help. me dumb... rates of change (1 Viewer)

[me dumb]

how do u do part (iii) the way i did it i got 7pi/6 for time and for max volume i got 4m^3
View attachment 18851

also is part (ii) emptying because the rate of change when t=o isa negative value?

thnx in advance

 

[Timothy.Siu]

dv/dt=root3sin t - cos t

when t=0, dv/dt=-1 so its emptying

uhh i dont think transformations is 2unit...but
V=2-2sin(t+pi/6) [i think]
so its max. at t=4pi/3

and thats V=4.

 

[me dumb]

dv/dt=root3sin t - cos t

when t=0, dv/dt=-1 so its emptying

uhh i dont think transformations is 2unit...but
V=2-2sin(t+pi/6) [i think]
so its max. at t=4pi/3

and thats V=4.

this was in my schools trial paper last year for 2u. its q10a. how come we got the same max volume of 4 but different times?
i differentiated volume then let it equal 0. there are 2 answers pi/6 and 7pi/6 pi/6 gives v=0, while the other one gives v=4 so ones obviously max and ones min. wats taht transformations stuff ur talkin bout?

 

[Timothy.Siu]

this was in my schools trial paper last year for 2u. its q10a. how come we got the same max volume of 4 but different times?
i differentiated volume then let it equal 0. there are 2 answers pi/6 and 7pi/6 pi/6 gives v=0, while the other one gives v=4 so ones obviously max and ones min. wats taht transformations stuff ur talkin bout?

ah i see, dont worry about what i did

dv/dt=root3sin t - cos t
dv/dt=0 when root3sint-cost=0
root3tan t=1
tan t=1/root3
t=pi/6, 7pi/6,13pi/6....

now we have to find the max.
we can differentiate again.
v''=root3cos t+sin t
subbing in pi/6, v''>0 therefore its a minimum
subbing in 7pi/6, v''<0 therefore its a max.
so i guess u got it right, i have no idea what i did

 

[me dumb]

ah i see, dont worry about what i did

dv/dt=root3sin t - cos t
dv/dt=0 when root3sint-cost=0
root3tan t=1
tan t=1/root3
t=pi/6, 7pi/6,13pi/6....

now we have to find the max.
we can differentiate again.
v''=root3cos t+sin t
subbing in pi/6, v''>0 therefore its a minimum
subbing in 7pi/6, v''<0 therefore its a max.
so i guess u got it right, i have no idea what i did

k lol i got another 2 questions but ill post them up later after i have another crack at it. they are from the same paper