Question

Can someone please help me with this problem see attachment

Answer 1

@ash2326 can you please help me with this problem

Answer 2

@farmergirl411 Is this a home work question?

Answer 3

yes

Answer 4

cool, ok
Boat is bobbing up and down with the equation:
\[y(t)=40+\sin {3\pi t}\]
Do you understand what the equation implies?

Answer 5

yes

Answer 6

I understand what it means but how do you find the y'(5)?

Answer 7

Ash knows what he's doing.

Answer 8

ok but oh he is back sorry I thought he left

Answer 9

@ash2326 what do I do next

Answer 10

It would help if you take notes on how you solve these problems. You keep asking how to do problems that are very close to the same problem (or at least use the same ideas)

Answer 11

are you still there ash can you help me

Answer 12

ARE U STILL THERE?

Answer 13

can you take the derivative with respect to t of
\[ y(t)=40+\sin {3\pi t} \]

Answer 14

yes ans you get 3piecos(3piet)

Answer 15

pie is something you eat. pi is a Greek letter. in math, it stands for 3.14159....

you now know
\[ y'(t)= 3 \pi \cos(3 \pi t) \]

what is y'(5) ?

Answer 16

That is where I get confused do you just put the 5 where the t is

Answer 17

yes, if you have a function f(x) and they ask for f(5), that means replace x with 5 in the definition, and simplify

Answer 18

right I knew that but when you get the derivative in there that is where I get confused

Answer 19

=6.4128 correct for final answer

Answer 20

sorry farmer girl, I had to go out for sometime. Are you through the problem?

Answer 21

yes thats ok I just didn;t know where you went I got hat for my final answer can you check to just make sure it is ok

Answer 22

you should get - 3 pi

Answer 23

If you put t=5
\[y'(5)=3\pi\cos {15\pi}\]
\[\cos{15\pi}=-1\]
so
\[y'(5)=-3\pi=-9.42\]
Do you get it?

Answer 24

where si you get 15 from

Answer 25

\[\cos {3\pi}[t\]
t=5\[\cos {3\times \pi\times 5}=\cos{15\pi}\]

Answer 26

ok gotcha and then that number we got means minutes since the boat anchored correct?

Answer 27

y(t) is the height of boat at time t
y'(t) is the speed of boat in vertical direction at time t
y'(5) is the speed of boat in vertical direction at time t=5
this is negative which indicates that boat is going down at t=5
Do you get this? @farmergirl411

Answer 28

yes so the -9.42 means that the boat is going down at t=5

Answer 29

yes, had it been a positive no. the boat's speed would be positive and the boat would be going up.

Answer 30

ok gotcha thanks

Answer 31

yeah :D