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Question Number 34169 Answers: 1 Comments: 0

if the sum S_4 of the first 4 terms of a G P is 24 and the sum S_6 of the first 6 terms is 30 find the first term and common ratio..

$i f t h e s u m S_{4} o f t h e f i r s t 4 t e r m s$ $o f a G P i s 24 a n d t h e s u m S_{6} o f$ $t h e f i r s t 6 t e r m s i s 30 f i n d t h e$ $f i r s t t e r m a n d c o m m o n r a t i o . .$

Question Number 34159 Answers: 1 Comments: 1

let S=1+2+...+2018 compute S(mod 2)+S(mod8)+S(mod2018)

$l e t S = 1 + 2 + . . . + 2018$ $c o m p u t e S (\mod 2) + S (\mod 8) + S (\mod 2018)$

Question Number 34142 Answers: 0 Comments: 1

what is the derivative of (x+3)(x^2 + 5) and find the n sequence of Σ_(r=n+1 ) ^(2n) (4r^3 −3)

$w h a t i s t h e d e r i v a t i v e o f$ $(x + 3) (x^{2} + 5)$ $a n d f i n d t h e n s e q u e n c e o f$ $\underset{r = n + 1}{\sum^{2 n}} (4 r^{3} - 3)$

Question Number 34119 Answers: 3 Comments: 0

if u and v are real valued functions of x, then (d/dx)((u/v))= A. ((v(du/dx)− u(dv/dx))/u^2 ) B. ((v(du/dx)− u(dv/dx))/u^2 ) C. ((v(du/dx)−u (dv/dx))/v^2 ) D. ((u(dv/dx) − v(du/dx))/v^2 )

$i f u a n d v a r e r e a l v a l u e d f u n c t i o n s$ $o f x, t h e n \frac{d}{d x} (\frac{u}{v}) =$ $A . \frac{v \frac{d u}{d x} - u \frac{d v}{d x}}{u^{2}} B . \frac{v \frac{d u}{d x} - u \frac{d v}{d x}}{u^{2}}$ $C . \frac{v \frac{d u}{d x} - u \frac{d v}{d x}}{v^{2}} D . \frac{u \frac{d v}{d x} - v \frac{d u}{d x}}{v^{2}}$

Question Number 34098 Answers: 0 Comments: 13

Since the beginning several persons with their experties had left the forum... Newcommers don′t know them,but they can explore the past of the forum and recognise their precious work! Think the forum as cricket. Some were ′bowlers′ and others were ′batsmen′. Bowlers: questioners and batsmen: answerers. In my period(When I was somewhat more active) some good ′bowlers′ were sanusihammed,tawakalitu,tawa.Some good ′batsmen′ were prakash jain, Yozzi. 123556 was ′all rounder′.An other energetic ′all-rounder player′ was filups. ′Bowlers′ also play vital role... ... Speaking of present period. Recently our ′Captain′ has left the forum.An expert,an honest and a hardworker ′player′ and leader. Also a good ′bowler′ of the present period has left us. I request mrW and Mr tinkutara to come back please! The forum needs you! Also request Ajeet bhaya(a lovely name of Mr Ajfour) to become more active.He is, like mrW, an important figure. Request by a 12th player.

$Since the beginning$ $several persons with their experties$ $had left the forum . . .$ $Newcommers {don}^{'} t know them, but$ $they can explore the past of the forum$ $and recognise their precious work!$ $Think the forum as cricket .$ $Some were^{'} {bowlers}^{'} and others were$ $^{'} {batsmen}^{'} . Bowlers : questioners and$ $batsmen : answerers .$ $In my period (When I was somewhat$ $more active) some good^{'} {bowlers}^{'} were$ $sanusihammed, tawakalitu, tawa . Some$ $good^{'} {batsmen}^{'} were prakash jain,$ $Yozzi . 123556 was^{'} all {rounder}^{'} . An other$ $energetic^{'} all - rounder {player}^{'} was filups .$ $^{'} {Bowlers}^{'} also play vital role . . .$ $. . .$ $Speaking of present period .$ $Recently our^{'} {Captain}^{'} has left the$ $forum . An expert, an honest and a$ $hardworker^{'} {player}^{'} and leader .$ $Also a good^{'} {bowler}^{'} of the present$ $period has left us .$ $I request mrW and Mr tinkutara$ $to come back please! The forum$ $needs you!$ $Also request A j e e t b h a y a (a lovely$ $name of Mr Ajfour) to become more$ $active . He is, like mrW, an important$ $figure .$ $Request by a 12 th player .$

