Question

Check my answers? :3
f(t) = 6 + cos(t/10) + 3sin(7t/40)
is used to model the velocity of the plane, in miles per minute,
for 0 ≤ t ≤ 40

what is the total distance traveled by the plane over the time interval 0 ≤ t ≤ 40?
(I got 236.651 miles ???)

If at time t=5 the test plane is at mile marker 15 along the straight test track, determine the position of the plane at time t=25.
(I got 161.659 miles ???)

Answer 1

JIGGLY! LONG TIME NO SEE

Answer 2

part a is correct
http://www.wolframalpha.com/input/?i=%5Cint_0%5E%7B40%7D++6+%2B+cos%28t%2F10%29+%2B+3sin%287t%2F40%29

Answer 3

you can do that cuz the given velocity function is never negative

Answer 4

yeah, even then all you would have to do is put abs value in there somewhere XD :P
thanks :)

Answer 5

how about for the other part? :3

Answer 6

the other part requires taking indefinite integral,
solving for the constant
and finding d(25) uhmm

Answer 7

let me check quick...

Answer 8

6t + 10sin(t/10) - (120/7)cos(7t/40) + C
plugged in t=5 found C= 1.194 ?
plugged in t=25 -> 161.658 ?

Answer 9

\(\large d(t) = 6t + 10\sin(\frac{t}{10}) - \frac{120}{7}\cos(\frac{7t}{40})+c\)

Answer 10

wolfram says c = -8.8 ?

http://www.wolframalpha.com/input/?i=+6*5+%2B+10%5Csin%28%5Cfrac%7B5%7D%7B10%7D%29+-+%5Cfrac%7B120%7D%7B7%7D%5Ccos%28%5Cfrac%7B7*5%7D%7B40%7D%29%2Bc+%3D+15

Answer 11

check once.. .

Answer 12

oh yeah I see what I did wrong, I made it equal 25 instead of 15 :P whoops

Answer 13

ohk :)

Answer 14

so plugged in 25 -> 152.854 ??? :3

Answer 15

http://www.wolframalpha.com/input/?i=+6*25+%2B+10%5Csin%28%5Cfrac%7B25%7D%7B10%7D%29+-+%5Cfrac%7B120%7D%7B7%7D%5Ccos%28%5Cfrac%7B7*25%7D%7B40%7D%29+-+8.8

Answer 16

\(\large \color{red}{\checkmark}\)

Answer 17

great! :D Thanks!!! :)

Answer 18

np :)