) is new point
The length of the radius would sqrt(1+4), or sqrt(5).
2
The angle would be in Quadrant II and would be arctan ------ , or arctan (-2).
-1
Find this angle using a calculator or table.
Then you end up with -1+2i = sqrt(5) angle arctan(-2). The angle would be + and measured from the + horizontal axis.