Question Number 33907 Answers: 0 Comments: 1

Question Number 33897 Answers: 2 Comments: 0

let consider ψ(x)=((Γ^′ (x))/(Γ(x))) 1) prove that ∀ a>0 ∫_0 ^1 ψ(a+x)dx=ln(a) 2) prove that ∀ n∈ N^★ ∫_0 ^1 ψ(x)sin(2πnx)dx=−(π/2)

$l e t c o n s i d e r ψ (x) = \frac{Γ^{^{'}} (x)}{Γ (x)}$ $1) p r o v e t h a t \forall a > 0 \int_{0}^{1} ψ (a + x) d x = l n (a)$ $2) p r o v e t h a t \forall n \in N^{★} \int_{0}^{1} ψ (x) s i n (2 π n x) d x = - \frac{π}{2}$

Question Number 33800 Answers: 1 Comments: 0

Question Number 33753 Answers: 1 Comments: 0

Question Number 33575 Answers: 3 Comments: 0

simplify (√((3+2(√(2)))))

$simplify \sqrt{(3 + 2 \sqrt{2)}}$

Question Number 33557 Answers: 0 Comments: 0

This^ is^ a^ formula. working^ out^ the^ area^ between^ two Toroidal^ coils. Both^ with^ a^ magnetic^ spring^ constant. r=radius=1 a=area=2 k^z =(1/((r+a)))−(1/r^2 )=−a(((2∙r+a))/([(r+a)^2 ∙r^2 ])) ratio=? what^ is^ the^ ratio?

${T h i s}^{} {i s}^{} a^{} f o r m u l a .$ ${w o r k i n g}^{} {o u t}^{} {t h e}^{} {a r e a}^{} {b e t w e e n}^{} t w o$ ${T o r o i d a l}^{} c o i l s .$ ${B o t h}^{} {w i t h}^{} a^{} {m a g n e t i c}^{} {s p r i n g}^{} c o n s t a n t .$ $r = r a d i u s = 1$ $a = a r e a = 2$ $k^{z} = \frac{1}{(r + a)} - \frac{1}{r^{2}} = - a \frac{(2 \cdot r + a)}{[{(r + a)}^{2} \cdot r^{2}]}$ $r a t i o = ?$ ${w h a t}^{} {i s}^{} {t h e}^{} r a t i o ?$

Question Number 33508 Answers: 0 Comments: 2

((3^x ×8^x )/(12^(x+1) ))

$\frac{3^{x} \times 8^{x}}{12^{x + 1}}$

Question Number 33462 Answers: 1 Comments: 0

using PMI show that ∀ n≥2 the number 5^n ends with the digits 25

$u s i n g P M I s h o w t h a t \forall n ⩾ 2 t h e$ $n u m b e r 5^{n} e n d s w i t h t h e d i g i t s 25$

Question Number 33460 Answers: 1 Comments: 0

why do we use greek letters like α,β,θ,π,Ω,ρ in mathematics

$w h y d o w e u s e g r e e k l e t t e r s l i k e$ $α, β, θ, π, Ω, ρ i n m a t h e m a t i c s$

Question Number 33455 Answers: 1 Comments: 2

Please can someone help with a simplier method of solving this question Q1; Given that the expression x^3 +x^2 −4x +5 and x^3 +3x−7 leave same remainder when divided by (x−a) find the possible values of a

$P l e a s e c a n s o m e o n e h e l p w i t h a$ $s i m p l i e r m e t h o d o f s o l v i n g t h i s q u e s t i o n$ $Q 1;$ $G i v e n t h a t t h e e x p r e s s i o n x^{3} + x^{2} - 4 x + 5$ $a n d x^{3} + 3 x - 7 l e a v e s a m e r e m a i n d e r$ $w h e n d i v i d e d b y (x - a) f i n d t h e p o s s i b l e$ $v a l u e s o f a$

Question Number 33425 Answers: 1 Comments: 3

find k if the deteminant of (((3 k)),((2 3)) ) is 2 can someone please teach me how to find the deteminant of a 3×3 matrix ?

$f i n d k i f t h e d e t e m i n a n t o f$ $(\begin{matrix} 3 k \\ 2 3 \end{matrix}) i s 2$ $c a n s o m e o n e p l e a s e t e a c h m e h o w$ $t o f i n d t h e d e t e m i n a n t o f a 3 \times 3$ $m a t r i x ?$

Question Number 33413 Answers: 0 Comments: 2

the value of θ,in the range 0° ≤ θ≤90° for which sinθ = cos θ is...?

