Question

can someone check the answer to my rates problem?

Answer 1

The depth of the liquid is increasing at 1.7 m^3/sec
is that right?

Answer 2

@satellite73

Answer 3

im a little confused about whether its increasing or decreasing, tho i think the math is correct

Answer 4

lets work thru it, what is the formula for the volume of this 'cube'

Answer 5

v= lwh or in this case v= side*end*height
we know that at that moment, the side = 5 and end = 2, and that the volume is 20 so height is 2

Answer 6

now, is the rate of the sides moving apart negative or positive? and same for the rates of the ends moving together?

Answer 7

i like the

V = sed

V' = s'ed + se'd + sed'

hence we need to solve for d'

sides are decreasing at .3; s' = -.3
ends are increasing at .1; e' = .1
s=5, e=2, d=20/(10)

and since V is constant, V' = 0

Answer 8

wait, isnt the volume changing?

Answer 9

nothing suggests that the volume is changing to me

Answer 10

the depth of the liquid, does that mean we are looking for the derivative of the height? it seemed to me that as the depth changed, the volume was also changing

Answer 11

we are given no starting values, and nothing to attribute to a changing volume. parts of the room are moving

lets try this:
s e d
V = 5.2.2

what was it a second ago?

s = 5.1; e = 1.7; d = 20/se so that the volume remains constant

Answer 12

2 - 20/((5.1)(1.7)) should be the change right?

Answer 13

wait, so what are we looking for? now im confused

Answer 14

in order for the volume to remain constant, the the depth has to change at a given rate in accordance ot the rest of it

Answer 15

o, wait by depth it means height?

Answer 16

yes, the are 3 directions, they labeled them as side, end, and want to know depth ...

V = sed instead of lwh since what we name something is rather inconsequential

Answer 17

since the question is asking for change in depth, lets use d instead of h

Answer 18

now it makes more sense o.o

Answer 19

copy/paste

V' = s'ed + se'd + sed'

hence we need to solve for d'

sides are decreasing at .3; s' = -.3
ends are increasing at .1; e' = .1
s=5, e=2, d=20/(10)
-----------------------

0 = -.3.2.2 + 5..1.2 + 5.2.d'

0 = -.3(4) + 10(.1) + 10d'

0 = -1.2 + 1 + 10d'

.2 = 10d'

Answer 20

since we have a positive value, the depth is increaseing

Answer 21

i understand, but i have one question, why is s' -.3 rather than .1?

Answer 22

ah, i get it, sorry for that o.o