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Question Number 66868 Answers: 0 Comments: 3

A town N is 340km due west of town G and town K is due west of town N. A helicopter Zebra left G for K at 9a.m. Another helicopter Buffalo left N for K at 11a.m. Helicopter Buffalo travelled at an average speed of 20km/h faster than helicopter Zebra. If both helicopters reached K at 12.30p.m, find the speed of helicopter Buffalo.

$A t o w n N i s 340 k m d u e w e s t o f$ $t o w n G a n d t o w n K i s d u e w e s t$ $o f t o w n N . A h e l i c o p t e r Z e b r a$ $l e f t G f o r K a t 9 a . m . A n o t h e r$ $h e l i c o p t e r B u f f a l o l e f t N f o r K$ $a t 11 a . m . H e l i c o p t e r B u f f a l o$ $t r a v e l l e d a t a n a v e r a g e s p e e d o f$ $20 k m / h f a s t e r t h a n h e l i c o p t e r$ $Z e b r a . I f b o t h h e l i c o p t e r s r e a c h e d$ $K a t 12.30 p . m, f i n d t h e s p e e d o f$ $h e l i c o p t e r B u f f a l o .$

Question Number 66856 Answers: 1 Comments: 0

Two towns T and S are 300 km apart. Two buses A and B started from T at the same time travelling towards S. Bus B, travelling at an average speed of 10km/h greater than that of A reached S 1(1/4) hours earlier. (a) Find the average speed of A (b) How far was A from T when B reached S.

$T w o t o w n s T a n d S a r e 300 k m a p a r t .$ $T w o b u s e s A a n d B s t a r t e d f r o m$ $T a t t h e s a m e t i m e t r a v e l l i n g t o w a r d s$ $S . B u s B, t r a v e l l i n g a t a n a v e r a g e$ $s p e e d o f 10 k m / h g r e a t e r t h a n t h a t$ $o f A r e a c h e d S 1 \frac{1}{4} h o u r s e a r l i e r .$ $(a) F i n d t h e a v e r a g e s p e e d o f A$ $(b) H o w f a r w a s A f r o m T w h e n$ $B r e a c h e d S .$

Question Number 66852 Answers: 0 Comments: 3

Question Number 66851 Answers: 2 Comments: 1

Question Number 66849 Answers: 0 Comments: 2

Question Number 66846 Answers: 0 Comments: 2

Question Number 66842 Answers: 0 Comments: 2

Question Number 66845 Answers: 0 Comments: 1

A cylindrical tank of radius 2m and height 1.5m initially contains water to a depth of 50cm. Water is added to the tank at the rate of 62.84l per minute for 15 minutes. Find the new height of water in the tank.

$A c y l i n d r i c a l t a n k o f r a d i u s 2 m$ $a n d h e i g h t 1.5 m i n i t i a l l y c o n t a i n s$ $w a t e r t o a d e p t h o f 50 c m . W a t e r$ $i s a d d e d t o t h e t a n k a t t h e r a t e o f$ $62.84 l p e r m i n u t e f o r 15 m i n u t e s .$ $F i n d t h e n e w h e i g h t o f w a t e r i n$ $t h e t a n k .$

Question Number 66832 Answers: 2 Comments: 0

solve the system of congruence {: ((x≡ 1 (mod 5))),((x ≡ 2 (mod 7))),((x≡ 3(mod 9))),((x ≡ 4( mod 11))) }

$s o l v e t h e s y s t e m o f c o n g r u e n c e$ $\begin{matrix} x \equiv 1 (m o d 5) \\ x \equiv 2 (m o d 7) \\ x \equiv 3 (m o d 9) \\ x \equiv 4 (m o d 11) \end{matrix}}$

Question Number 66830 Answers: 0 Comments: 4

evaluate. ∫_1 ^( ∞) (1/x^(2 ) ) dx. can i assume lim_(t→0) ∫_1 ^( t) (1/x^(2 ) ) dx ????

$e v a l u a t e .$ $\int_{1}^{\infty} \frac{1}{x^{2}} d x .$ $c a n i a s s u m e \lim_{t \to 0} \int_{1}^{t} \frac{1}{x^{2}} d x ? ? ? ?$

Question Number 66803 Answers: 1 Comments: 3

prove that Σ_(r=k) ^n r = (1/2)n(n+1) show with a diagram that the volume of a parallepipe is a.(b×c)

$p r o v e t h a t$ $\underset{r = k}{\sum^{n}} r = \frac{1}{2} n (n + 1)$ $s h o w w i t h a d i a g r a m t h a t t h e v o l u m e o f a p a r a l l e p i p e i s a . (b \times c)$

Question Number 66802 Answers: 0 Comments: 6

given that f(x) = 3x^3 − 2x^2 + 5x + 7 find a) α + β + γ b) αβγ c) α^2 + β^2 + γ^2 d) α^3 + β^3 + γ^3 any solutions directly?

