Answer:
wats the equation?
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)
2,508 divided by 152 is equal to 16.5
I say 17 minutes, since 152x16=2,432 so a extra minute is needed to get to 2,508
Answer:
Part A: yes it is a function because every input value (x) produces only one output value (y).
Note: It is still a function if different x values produce the same y value, in this case, x=1 and x=-1 produce the same y value 1, but it is NOT a function if y=1 and y=-1 have the same x value x=1.
Part B: when x=30: f(30)=17*30+50=560
if means that the cost of renting the truck for 30 hours is 560 dollars.
this help?
