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Average Boreduser

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After,
Water is flowing into a hemispherical container of radius 10cm at a constant rate of 6cm^3 per second. It is known that the formula for the volume of a solid segment cut off a sphere is V=pi/3 h^2 (3r-h), Where r is the radius of the sphere and h is the height of the segment.
a) Find the rate at which the height of the water is rising when the water height is 2cm.
b) Use Pythag to find the radius of the circular water surface when the height is h, and hence find the rate of increase of the surface area when the water height is 2cm.
 

howcanibesmarter

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After,
Water is flowing into a hemispherical container of radius 10cm at a constant rate of 6cm^3 per second. It is known that the formula for the volume of a solid segment cut off a sphere is V=pi/3 h^2 (3r-h), Where r is the radius of the sphere and h is the height of the segment.
a) Find the rate at which the height of the water is rising when the water height is 2cm.
b) Use Pythag to find the radius of the circular water surface when the height is h, and hence find the rate of increase of the surface area when the water height is 2cm.
is the answer a) 0.053cm/sec b) 2.67sqcm/sec?
 

synthesisFR

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pentel energel 0.7 😍
my holy grail, doesn't smudge at all
nah cuz ive acually been using the trashiest pen in existence so far idek why
is this even true like if i can use a trash one i will be able to use a good pen much better or not true in this case? since u might need to adapt to a good pen lmfao
 

nsw..wollongong

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nah cuz ive acually been using the trashiest pen in existence so far idek why
is this even true like if i can use a trash one i will be able to use a good pen much better or not true in this case? since u might need to adapt to a good pen lmfao
bro i used a rlly bad pen on my prelims and literally all my feedback on my English paper was how i HAVE to change pens πŸ’€ honestly it doesn't matter if u use a bad pen now and a good one later, it doesn't make u write better in the actual test (different pen grip, ink??). just pick one or two and stick with them
 

scaryshark09

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or its just that my English teachers are shit at giving feedback so they focus on the most tedious details instead 😍
omg lol, most of my English feedback is literally copied and pasted from the marking criteria but they just change a few words here and there like "skillfully" to "effectively" to justify why i didnt get full
 

Average Boreduser

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cus i will do them all :) is the answer = -x+3/sqrt2 tan^-1(sqrt2 tanx/2) + C ?

also is there a faster way? i feel like im missing something...
View attachment 38802
nah its a last qn I found from a past paper lol. idek how to integrate.... in fact, my school only just started diff πŸ’€
1688476266095.png
this is the answer
 

Average Boreduser

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and yeah i think ur right given tan^-1(tanx)=x (unless theres smn im missing? idk)
 

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