Answer:
The factors of 3 are: 1, 3
The factors of 9 are: 1, 3, 9
The factors of 27 are: 1, 3, 9, 27
Then the greatest common factor is 3.
Step-by-step explanation:
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)
<u>Let's solve this problem step-by-step</u>:
<u>Thus v = 14</u>
<u />
<u>Answer: v= 14</u>
<u></u>
Hope that helps!
Answer:
F. a1 = –5, an = 5an-1
Step-by-step explanation:
a1 = -5 <---- Answer
r = -25/-5 = 5
an = r(an - 1)
an = 5(an - 1) <---- Answer
Hope this helps!