$t h e v a l u e o f θ, i n t h e r a n g e 0 ° ⩽ θ ⩽ 90 °$ $f o r w h i c h s i n θ = c o s θ i s . . . ?$

Question Number 33411 Answers: 0 Comments: 1

Given that u and v are real valued functions in x ,then (d/dx)((u/v)) is equal to?

$Given that u and v are real valued$ $functions in x, then \frac{d}{d x} (\frac{u}{v}) i s e q u a l t o ?$

Question Number 33322 Answers: 0 Comments: 4

a) px^2 + 3x + q=0 has roots [((α+β)/(αβ))]× αβ find p and q if x^2 − 7x + 4 = 0 with real and distinct roots has same roots.. b)if α and β are roots of x^2 + kx +2k+8=0. a) find k if one root is twice the other.

$a) {p x}^{2} + 3 x + q = 0 h a s r o o t s$ $[\frac{α + β}{α β}] \times α β$ $f i n d p a n d q i f$ $x^{2} - 7 x + 4 = 0 w i t h r e a l a n d$ $d i s t i n c t r o o t s h a s s a m e r o o t s . .$ $b) i f α a n d β a r e r o o t s o f$ $x^{2} + k x + 2 k + 8 = 0 .$ $a) f i n d k i f o n e r o o t i s t w i c e t h e o t h e r .$

Question Number 33255 Answers: 0 Comments: 2

if the roots of the equation 3x^2 +5x+2=0 are (α+β)(αβ) then the value of p if x^2 + px − 6=0 is?

$i f t h e r o o t s o f t h e e q u a t i o n$ $3 x^{2} + 5 x + 2 = 0 a r e (α + β) (α β)$ $t h e n t h e v a l u e o f p i f x^{2} + p x - 6 = 0$ $i s ?$

Question Number 33252 Answers: 0 Comments: 1

if α and β are roots of the equation x^2 +px + q=0 then the value p and q when x^2 + 3x + 2=0 has same roots are?

$i f α a n d β a r e r o o t s o f t h e e q u a t i o n$ $x^{2} + p x + q = 0$ $t h e n t h e v a l u e p a n d q w h e n$ $x^{2} + 3 x + 2 = 0 h a s s a m e r o o t s a r e ?$

Question Number 33230 Answers: 1 Comments: 0

how many ways can the word MOGGOMBABA be arranged hence find S_∞ of a sequence a,ar,ar^2 in integral 1,(√2) , 2,...

$h o w m a n y w a y s c a n t h e w o r d$ $M O G G O M B A B A$ $b e a r r a n g e d h e n c e f i n d S_{\infty} o f a$ $s e q u e n c e a, a r, {a r}^{2} i n i n t e g r a l$ $1, \sqrt{2}, 2, . . .$

Question Number 33211 Answers: 0 Comments: 0

find lim_(x→+∞) x e^(−x^2 ) ∫_(x−1) ^x e^t^2 dt .

$f i n d {l i m}_{x \to + \infty} x e^{- x^{2}} \int_{x - 1}^{x} e^{t^{2}} d t .$

Question Number 33185 Answers: 1 Comments: 0

find k if Σ_(n=1) ^∞ (2k)(2)^(n−1) =64 hence find k if kx^2 +3x +4=0 has real roots.

$f i n d k i f$ $\underset{n = 1}{\sum^{\infty}} (2 k) {(2)}^{n - 1} = 64$ $h e n c e f i n d k i f {k x}^{2} + 3 x + 4 = 0 h a s$ $r e a l r o o t s .$

Question Number 33184 Answers: 0 Comments: 0

describe geometrically the matrice (((1 0)),((0 −1)) )

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

Question Number 33159 Answers: 0 Comments: 0

if y= 3x^4 find the percentage increase in y if x increases at (5/2)% or 2(1/2)%^ use the Binomial Expansion method (that is find new y and new x and simplify)

$i f y = 3 x^{4} f i n d t h e p e r c e n t a g e i n c r e a s e i n y$ $i f x i n c r e a s e s a t \frac{5}{2} % o r 2 \frac{1}{2} \overset{}{%}$ $u s e t h e B i n o m i a l E x p a n s i o n m e t h o d$ $(t h a t i s f i n d n e w y a n d n e w x a n d s i m p l i f y)$

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

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