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If the sum of the lengths of the hypotenuse and a side of a right angled triangle is given,show that the area of the triangle is maximum when the angle between them is $\large \frac{\pi}{3}$.
This question has multiple parts. Therefore each part has been answered as a separate question on Clay6.com
isc
class12
modelpaper
2011
sec-a
q6
q6-a
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asked
Apr 11, 2013
by
sreemathi.v
retagged
Apr 12, 2013
by
sreemathi.v
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If the sum of the lengths of the hypotenuse and a side of a right angled triangle is given, show that the area of traingle is maximum when the angle between them is \( \large\frac{\pi}{3} \).
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Jan 11, 2013
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Evaluate $\int_0^9f(x)$ dx,where f(x) is defined by $f(x)=\left\{\begin{array}{1 1}\sin x;if 0\leq x\leq \large\frac{\pi}{2}\\1;\large\frac{\pi}{2}\normalsize\leq x\leq 5\\e^{x-5};5\leq x\leq 9\end{array}\right.$
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If the sum of the lengths of the hypotenuse and a side of a right triangle is given, show that the area of the triangle is maximum, when the angle between them is $60^{\circ}$.
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(i) Evaluate $\int_0^{\large\frac{\pi}{2}}\log(\tan x)dx$.(ii) Evaluate $\int_0^5\big(x+\frac{1}{2}\big)dx$ as a limit of a sum.
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Apr 12, 2013
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Prove that the area of right-angled traingle of a given hypotenuse is maximum when the triangle is isosceles.
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