Volumes + connected rates

[north vortex]

PART D
help <@&791435371564892232>

[vapid moon]

do yk where to start?

u wanna find dh/dt and you're given dV/dt

notice that dh/dt = dh/dV ˣ dV/dt

make sure ur careful w units when u evaluate dh/dt

[north vortex]

I have dh/dt but some units are messed up

[rough terrace]

what paper is this from?

[north vortex]

cp2 2019

how is this cm/h^-1 (time) here as we had to differentiate volume with respect to height/depth here

[vapid moon]

dv/dh has units m²

that must be a mistake

[north vortex]

I have dh/dt as 15/3.539... cm min^-1 but how do I convert that into cm h^-1

[vapid moon]

hmm, you must've made a mistake somewhere

that's 4.2374... cmmin^-1

but dh/dt = 0.42374... cmmin^-1

[north vortex]

dv/dt in cm^3/min, dh/dv in cm^-2 so dh/dt in cm/min. Thats what I did but I can't spot the mistake

[vapid moon]

hold on, r u telling me what you've converted them to or

u could be right, even if u used different units

as long as u have the right values

tell me ur units & values for dV/dt and dh/dV

[north vortex]

Icl im stuck trying to get 15/3.539... into the right answer

I'm trying to understand the conversion by including units per with by differential equations

[vapid moon]

it'll help see what's going on

[north vortex]

dV/dT = cm^3/min, dV/dh = cm^3/metres (dh/dV = metres/cm^3)

[vapid moon]

values?

[north vortex]

dV/dT = 15, dV/dH = 3.539...

[vapid moon]

i see okay that makes sense

dV/dt is 15L/min

not cm^3/min

[vapid moon]

dV/dH m^3/m

not cm^3/m

so it'd be
dV/dt = 15Lmin^-1
dV/dh = 3.5399m^2

[north vortex]

when you find dv/dt what do they units become?

[vapid moon]

wdym?

dV/dt = 15Lmin^-1

[north vortex]

we need the answer in cm per hour (cm h^-1)

but I keep converting that part wrong

[vapid moon]

yes, how ru going about it? converting them individually first?

[north vortex]

nah I want to multiply it and keep the units until the end to figure out how I should convert it into cm h^-1

[vapid moon]

ya i think it's better that way

so when u multiply u get
dh/dt = 15/3.5399 as u said

and the units are Lmin^-1 * m^-2

that gives 4.2374 L min^-1 m^-2

L ---> m^3 = divide by 1000

0.0042374 min^-1 m^1

m --> cm = x100

0.42374 cm min^-1

min^-1 --> h^-1 = x60

25.4cmh^-1

[north vortex]

why do we have to do this, could we not just cancel m^3 with m^-2?

[vapid moon]

after u have L in m^3, yes

i had to get it in m^3 first

i cancelled on the next line

[north vortex]

it doesnt work if we do this first though

bc I'd have 4.23,,,, m min^-1

[vapid moon]

ya of course u can't do that

it's like pulling m^3 out of nowhere

4.2374 L min^-1 m^-2
≠ 4.2374 m^3 min^-1 m^-2

[north vortex]

L = m^3 no?

[vapid moon]

noo

1000L = 1m³

[north vortex]

do you remember this bc you do physics?

[north vortex]

got this now, thanks

[vapid moon]

fortunately ur calc has pretty much all the conversions so u don't need to remember anything

[vapid moon]

great no probs

[north vortex]

I swr it doesnt work in exam mode?

[vapid moon]

oh idk about the cg50

surely they wouldn't block it in exam mode

i use the 991ex which doesn't have an exam mode

[north vortex]

fairs

does your calculator have an a + bi mode?

[vapid moon]

yes

[north vortex]

alr