Answer:
525267262525226
Step-by-step explanation:
594944+757548484-848484%
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:
Step-by-step explanation:
You need to set up a ratio for the original recipe and then use that ratio for the new one.
If we need 3 cups of flour for every 4 cups of sugar, we have a 3 c flour/4 c sugar ratio, or 3/4
The new ratio is 9 c of flour for ? c of sugar. Those ratios have to be the same, so we set up an equation like this:
3/4 = 9/?
In order to keep the same ratio, you have to multiply by the same number. Since 3*3 = 9, multiply 4*3 to get your answer.
Hence the value of the expression above are as listed below
<em>f(6+4) = 25</em>
<em>f(6)+f(4) = 20</em>
<em>f(6-4) = 1</em>
<em>f(6)-f(4) = 6</em>
<em>f(6*4) = 67</em>
<em>f(6)*f(4) = 91</em>
<h3>Functions and values</h3>
Given the expression below f(x) = 3x - 5
f(6+4) = f(10) =3(10) - 5
f(6+4) = 25
f(6) = 3(6) - 5
f(6) = 18 - 5 = 13
f(4) = 3(4) - 5
f(4) = 7
f(6)+f(4) = 13+7
f(6)+f(4) = 20
f(6-4) = f(2) =3(2) - 5
f(6-4) = 1
f(6) = 3(6) - 5
f(6) = 18 - 5 = 13
f(4) = 3(4) - 5
f(4) = 7
f(6)-f(4) = 13-7
f(6)-f(4) = 6
f(6*4) = f(24) =3(24) - 5
f(6*4) = 67
f(6) = 3(6) - 5
f(6) = 18 - 5 = 13
f(4) = 3(4) - 5
f(4) = 7
f(6)*f(4) = 13*7
f(6)*f(4) = 91
Learn more on function and values here: brainly.com/question/2284360
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