1. -48v-5/45 2.44-r/2 3. x=2
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:
A is on a line with the slope of 2/3
Step-by-step explanation:
the rule is that you do y2-y1 over x2-x1 which you do 4-2 over 8-5 and your final answer you would get 2/3.
hope this helped!
i am new here and my name is arrianna call me arri for short
Answer:
-2(-2) + (12-9) = 2 + 9 + -2(-2)
Step-by-step explanation:
Answer:
42 cups of flour
Step-by-step explanation:
12 is 4 times more than 3 (3 × 4 = 12), so we know that we need 4 times 10 1/2 (equal to 10.5) cups of flour.
All we need to do for this is do 10.5 × 4 = x and solve for x.
10.5 × 4 = 42 cups of flour
