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Mathematics: Post your doubts here!

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A spherical balloon is allowed to deflate. The rate at which the air is leaving the balloon is proportional to the volume, V of the air left in the balloon. When the radius of the balloon is 15cm, air is leaving at a rate of 8cm3/s find the expression of dV/dt.....please help
 
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A spherical balloon is allowed to deflate. The rate at which the air is leaving the balloon is proportional to the volume, V of the air left in the balloon. When the radius of the balloon is 15cm, air is leaving at a rate of 8cm3/s find the expression of dV/dt.....please help
dV/dt = -kV
V = (4/3)(pi)( r^3)
dV/dt = - k * (4/3)(pi)( r^3) ------ 1
when dV/dt = 8, r = 15 you can now find the value of k!
Then substitute that value in equation 1 to obtain the expression of dV/dt :)

dV/dt = - (2/1125pi)*V is the answer m getting.
 
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tutorial-3.gif
 
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What is the easiest method to find term independent of x?
I will show u by an example
find the indep of x in (x-2/x)^6
It would be 6Cr*x^(6-r)*(-2/x)^r
the term of x would be x^(6-r)*x^(-r)
The equate the powers of x to zero
6-r-r=0
therefore r=3
then substitute r
6C3*x^2*(-2/x)^2 would be the answer
 
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may i ask a question?? If I retake my AS examination which mark will be considered in the end,the best or the most recent??
 
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Hey guys... Can anyone please me with the math below... It is paper 3 vectors 10 ii... I can do part 10i... Please help...
 

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Hey guys... Can anyone please me with the math below... It is paper 3 vectors 10 ii... I can do part 10i... Please help...
Take myu as 0 and 1
So now u will have 3 points on plane
give them any letters for instance C and D
then do AC x AD and the cross product u get will be the normal vector of plane.
Then substitute values of and vector A,C or D in the equation of plane to get value of d in the equation : ax + by + cz = d where abc are points of normal and x y z are the point in which u have to substitue value of any vector on plane to get value of d. :)
upload_2016-9-8_20-32-3.png
upload_2016-9-8_20-32-11.png
 
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