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GeometryQuestion and Answers: Page 116

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 ?

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

Question Number 1304 Answers: 1 Comments: 0

If 3^(log 3x) =4^(log 4x) , find x.

$I f 3^{l o g 3 x} = 4^{l o g 4 x}, f i n d x .$

Question Number 1343 Answers: 1 Comments: 0

3^(log 3x+4) =4^(log 4x+3)

$3^{l o g 3 x + 4} = 4^{l o g 4 x + 3}$

Question Number 1268 Answers: 1 Comments: 0

Prove that AM > HM.

$Prove that AM > HM .$

Question Number 1157 Answers: 1 Comments: 0

show that tan^(−1) ((((√(1+x^2 ))−1)/x))=(1/2)tan^(−1) x

$s h o w t h a t$ ${t a n}^{- 1} (\frac{\sqrt{1 + x^{2}} - 1}{x}) = \frac{1}{2} {t a n}^{- 1} x$

Question Number 1054 Answers: 0 Comments: 0

L(di/dt)+Ri+(1/C)∫_0 ^t idt=E i(0)=0

$L \frac{d i}{d t} + R i + \frac{1}{C} \underset{0}{\int^{t}} i d t = E$ $i (0) = 0$

Question Number 887 Answers: 1 Comments: 0

((−5+x)/(22))=1 what is x?

$\frac{- 5 + x}{22} = 1$ $w h a t i s x ?$

Question Number 860 Answers: 1 Comments: 1

f(x^2 )=[f(x)]^2 f(1)=1

$f (x^{2}) = {[f (x)]}^{2}$ $f (1) = 1$

Question Number 808 Answers: 1 Comments: 1

if the equations of the sides of the triangle are 7x+y−10=0,x−2y+5=0 and x+y+2=0, find the orhocentre of the triangle

$i f t h e e q u a t i o n s o f t h e s i d e s o f t h e t r i a n g l e a r e 7 x + y - 10 = 0, x - 2 y + 5 = 0 a n d x + y + 2 = 0, f i n d t h e o r h o c e n t r e o f t h e t r i a n g l e$

Question Number 758 Answers: 1 Comments: 1

∫xtan^(−1) xdx

$\int x \tan^{- 1} x d x$

Question Number 737 Answers: 1 Comments: 1

(1/T)∫_t_1 ^t_2 Vsin ωt−V_γ dt=? t_1 and t_2 are solution to Vsin ωt=V_γ V≥V_γ V_γ ≥0 and t_1 <t_2

$\frac{1}{T} \underset{t_{1}}{\int^{t_{2}}} V \sin ω t - V_{γ} d t = ?$ $t_{1} a n d t_{2} a r e s o l u t i o n t o$ $V \sin ω t = V_{γ}$ $V ⩾ V_{γ}$ $V_{γ} ⩾ 0$ $a n d t_{1} < t_{2}$

Question Number 652 Answers: 1 Comments: 0

if f:R→R is continuous and f(x+y)=f(x)+y 1. find f(x) 2. proof or disproof that f′(x)=1 3. if f(0)=0 proof or disproof that f(x)=x

$i f f : R \to R i s c o n t i n u o u s a n d$ $f (x + y) = f (x) + y$ $1 . f i n d f (x)$ $2 . p r o o f o r d i s p r o o f t h a t f^{'} (x) = 1$ $3 . i f f (0) = 0 p r o o f o r d i s p r o o f t h a t f (x) = x$

Question Number 650 Answers: 1 Comments: 0

f:R→R g:R→R f(x+y)=f(x)+f(y)g(y) g(x+y)=f(x)g(x)+g(y)

$f : R \to R$ $g : R \to R$ $f (x + y) = f (x) + f (y) g (y)$ $g (x + y) = f (x) g (x) + g (y)$

Question Number 630 Answers: 0 Comments: 1

∫_(−(π/2)) ^(+(π/2)) ((sin x)/(cos x))dx ∫_(−(π/2)) ^(+(π/2)) ((sin x)/(cos x))cos(2nx)dx ∫_(−(π/2)) ^(+(π/2)) ((sin x)/(cos x))sin(2nx)dx n∈N^∗

$\underset{- \frac{π}{2}}{\int^{+ \frac{π}{2}}} \frac{\sin x}{\cos x} d x$ $\underset{- \frac{π}{2}}{\int^{+ \frac{π}{2}}} \frac{\sin x}{\cos x} \cos (2 n x) d x$ $\underset{- \frac{π}{2}}{\int^{+ \frac{π}{2}}} \frac{\sin x}{\cos x} \sin (2 n x) d x$ $n \in N^{*}$

Question Number 516 Answers: 0 Comments: 1

Find all triangles with consecutive integer sides and having an angle twice another angle.

