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Question Number 33139 Answers: 1 Comments: 0

α and β are roots of ax^2 +bx +c=0 show that α+β= ((−b)/a) and αβ= (c/a) hence form an equation whose sum of roots and product of roots are respectively −(1/2) and 2.

$α a n d β a r e r o o t s o f$ ${a x}^{2} + b x + c = 0$ $s h o w t h a t α + β = \frac{- b}{a} a n d α β = \frac{c}{a}$ $h e n c e f o r m a n e q u a t i o n w h o s e$ $s u m o f r o o t s a n d p r o d u c t o f r o o t s$ $a r e r e s p e c t i v e l y$ $- \frac{1}{2} a n d 2 .$

Question Number 33136 Answers: 1 Comments: 0

given that y= 3x^4 find the percentage increase in y when x increases at (5/2)%.

$g i v e n t h a t y = 3 x^{4} f i n d t h e p e r c e n t a g e$ $i n c r e a s e i n y w h e n x i n c r e a s e s a t \frac{5}{2} % .$

Question Number 33134 Answers: 0 Comments: 0

describe geometrically the transformation with matrix 1) (((1 0)),((0 −1)) ) 2) (((1 0)),((2 1)) )

$d e s c r i b e g e o m e t r i c a l l y t h e t r a n s f o r m a t i o n$ $w i t h m a t r i x$ $1) (\begin{matrix} 1 0 \\ 0 - 1 \end{matrix}) 2) (\begin{matrix} 1 0 \\ 2 1 \end{matrix})$

Question Number 33135 Answers: 0 Comments: 0

the triangle with vertices A(−1,−3) ,B(2,1),and C(−2,2), is transformed by matrix (((a b)),((c d)) ) into the triangle with vertices A(−2,−3)^ , B(4,1),C(−4^ ,2) find the values of a,b,c and d

$t h e t r i a n g l e w i t h v e r t i c e s A (- 1, - 3)$ $, B (2, 1), a n d C (- 2, 2), i s t r a n s f o r m e d$ $b y m a t r i x (\begin{matrix} a b \\ c d \end{matrix}) i n t o t h e t r i a n g l e w i t h v e r t i c e s$ $Missing \left or extra \right$ $a, b, c a n d d$

Question Number 33096 Answers: 1 Comments: 0

z and w ∈ C proof ∣∣z∣−∣w∣∣ ≤ ∣z−w∣ and ∣z∣−∣w∣≤ ∣z+w∣

$z a n d w \in C$ $p r o o f ∣∣ z ∣ - ∣ w ∣∣ ⩽ ∣ z - w ∣ a n d ∣ z ∣ - ∣ w ∣⩽ ∣ z + w ∣$

Question Number 33095 Answers: 1 Comments: 0

z=x+yi ∈ C z^− =x−y ∈ C proof ∣z∣^2 =∣z^2 ∣=zz^− , so z≠0 →(1/z)=(z^− /(∣z∣^2 ))

$z = x + y i \in C$ $\bar{z} = x - y \in C$ $p r o o f ∣ z ∣^{2} =∣ z^{2} ∣= z \bar{z}, s o z \neq 0 \to \frac{1}{z} = \frac{\bar{z}}{∣ z ∣^{2}}$

Question Number 33153 Answers: 0 Comments: 1

it is given that Σ_(r=1 ) ^(20) [f(r)−10]=200 and Σ_(r=1) ^(20) [f(r)−10]^2 =2800 find the value of Σ_(r=1) ^(20) [f(r)]^2

$i t i s g i v e n t h a t$ $\underset{r = 1}{\sum^{20}} [f (r) - 10] = 200$ $a n d$ $\underset{r = 1}{\sum^{20}} {[f (r) - 10]}^{2} = 2800$ $f i n d t h e v a l u e o f$ $\underset{r = 1}{\sum^{20}} {[f (r)]}^{2}$

