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:
19 weeks
Step-by-step explanation:
Given equation:
P = w
Where,
w = the number of weeks he has taken piano lessons
p = the total number of pieces he has learned
how many weeks of piano lessons will Lamar need before he will be able to play a total of 19 pieces?
Find w when p = 19
P = w
p = 19
Since P = w
19 = w
Therefore,
w = 19
Lamar need 19 weeks before he will be able to play a total of 19 pieces
As you can see, the diagonal actually creates a right triangle. Not only that, but you’re given two legs. Therefore, you can use the Pythagorean theorem to find the distance. Specifically, 78 (73?) feet and 27 feet.
Plug in for “a” and “b” to find your distance in:
a^2 + b^2 = c^2
sqrt(a^2 + b^2) = c
Plug in and solve
It would help for more information
Answer:
40 cm
Step-by-step explanation:
<em>Diagonal side: use pythagorean</em>
8^2 + 6^2 = 10^2 => the side is equal to 10
add up w/ 3 others side is 8, 8 and 14
So it is 10 + 8 + 8 + 14 = 40