$F i n d a l l t r i a n g l e s w i t h c o n s e c u t i v e$ $i n t e g e r s i d e s a n d h a v i n g a n a n g l e t w i c e$ $a n o t h e r a n g l e .$

Question Number 510 Answers: 0 Comments: 1

proof or given a counter example: if p,q are prines with p>q, and ∃s prime such s∈(q,p) then p−q≤Σ_(r∈(q,p),r is prime) r

$p r o o f o r g i v e n a c o u n t e r e x a m p l e :$ $i f p, q a r e p r i n e s w i t h p > q, a n d \exists s p r i m e$ $s u c h s \in (q, p) t h e n$ $p - q ⩽ \sum_{r \in (q, p), r i s p r i m e} r$

Question Number 497 Answers: 1 Comments: 0

∫e^x sin 2x dx

$\int e^{x} \sin 2 x d x$

Question Number 495 Answers: 1 Comments: 0

∫sec^3 xdx

$\int \sec^{3} x d x$

Question Number 487 Answers: 1 Comments: 0

∫(1/(1+(√(2x)))) dx

$\int \frac{1}{1 + \sqrt{2 x}} d x$

Question Number 483 Answers: 1 Comments: 0

∫(1/(√(x−1)))dx

$\int \frac{1}{\sqrt{x - 1}} d x$

Question Number 480 Answers: 0 Comments: 1

proof or given a counter example: for s∈{2,3,4,5} Σ_(i=1) ^n [(1/s^i )−(((−1)^i )/i^s )]≤Σ_(i=1) ^n ((s+1)/(si^s ))

$p r o o f o r g i v e n a c o u n t e r e x a m p l e :$ $f o r s \in {2, 3, 4, 5}$ $\underset{i = 1}{\sum^{n}} [\frac{1}{s^{i}} - \frac{{(- 1)}^{i}}{i^{s}}] ⩽ \underset{i = 1}{\sum^{n}} \frac{s + 1}{{s i}^{s}}$

Question Number 472 Answers: 1 Comments: 0

proof or give a counter−example: if nm is prime then mdc(n^2 ,m^2 )=1

$p r o o f o r g i v e a c o u n t e r - e x a m p l e :$ $i f n m i s p r i m e t h e n mdc (n^{2}, m^{2}) = 1$

Question Number 465 Answers: 0 Comments: 1

A particle moves with a central acceration varies as the cube of the distance. if it be projected from an apse at distance a from the origin with a velocity which is (√(2 )) times the velocity for a circle of radius a. show that the equation of path is its rcosθ/(√2) = a

$A p a r t i c l e m o v e s w i t h a c e n t r a l a c c e r a t i o n v a r i e s a s t h e c u b e o f t h e d i s t a n c e . i f i t b e p r o j e c t e d f r o m a n a p s e a t d i s t a n c e a f r o m t h e o r i g i n w i t h a v e l o c i t y w h i c h i s \sqrt{2} t i m e s t h e v e l o c i t y f o r a c i r c l e o f r a d i u s a . s h o w t h a t t h e e q u a t i o n o f p a t h i s i t s r \cos θ / \sqrt{2} = a$

Question Number 433 Answers: 1 Comments: 0

find tagent plane of surface x^2 +y^3 =z^4 at the point (28,8,6)

$find tagent plane of surface$ $x^{2} + y^{3} = z^{4}$ $at the point (28, 8, 6)$

Question Number 435 Answers: 0 Comments: 2

∫(√(cos x)) dx =....

$\int \sqrt{c o s x} d x = . . . .$

Pg 111 Pg 112 Pg 113 Pg 114 Pg 115 Pg 116 Pg 117 Pg 118 Pg 119 Pg 120

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