The solution to the given differential equation is yp=−14xcos(2x)
The characteristic equation for this differential equation is:
P(s)=s2+4
The roots of the characteristic equation are:
s=±2i
Therefore, the homogeneous solution is:
yh=c1sin(2x)+c2cos(2x)
Notice that the forcing function has the same angular frequency as the homogeneous solution. In this case, we have resonance. The particular solution will have the form:
yp=Axsin(2x)+Bxcos(2x)
If you take the second derivative of the equation above for yp , and then substitute that result, y′′p , along with equation for yp above, into the left-hand side of the original differential equation, and then simultaneously solve for the values of A and B that make the left-hand side of the differential equation equal to the forcing function on the right-hand side, sin(2x) , you will find:
A=0
B=−14
Therefore,
yp=−14xcos(2x)
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9514 1404 393
Answer:
yes, about 2.05 inches
Step-by-step explanation:
The Pythagorean theorem can be used to find the width of the TV.
w^2 +h^2 = d^2
w = √(d^2 -h^2)
w = √(42^2 -18^2) = √1440 = 12√10
w ≈ 37.95 . . . inches
This dimension is less than 40 inches by a margin of ...
40 -37.95 = 2.05 . . . inches
The TV will fit, with 2.05 inches of space remaining.
I would say A. is the correct answer. Definitely a weird one. Hope this helps!
Positive numbers is the last one
Answer:
x = 18
m∠HCB = 36
Step-by-step explanation:
The measure of angle FBC is 8x and the measure of angle HCB is 2x. If you add the measures of both angles it will equal to 180 degrees. This can be represented in an equation:
8x + 2x = 180
10x = 180
Divide both sides of the equation by 10 to isolate the x:
10x/10 = 180/10
x = 18
Now that we know the value of x, we can find the measure of angle HCB:
2x
2(18)
36
The measure of angle HCB is 36.
I hope this helps :)