At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
a(t) = dv/dt so v(t) = int(2t+sint)
replace a(t) with dv/dt and write a= 2t+sin t as dv/dt = 2t + sin t dv = (2t +sin t ) dt
now integrate both sides
can you do the integration ?
Kind of lost on what you're doing
|dw:1446429240051:dw| @Ephemera hopefully you agree that a(t) = dv/dt ?
multiply both sides by dt |dw:1446429315716:dw|
so we now have \[\Large dv = (2t+\sin(t))dt\]
now integrate both sides \[\Large dv = (2t+\sin(t))dt\] \[\Large \int dv = \int(2t+\sin(t))dt\] \[\Large \int 1 dv = \int(2t+\sin(t))dt\] \[\Large \int 1 dv = \int(2t)dt+\int(\sin(t))dt\] \[\Large v = t^2-\cos(t)+C\]
We're given `v(0) = 4` so that means `t = 0 and v(t) = 4` \[\Large v = t^2-\cos(t)+C\] \[\Large v(t) = t^2-\cos(t)+C\] \[\Large 4 = (0)^2-\cos(0)+C\] what is C equal to?
any ideas @Ephemera ?
I got a problem with different numbers so if you could finish this one up so I can apply the same method, I'd appreciate it.
what is `cos(0)` equal to?
so \[\Large 4 = (0)^2-\cos(0)+C\] \[\Large 4 = 0-1+C\] \[\Large 4 = -1+C\] \[\Large 4+1 = -1+C+1\] \[\Large 5 = C\] \[\Large C = 5\] agreed?
you gave him the answer and he just disappeared!! no thank you and no nothing. he didn't even attempt to try and solve any part of the problem. thats gratitude for you!!!
@alekos How about you mind your own business? I haven't even finished up my assignment and didn't have the time to check the progress made on the question. I was visiting my grandfather who has non treatable brain cancer. Your response is so unneeded, either delete it or I will be reporting it. And @jim_thompson5910 has helped me out multiple times so I am sure he is well aware that I appreciate his help, I always attempt to solve instead of just getting the answer.
I still haven't seen a thankyou to Jim who spent all that time and trouble to help you out