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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The answer is $4.40
mutiply 350 by 5% and get 17.5 then divide thag by 4 and you get 4.37 and you supposed to round it up which will be 4.40
34 less than (-34) the product of (multiply) 14 (14) and an unknown (x) is (=) 78 (78)
-34+14 times x=78
14 times x=14x
14x-34=78
add 34 to both sides
14x=112
divide both sdies by 14
x=8
the number is 8
Answer: 242 = 190 + 4t
Step-by-step explanation:
You know that the maximum capacity of the restaurant is 242 people, meaning that at most there can only be that many customers seated at that time. Normally, the equation would be 242 = 10b + 4t, but since you already know the number of booths, your work is cut in half, giving you 242 = 10(19) + 4t. The equation would be this because you have the capacity being equal to the number of tables x the number of people at each table and the number of booths x the number of people seated at each of them.
Answer:
6, 24, 96, 384
Step-by-step explanation:
a₁ = 6
a₂ = 4 x a₁ = 4 x 6 = 24
a₃ = 4 x a₂ = 4 x 24 = 96
a₄ = 4 x a₃ = 4 x 96 = 384
