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GeometryQuestion and Answers: Page 111

Question Number 7665 Answers: 1 Comments: 0

(d/dx)(√(x^2 −4))

$\frac{d}{d x} \sqrt{x^{2} - 4}$

Question Number 7655 Answers: 2 Comments: 1

((8/x))^x = x^2 Show that x = 4

${(\frac{8}{x})}^{x} = x^{2}$ $S h o w t h a t x = 4$

Question Number 7600 Answers: 1 Comments: 0

solve ∣((x^2 −3x−1)/(x^2 +x+1))∣<3 give solution

$s o l v e ∣ \frac{x^{2} - 3 x - 1}{x^{2} + x + 1} ∣< 3 g i v e s o l u t i o n$

Question Number 7608 Answers: 1 Comments: 3

If x = cosΘ − sinΘ and y = cos2Θ Show that, y = x(√(2 − x^2 ))

$I f x = c o s Θ - s i n Θ$ $a n d y = c o s 2 Θ$ $S h o w t h a t,$ $y = x \sqrt{2 - x^{2}}$

Question Number 7544 Answers: 0 Comments: 7

Question Number 7326 Answers: 0 Comments: 2

Is it correct? floor(x)=⌊x⌋=[x] floor(x)={n ∣ n∈Z , x−1<n≤x} e.g.... floor(3)=3 floor(3.4)=3 floor(−2.5)=−3 floor(−π)=−4

$I s i t c o r r e c t ?$ $f l o o r (x) = ⌊ x ⌋ = [x]$ $f l o o r (x) = {n ∣ n \in Z, x - 1 < n ⩽ x}$ $e . g . . . .$ $f l o o r (3) = 3$ $f l o o r (3.4) = 3$ $f l o o r (- 2.5) = - 3$ $f l o o r (- π) = - 4$

Question Number 7314 Answers: 1 Comments: 1

Question Number 7316 Answers: 0 Comments: 1

x−y and y−x x={−2,−1,0,2,5} y={0,5,7,8,10}

$x - y a n d y - x$ $x = {- 2, - 1, 0, 2, 5}$ $y = {0, 5, 7, 8, 10}$

Question Number 7238 Answers: 0 Comments: 1

um numero somado ao seu triplo e igual a 36. qual e esse numero?

$u m n u m e r o s o m a d o a o s e u t r i p l o e i g u a l a 36 . q u a l e e s s e n u m e r o ?$

Question Number 7239 Answers: 0 Comments: 1

A soma de um numero com seu sextuplo e ingual a 280.Quale e o numero?

$A s o m a d e u m n u m e r o c o m s e u s e x t u p l o e i n g u a l a 280 . Q u a l e e o n u m e r o ?$

Question Number 7243 Answers: 0 Comments: 2

lim_(x→∞) ((√(x^2 +x+1)))−((√(x^2 +1))) <

$\lim_{x \to \infty} (\sqrt{x^{2} + x + 1)} - (\sqrt{x^{2} + 1)}$ $<$

Question Number 7031 Answers: 1 Comments: 5

Question Number 6830 Answers: 0 Comments: 0

A, B, and C are three non-collinear points such that ∣AB∣=c , ∣BC∣=a and ∣CA∣=b. What will be the condition for a point D to be concircle with A, B and C when all the four points belong to same plane?

$A, B, a n d C a r e t h r e e n o n - c o l l i n e a r p o i n t s s u c h$ $t h a t ∣ A B ∣= c, ∣ B C ∣= a a n d ∣ C A ∣= b .$ $W h a t w i l l b e t h e c o n d i t i o n f o r a p o i n t D t o b e$ $c o n c i r c l e w i t h A, B a n d C w h e n a l l t h e f o u r$ $p o i n t s b e l o n g t o s a m e p l a n e ?$

Question Number 6758 Answers: 0 Comments: 4

A circle of radius r has a point O as its centre. Points A and B are points on the circumference. For △OAB, OA^(−) =OB^(−) =r, AB^(−) =d, ∠AOB=θ. What is (r/d)?

$A circle of radius r has a point O as its$ $centre . Points A and B are points on the$ $circumference .$ $For △ O A B, \overset{―}{O A} = \overset{―}{O B} = r, \overset{―}{A B} = d, ∠ A O B = θ .$ $What is \frac{r}{d} ?$

Question Number 6725 Answers: 0 Comments: 1

a+b=c a+a=ac c−a=b b+b=bc a^2 +b=c^3 a+D=b^2 b+D=a^2 a′b′+D=c′D ab+D=c_D ab+c=abc a′b′c′+D=D_(abc) abc+D=abc_D a^2 +b^± =Dab^(±2) (√(a^b +b^+_− ))=D^± (((a/b)+D))^(1/∂) =cot^(−1) a′b′

$a + b = c$ $a + a = a c$ $c - a = b$ $b + b = b c$ $a^{2} + b = c^{3}$ $a + D = b^{2}$ $b + D = a^{2}$ $a^{'} b^{'} + D = c^{'} D$ $a b + D = c_{D}$ $a b + c = a b c$ $a^{'} b^{'} c^{'} + D = D_{a b c}$ $a b c + D = {a b c}_{D}$ $a^{2} + b^{\pm} = {D a b}^{\pm 2}$ $\sqrt{a^{b} + b^{+_{-}}} = D^{\pm}$ $\sqrt[\partial]{\frac{a}{b} + D} = \cot^{- 1} a^{'} b^{'}$

Question Number 6640 Answers: 0 Comments: 4

ABC is a triangle,whose one vertex is moving along a circular path. Discuss the nature of the path, along which the centroid of the triangle is moving.

$ABC i s a t r i a n g l e, w h o s e o n e v e r t e x$ $i s m o v i n g a l o n g a c i r c u l a r p a t h .$ $D i s c u s s t h e n a t u r e o f t h e p a t h, a l o n g$ $w h i c h t h e c e n t r o i d o f t h e t r i a n g l e$ $i s m o v i n g .$

Question Number 6635 Answers: 1 Comments: 2

Question Number 6564 Answers: 1 Comments: 5

Let φ={ l_1 , l_2 , l_3 } be a set of three, nonparallel lines that all meet at one point R in the plane. Investigate conditions on φ such that R is the centroid of some triangle.

$L e t ϕ = {l_{1}, l_{2}, l_{3}} b e a s e t o f t h r e e, n o n p a r a l l e l$ $l i n e s t h a t a l l m e e t a t o n e p o i n t R i n$ $t h e p l a n e . I n v e s t i g a t e c o n d i t i o n s o n ϕ$ $s u c h t h a t R i s t h e c e n t r o i d o f s o m e t r i a n g l e .$