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GeometryQuestion and Answers: Page 117

Question Number 2001 Answers: 0 Comments: 0

Prove that : (1/(15)) < (1/2) ∙ (3/4) ∙ (5/6) ∙ ∙ ∙ ∙ ∙ ((99)/(100)) < (1/(10))

$P r o v e t h a t :$ $\frac{1}{15} < \frac{1}{2} \cdot \frac{3}{4} \cdot \frac{5}{6} \cdot \cdot \cdot \cdot \cdot \frac{99}{100} < \frac{1}{10}$

Question Number 1928 Answers: 2 Comments: 10

Prove that, if p>q>0 and x≥0, then (1/p)((x^p /(p+1))−1)≥(1/q)((x^q /(q+1))−1).

$P r o v e t h a t, i f p > q > 0 a n d x ⩾ 0, t h e n$ $\frac{1}{p} (\frac{x^{p}}{p + 1} - 1) ⩾ \frac{1}{q} (\frac{x^{q}}{q + 1} - 1) .$

Question Number 1793 Answers: 0 Comments: 0

Evaluate ∫_(1/2) ^2 ((sinx)/(x(sinx+sin(1/x))))dx .

$E v a l u a t e$ $\int_{1 / 2}^{2} \frac{s i n x}{x (s i n x + s i n \frac{1}{x})} d x .$

Question Number 1740 Answers: 1 Comments: 1

how 0!=1

$h o w 0! = 1$

Question Number 1750 Answers: 1 Comments: 0

(x+3)^3

${(x + 3)}^{3}$

Question Number 1611 Answers: 0 Comments: 1

A right angled triangle has fixed hypotenuse measuring h units. What are the measures of its legs, for maximum perimeter P units. Will the area be also maximum, when the perimeter be maximum?

$A right angled triangle has fixed hypotenuse measuring$ $h units . What are the measures of its legs,$ $for maximum perimeter P units .$ $Will the area be also maximum, when the perimeter be$ $maximum ?$

Question Number 1592 Answers: 1 Comments: 1

I have a loop of string of length(perimeter) p units. I want to make a triangle of largest area from the loop. What will be the dimensions of that triangle?

$I have a loop of string of length (perimeter) p units .$ $I want to make a triangle of largest area from the$ $loop . What will be the dimensions of that triangle ?$

Question Number 1581 Answers: 0 Comments: 2

Find a function f(x) satisfying the following equation. ∫_a ^( b) [(1/2){f(x)}^2 −(√({f(x)}^2 +{(d/dx)(f(x))}^2 ))]dx=0 b>0,a>0 , b≠a.

$F i n d a f u n c t i o n f (x) s a t i s f y i n g$ $t h e f o l l o w i n g e q u a t i o n .$ $\int_{a}^{b} [\frac{1}{2} {f (x)}^{2} - \sqrt{{f (x)}^{2} + {\frac{d}{d x} (f (x))}^{2}}] d x = 0$ $b > 0, a > 0, b \neq a .$

Question Number 1387 Answers: 0 Comments: 1

Q. is there any angle in a circle?

$Q . i s t h e r e a n y a n g l e i n a c i r c l e ?$

Question Number 1395 Answers: 0 Comments: 5

Consider quadrilateral ABCD same as in Q 1378 with same conditions/restrictions (Pl refer the Question again). • What could be possible minimum and maximum area of the quadrilateral? •When qusdrilateral has minimum area what is the value/s of m∠A? Similarly what is value/s of m∠A in case of maximum area?

$C o n s i d e r quadrilateral ABCD s a m e a s i n Q 1378 w i t h$ $s a m e c o n d i t i o n s / r e s t r i c t i o n s (P l r e f e r t h e Q u e s t i o n a g a i n) .$ $∙ W h a t c o u l d b e p o s s i b l e minimum a n d maximum area$ $o f t h e q u a d r i l a t e r a l ?$ $∙ W h e n q u s d r i l a t e r a l h a s minimum area w h a t i s t h e v a l u e / s$ $o f m ∠ A ? S i m i l a r l y w h a t i s v a l u e / s o f m ∠ A i n c a s e o f$ $maximum area ?$

Question Number 1378 Answers: 0 Comments: 4

Four sides mAB^(−) , mBC^(−) , mCD^(−) and mDA^(−) of a quadrilateral ABCD have measurement a , b , c and d units respectively. Let the sum of any adjacent sides is not equal to the sum of remaining adjacent sides and measurement of all the sides is positive and real. What could be the possible minimum and maximum values of its one angle m∠A ?

$F o u r s i d e s m \overset{―}{AB}, m \overset{―}{BC}, m \overset{―}{CD} a n d m \overset{―}{DA} o f a quadrilateral$ $ABCD h a v e m e a s u r e m e n t a, b, c a n d d u n i t s r e s p e c t i v e l y .$ $L e t t h e s u m o f a n y a d j a c e n t s i d e s i s n o t e q u a l t o t h e s u m o f$ $r e m a i n i n g a d j a c e n t s i d e s a n d m e a s u r e m e n t o f a l l t h e s i d e s$ $i s p o s i t i v e a n d r e a l .$ $W h a t c o u l d b e t h e p o s s i b l e m i n i m u m a n d m a x i m u m v a l u e s$ $o f i t s o n e a n g l e m ∠ A ?$