I think the answer is 4:24
The question is:
Check whether the function:
y = [cos(2x)]/x
is a solution of
xy' + y = -2sin(2x)
with the initial condition y(π/4) = 0
Answer:
To check if the function y = [cos(2x)]/x is a solution of the differential equation xy' + y = -2sin(2x), we need to substitute the value of y and the value of the derivative of y on the left hand side of the differential equation and see if we obtain the right hand side of the equation.
Let us do that.
y = [cos(2x)]/x
y' = (-1/x²) [cos(2x)] - (2/x) [sin(2x)]
Now,
xy' + y = x{(-1/x²) [cos(2x)] - (2/x) [sin(2x)]} + ([cos(2x)]/x
= (-1/x)cos(2x) - 2sin(2x) + (1/x)cos(2x)
= -2sin(2x)
Which is the right hand side of the differential equation.
Hence, y is a solution to the differential equation.
Answer:
mean = $11.15
median = $11.30
mode = $9.90, $10.70, $11.90, $12.05
Step-by-step explanation:
Ordered from smallest to largest
9.89, 10.71, 11.90, 12.06
The mean is the middle number.
There are two numbers in the middle so you have to add them together and divide by 2.
(10.71 + 11.90)/2 = 11.305
rounded 11.30
Mode is the number that appears the most. All of the prices are listed once. They are all the mode.
Mean is (10.71+11.90+9.89+12.06)/4 = 11.14
round 11.15