Question Number 33005 Answers: 0 Comments: 1

Given that y= ((sin x)/(1 + cos x)) find (dy/dx) Evaluate ∫_1 ^2 (x + 4)dx

$G i v e n t h a t$ $y = \frac{s i n x}{1 + c o s x} f i n d \frac{d y}{d x}$ $E v a l u a t e$ $\int_{1}^{2} (x + 4) d x$

Question Number 33152 Answers: 0 Comments: 1

it is given that (1/n)Σ_(r=1) ^n x^r =2 and (√((1/n)Σ_(r=1) ^n (x_r )^2 −(1/n^2 )(Σ_(r=1) ^n )^2 ))= 3 determine in terms of n the value of. Σ_(r=1) ^n (x_r +1)^2

$i t i s g i v e n t h a t$ $\frac{1}{n} \underset{r = 1}{\sum^{n}} x^{r} = 2 a n d \sqrt{\frac{1}{n} \underset{r = 1}{\sum^{n}} {(x_{r})}^{2} - \frac{1}{n^{2}} {(\underset{r = 1}{\sum^{n}})}^{2}} = 3$ $d e t e r m i n e i n t e r m s o f n t h e v a l u e$ $o f .$ $\underset{r = 1}{\sum^{n}} {(x_{r} + 1)}^{2}$

Question Number 32869 Answers: 1 Comments: 1

A= (((2 0)),((1 2)) ) ;h and k are numbers so that A^2 =hA + kI,where I= (((1 0)),((0 1)) ). find the value of h and k.

$A = (\begin{matrix} 2 0 \\ 1 2 \end{matrix}); h and k are numbers so$ $that A^{2} = h A + k I, where I = (\begin{matrix} 1 0 \\ 0 1 \end{matrix}) .$ $find the value of h and k .$

Question Number 32850 Answers: 0 Comments: 1

evaluate ∫_0 ^π 42(2)dx

$e v a l u a t e$ $\int_{0}^{π} 42 (2) d x$

Question Number 32845 Answers: 1 Comments: 0

how many moles are there in 3g of Na_2_ CO_3

$h o w m a n y m o l e s a r e t h e r e i n 3 g o f$ ${N a}_{2_{}} {C O}_{3}$

Question Number 32844 Answers: 0 Comments: 1

sketch on the x−y plain the locus of a point,P which moves such that its x and y coordinates are same. state the locus.

$s k e t c h o n t h e x - y p l a i n t h e l o c u s$ $o f a p o i n t, P w h i c h m o v e s s u c h t h a t$ $i t s x a n d y c o o r d i n a t e s a r e s a m e .$ $s t a t e t h e l o c u s .$

Question Number 32837 Answers: 0 Comments: 1

the length of the line segment joining A and B is (√(10)) .Given that its double the line segment joining the points (7,n) and (6,2) find the possible values of n.

$t h e l e n g t h o f t h e l i n e s e g m e n t j o i n i n g$ $A a n d B i s \sqrt{10} . G i v e n t h a t i t s d o u b l e$ $t h e l i n e s e g m e n t j o i n i n g t h e p o i n t s$ $(7, n) a n d (6, 2) f i n d t h e p o s s i b l e v a l u e s o f n .$

Question Number 32838 Answers: 2 Comments: 2

the points M(1,1),N(2,4) andR (3 ,q) lie on theresame straight line. find the coordinates of R

$t h e p o i n t s M (1, 1), N (2, 4) a n d R (3, q)$ $l i e o n t h e r e s a m e s t r a i g h t l i n e .$ $f i n d t h e c o o r d i n a t e s o f R$

Question Number 32834 Answers: 1 Comments: 0

find the value of k for which the length of the line segment joining (k^ ,2) and (−1,4) is 2(√2) units. show full working...

