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Differential Equations
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A population grows at the rate of 8% per year. How long does it take for the population to double?
cbse
class12
additionalproblem
kvquestionbank2012
ch9
q21
p34
sec-b
math
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asked
Feb 4, 2013
by
meena.p
retagged
Dec 19, 2013
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When the interest is compounded continuously, the amount of money invested increases at a rate proportional to its size. If Rs.1000 is invested at 10% compounded continuously, in how many years will the original investment double itself?
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meena.p
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kvquestionbank2012
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A wet porous substance in the open air losses its moisture at a rate proportional to the moisture content. If a sheet hung in the wind loses half of its moisture during the first hour, when will it have lost 95% moisture, weather conditions remaining the same.
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Feb 4, 2013
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meena.p
cbse
class12
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kvquestionbank2012
ch9
q22
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Newtons law of cooling states that the rate of change of the temperature T of an object is proportional to the difference between T and the (constant) temperature t of the surrounding medium. We can write it as \[\frac{dT}{dt}=-K(T-t),K>0\; constant.\]A cup of coffee is served at $ 185^\circ F$ in a room where the temperature is $65^\circ F .$ Two minutes later the temperature of the coffee has dropped to $155^\circ F.$(log 3/4=0.144, log3 = 1.09872). Find the time required for coffee to have $105^\circ F$ temperature.
asked
Feb 4, 2013
by
meena.p
cbse
class12
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kvquestionbank2012
ch9
q25
p34
sec-c
math
0
votes
0
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The surface area of a balloon being inflated, changes at a rate proportional to time t. If initially its radius is 1 unit and after 3 seconds it is 2 units, find the radius after time 't'.
asked
Feb 4, 2013
by
meena.p
cbse
class12
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kvquestionbank2012
ch9
q23
p34
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–1
vote
0
answers
Solve: \[\frac{xdx+ydy}{xdy-ydx}=\sqrt{\frac{a^2-x^2-y^2}{x^2+y^2}}\] (Hint : take $ x=r\cos \theta,y=r \sin \theta,$ so that $x^2+y^2=r^2)$
asked
Feb 4, 2013
by
meena.p
cbse
class12
additionalproblem
kvquestionbank2012
ch9
q19
p34
sec-c
math
0
votes
0
answers
A curve passing through the point (1,1) has the property that the perpendicular distance of the origin from the normal at any point P of the curve is equal to the distance of p from the x-axis. Determine the equation of the curve.
asked
Feb 4, 2013
by
meena.p
cbse
class12
additionalproblem
kvquestionbank2012
ch9
q24
p34
sec-b
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0
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0
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Solve:\[(x^3-3xy^2)dx=(y^3-3x^2y)dy\]
asked
Feb 4, 2013
by
meena.p
cbse
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kvquestionbank2012
ch9
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