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.
The answer is 60 feet.
Step by step explanation:
The area of a triangle is Area= base x height divided by 2.
Solve for the base:
Base= 2* area/ height and plug in the data:
Base= 2* 600/20
Final answer:
Base: 60 feet.
20 = 8 + v equals v = 12.
First, subtract 8 from both sides. Your problem should look like: 20 - 8 = v
Second, simplify 20 - 8 to get 12. Your problem should look like: 12 = v.
Third, switch sides to get v = 12, which is the correct answer.
Answer:
1) First, add or subtract both sides of the linear equation by the same number. 2) Secondly, multiply or divide both sides of the linear equation by the same number. 3)* Instead of step #2, always multiply both sides of the equation by the reciprocal of the coefficient of the variable.
Step-by-step explanation:
Answer: B is the same length away from 0 as A is
Step-by-step explanation:
