Question

Since YouTube first became available to the public in mid-2005, the rate at which video has been uploaded to the site can be approximated by
v(t) = 525,600(0.42t^2 + 2.7t − 1) hours of video per year (0.5 ≤ t ≤ 7),
where t is the time in years since the start of 2005.†
(a) Find an expression for the total number of hours
V(t) of video at time t
(starting from zero hours of video at t = 0.5).

(b) Use the answer to part (a) to estimate the total number of hours of video uploaded by the start of 2011. (Round your answer to the nearest million hours of video.)

_______ million hours of video

Answer 1

for part (a) you are given the rate function and the time, to find the # of videos you can take the integral of v(t) = 525,600(0.42t^2 + 2.7t − 1) between t = 0.5 and v = 7 (try factoring out 525,600 from the integral first)

Answer 2

yeah thats right

Answer 3

thanks for the answer vocaloid, it helped me!

Answer 4

still working on part (b) just a moment

Answer 5

yea ik

Answer 6

hi Stevie!

Answer 7

actually I believe part (a) is just setting up the integral and part (b) is just solving it

so for part (a) simply write down the integral and for part (b) evaluate it

Answer 8

oki

Answer 9

i think I have the integral right but im pretty sure i have to solve for c as well to be able to get the answer to part b and im strggling with that

Answer 10

it's a definite integral so there shouldn't be a c value

Answer 11

yea

Answer 12

what did you guys get for the integral?

Answer 13

the integral of t^2 is (1/3)t^3
the integral of t is (1/2)t^2
integral of 1 is t

putting that together

integral of 525,600(0.42t^2 + 2.7t − 1)
=
525,600(0.42 * (1/3) * t^3 + 2.7(1/2)t^2 - t)

evaluate that at 7 and 0.5 then subtract the two values

Answer 14

ye thats true

Answer 15

so do you guys like anime????? just curious

Answer 16

let's please try and stay on topic (there are chat boxes at the bottom for casual conversation)

Answer 17

where are the chat boxes?

Answer 18

at the bottom of your screen

Answer 19

oki saw it

Answer 20

@steviej148 you still there?

can you try evaluating:

A) 525,600(0.42 * (1/3) * t^3 + 2.7(1/2)t^2 - t) for t = 7
and
B) 525,600(0.42 * (1/3) * t^3 + 2.7(1/2)t^2 - t) for t = 0.5

then subtracting A ) - B ) ?

Answer 21

yes one second

Answer 22

son¡Steve u like anime?

Answer 23

sorry meant to say so

Answer 24

why is there so many little people on question cove????