$f i n d t h e v a l u e o f k f o r w h i c h t h e$ $l e n g t h o f t h e l i n e s e g m e n t j o i n i n g$ $(\bar{k}, 2) a n d (- 1, 4) i s 2 \sqrt{2} u n i t s .$ $s h o w f u l l w o r k i n g . . .$

Question Number 33004 Answers: 0 Comments: 3

how do i solve for x a) 2^(3−x) +2^x = 6 b) (log_3 x)^2 − 6(log_3 x) + 9=0

$h o w d o i s o l v e$ $f o r x$ $a) 2^{3 - x} + 2^{x} = 6$ $b) {({l o g}_{3} x)}^{2} - 6 ({l o g}_{3} x) + 9 = 0$

Question Number 32765 Answers: 0 Comments: 0

Question Number 32760 Answers: 1 Comments: 0

if y=3x^(4 ) .find the approximate percentage increase in y when x increase by 2(1/2)%.

$if y = 3 x^{4} . f i n d t h e a p p r o x i m a t e p e r c e n t a g e$ $i n c r e a s e i n y w h e n x i n c r e a s e b y 2 \frac{1}{2} % .$

Question Number 32688 Answers: 1 Comments: 0

Evaluate 1) ∫_(−1) ^0 (x^2 + x 1) dx 2) ∫_1 ^5 (x −1+ (1/x^2 ))dx

$Evaluate$ $1) \int_{- 1}^{0} (x^{2} + x 1) dx$ $2) \int_{1}^{5} (x - 1 + \frac{1}{x^{2}}) dx$

Question Number 32792 Answers: 1 Comments: 2

the equation 3x− 5=15 represents a straight line. a) find one point on this line. b)find the coordinates of the points when the line cuts the x−axis and the y−axis c)find the gradient of this line.

$t h e e q u a t i o n$ $3 x - 5 = 15 r e p r e s e n t s a s t r a i g h t l i n e .$ $a) f i n d o n e p o i n t o n t h i s l i n e .$ $b) f i n d t h e c o o r d i n a t e s o f t h e p o i n t s w h e n$ $t h e l i n e c u t s t h e x - a x i s a n d t h e y - a x i s$ $c) f i n d t h e g r a d i e n t o f t h i s l i n e .$

Question Number 32793 Answers: 1 Comments: 0

Given that the point (−3^ ,2) lies on the line y=2x + c.find the coordinates of the point of intersection of this line and the y−axis

$G i v e n t h a t t h e p o i n t (- \bar{3}, 2) l i e s o n t h e$ $l i n e y = 2 x + c . f i n d t h e c o o r d i n a t e s$ $o f t h e p o i n t o f i n t e r s e c t i o n o f t h i s l i n e a n d t h e y - a x i s$

Question Number 32794 Answers: 1 Comments: 0

given that the point (t^ ,0) lies on the curve y=2x^2 −x. find the value of t.

$g i v e n t h a t t h e p o i n t (\bar{t}, 0) l i e s o n t h e$ $c u r v e y = 2 x^{2} - x . f i n d t h e v a l u e o f t .$

Question Number 32707 Answers: 1 Comments: 0

1)find u the value of u if Σ_(n=1) ^4 2u.2^(n−1) =64 2) find k if Σ_(n=1) ^∞ k.((1/3))^(n−1) =(2/3)

$1) find u the value of u if$ $\sum_{n = 1}^{4} 2 u . 2^{n - 1} = 64$ $2) find k if$ $\sum_{n = 1}^{\infty} k . {(\frac{1}{3})}^{n - 1} = \frac{2}{3}$

Question Number 32396 Answers: 1 Comments: 0

roots 2x×x+x+3

$r o o t s$ $2 x \times x + x + 3$

Question Number 32220 Answers: 0 Comments: 3

Find the value of a for which the equation sin^4 x+asin^2 x+1=0 will have a solution.

$F i n d t h e v a l u e o f a f o r w h i c h t h e e q u a t i o n$ $\sin^{4} x + a \sin^{2} x + 1 = 0 w i l l h a v e a s o l u t i o n .$

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