Question

Help with related rate problem please! (DISTANCE)

Answer 1

hint ->
you want dy/dt
so:
dy/dt = (dy/dx) * (dx/dt)

Answer 2

which formula do i use?

Answer 3

you have dx/dt at this point and you have the point itself. that should help you

Answer 4

right.

Answer 5

got that.

Answer 6

dy/dt = (dy/dx) * (dx/dt)

Answer 7

dy/dx means derivative of y with respect to x
dx/dt is given at this point

Answer 8

i know.

Answer 9

so?

Answer 10

but what formula should i use, for example there are problems for volume, circle, triangle, etc.

Answer 11

distance formula?

Answer 12

ok
so distance from the origin is
s = sqrt(x^2 + y^2)

so you want
ds/dt = (ds/dy) * (dy/dt) + (ds/dx) * (dx/dt)

Answer 13

what does s symbolize?

Answer 14

right.

Answer 15

s - distance

Answer 16

so that is it. now you have it all

Answer 17

thanks let me try

Answer 18

you can, as well, to express y in terms of x in the distance formula
and then find
ds/dt = (ds/dx) * (dx/dt)

it will be much more simple

Answer 19

right the whole 5*sqrt(2x+2) is throwing me off though,

Answer 20

im not sure if i should find the derivative of that function with respect to time.

Answer 21

and the whole distance formula too.

Answer 22

ok so if we do it the way i said at the end :
"you can, as well, to express y in terms of x in the distance formula
and then find
ds/dt = (ds/dx) * (dx/dt)

it will be much more simple"

then you dont have to do much

Answer 23

cause

s=sqrt(x^2 + y^2) = sqrt(x^2+50x+50)
now
ds/dt = (ds/dx) * (dx/dt)

Answer 24

you just need to find ds/dx

Answer 25

i did this:

i found s=10.0499
then i found the derivative which i got 5/sqrt(2x+2) *dx/dt

Answer 26

i got ds/dt as 10 but i know it's wrong.

Answer 27

you dont need to find s.

you need to find ds/dx

Answer 28

ds/dx=10

Answer 29

what about dy?

Answer 30

since we express y in terms of x
we dont need to worry about it anymore.

Answer 31

ok

Answer 32

ds/dx = (x + 25)/sqrt(x^2+50x+50)
at the point x=1 it is
ds/dx = 26 / sqrt(101)

so ds/dt = (26 / sqrt(101))* 4

i might done some mistake though

Answer 33

yeah im not sure what's happening.

Answer 34

why?

s = sqrt(x^2+y^2) = sqrt(x^2+50x+50)
so we want ds/dt

ds/dt = ds/dx * dx/dt

ds/dx = (x + 25)/sqrt(x^2+50x+50)
ds/dx at this point = 26/sqrt(101)

so ds/dt at this point = 26 * 4 /sqrt(101)

Answer 35

plugged into the derivative x=1 and dx/dt = 4

Answer 36

understand what i did ?

Answer 37

sqrt(x^2+50x+50) ?

Answer 38

this is the distance..
s=sqrt(x^2 + y^2) = sqrt(x^2 + 50x + 50)

Answer 39

i know, how'd you come up with this sqrt(x^2+50x+50)

Answer 40

x^2+50x+50)

Answer 41

plugged y=5sqrt(2x+2)

Answer 42

10=10

Answer 43

50x+50?

Answer 44

i plugged in y and x

Answer 45

what ?

Answer 46

y=5sqrt(2x+2)

y^2 = 50x+50

Answer 47

plugged y=5sqrt(2x+2). i plugged in y and x.
10=10

Answer 48

so now
s = sqrt(x^2 + y^2)
but since y^2 = 50x+50
s = sqrt(x^2+50x+50)

Answer 49

not the value of y at the point. plug y as a function of x

Answer 50

okay thanks alot.

Answer 51

i got it

Answer 52

are you sure ?

Answer 53

s = sqrt(x^2+y^2) = sqrt(x^2+50x+50)
so we want ds/dt

ds/dt = ds/dx * dx/dt

when we calculate ds/dx we calculate is using s as a function of x. not plugging numerical values yet.
ds/dx = (x + 25)/sqrt(x^2+50x+50)
now plug x=1
ds/dx at this point = 26/sqrt(101)

so ds/dt at this point = 26 * 4 /sqrt(101)