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:
149.5, 150.5 , 151.5, 152.5
Step-by-step explanation:
n+(n+1)+(n+2)+(n+3)= 604
Combine Like Terms
4n + 6 = 604
Subtract 6
4n = 598
Divide by 4
n=149.5
Check Your Work:
149.5+150.5+151.5+152.5 = 604
Answer:
<u>Circumference</u><u> </u><u>of </u><u>a </u><u>circle </u><u>is </u><u>given </u><u>by </u>
<u>
</u>
- Given - <u>Diameter</u><u> </u><u>of </u><u>circle </u><u>=</u><u> </u><u>1</u><u>0</u><u> </u><u>yards</u>
now ,
<u>substituting</u><u> </u><u>the </u><u>value </u><u>of </u><u>r </u><u>in </u><u>the </u><u>formula </u><u>of </u><u>circumference</u><u> </u><u>~</u>
hope helpful :D
Answer:
It will take 12 months to get $600 dollars.
Step-by-step explanation:
All you have to do is 600/50 and 600/50 is 12.
Hope I Helped!
Find the area of the circle using A=pi * r^2 and then divide that answer by 2 and that will get you the area of the semicircle.
