Using Laplace transform we have:L(x')+7L(x) = 5L(cos(2t))sL(x)-x(0) + 7L(x) = 5s/(s^2+4)(s+7)L(x)- 4 = 5s/(s^2+4)(s+7)L(x) = (5s - 4s^2 -16)/(s^2+4)
=> L(x) = -(4s^2 - 5s +16)/(s^2+4)(s+7)
now the boring part, using partial fractions we separate 1/(s^2+4)(s+7) that is:(7-s)/[53(s^2+4)] + 1/53(s+7). So:
L(x)= (1/53)[(-28s^2+4s^3-4s^2+35s-5s^2+5s)/(s^2+4) + (-4s^2+5s-16)/(s+7)]L(x)= (1/53)[(4s^3 -37s^2 +40s)/(s^2+4) + (-4s^2+5s-16)/(s+7)]
denoting T:= L^(-1)and x= (4/53) T(s^3/(s^2+4)) - (37/53)T(s^2/(s^2+4)) +(40/53) T(s^2+4)-(4/53) T(s^2/s+7) +(5/53)T(s/s+7) - (16/53) T(1/s+7)
Hello,
Let's calculate the radius:
r²=5²+7²=74
The circle's equation is (x+5)²+(y+7)²=74
Answer C
353/12 =29.41. But will have to round up to 30 so the answer is 30
Answer:
The top right graph.
Step-by-step explanation:
In the figure, tx is perpendicular to line RS.this means we can use the pythagorean theorem to determine RX length the long way or simply apply the theorem that each divided triangle becomes a 30-60-90 angle. If opposite to 60 deg is equal to 6 units, then the side's length is equal to 2*6/sq rt 3 or equal to 6.93 units. The answer is half of this equal to 3.47 units.