$g i v e n t h a t$ $f (x) = 3 x^{3} - 2 x^{2} + 5 x + 7 f i n d$ $a) α + β + γ$ $b) α β γ$ $c) α^{2} + β^{2} + γ^{2}$ $d) α^{3} + β^{3} + γ^{3}$ $a n y s o l u t i o n s d i r e c t l y ?$

Question Number 66767 Answers: 0 Comments: 2

In a school there are 30 more boys than girls. One-quarter of the boys and two-thirds of the girls are boarders. If there are 255 boarders, find the number of students in the school.

$I n a s c h o o l t h e r e a r e 30 m o r e b o y s$ $t h a n g i r l s . O n e - q u a r t e r o f t h e b o y s$ $a n d t w o - t h i r d s o f t h e g i r l s a r e b o a r d e r s .$ $I f t h e r e a r e 255 b o a r d e r s, f i n d t h e$ $n u m b e r o f s t u d e n t s i n t h e s c h o o l .$

Question Number 66765 Answers: 0 Comments: 2

Simba had 57 denomination notes which he deposited in his account. He had six times as many two-hundred shilling notes as one-thousand shilling notes and twice as many one-hundred shilling notes as two- hundred shilling notes. The rest were fifty shilling notes. If he deposited a total of sh 7750, find the number of fifty shilling notes he had.

$S i m b a h a d 57 d e n o m i n a t i o n n o t e s$ $w h i c h h e d e p o s i t e d i n h i s a c c o u n t .$ $H e h a d s i x t i m e s a s m a n y t w o - h u n d r e d$ $s h i l l i n g n o t e s a s o n e - t h o u s a n d$ $s h i l l i n g n o t e s a n d t w i c e a s m a n y$ $o n e - h u n d r e d s h i l l i n g n o t e s a s t w o -$ $h u n d r e d s h i l l i n g n o t e s . T h e r e s t w e r e$ $f i f t y s h i l l i n g n o t e s . I f h e d e p o s i t e d$ $a t o t a l o f s h 7750, f i n d t h e n u m b e r$ $o f f i f t y s h i l l i n g n o t e s h e h a d .$

Question Number 66756 Answers: 2 Comments: 0

solve the equations, x+y=17 xy−5x=32

$s o l v e t h e e q u a t i o n s,$ $x + y = 17$ $x y - 5 x = 32$

Question Number 66746 Answers: 2 Comments: 0

A point T divides a line AB internally in the ratio 5:2. Given that A is (-4,10) and B is (10,3), find the coordinates of T.

$A p o i n t T d i v i d e s a l i n e A B i n t e r n a l l y i n t h e r a t i o 5 : 2 . G i v e n t h a t A i s (- 4, 10) a n d B i s (10, 3), f i n d t h e c o o r d i n a t e s o f T .$

Question Number 66562 Answers: 1 Comments: 1

given that ∣z − i∣ = ∣z − 4 +3 i∣ sketch the locus of z find the catersian equation of this locus.

$g i v e n t h a t ∣ z - i ∣ = ∣ z - 4 + 3 i ∣$ $s k e t c h t h e l o c u s o f z$ $f i n d t h e c a t e r s i a n e q u a t i o n o f t h i s l o c u s .$

Question Number 66548 Answers: 0 Comments: 1

Evaluate:∫(√(x(√(x+1)) ))dx

$E v a l u a t e : \int \sqrt{x \sqrt{x + 1}} d x$

Question Number 66513 Answers: 1 Comments: 4

when finding ∫_0 ^2 (2x +4)^5 dx must we change limits?

$w h e n f i n d i n g \int_{0}^{2} {(2 x + 4)}^{5} d x$ $m u s t w e c h a n g e l i m i t s ?$

Question Number 66497 Answers: 1 Comments: 0

Question Number 66489 Answers: 3 Comments: 0

Question Number 66467 Answers: 0 Comments: 1

calculate A_n =∫_0 ^∞ (dx/((n+x^n )^2 )) with n>1

$c a l c u l a t e A_{n} = \int_{0}^{\infty} \frac{d x}{{(n + x^{n})}^{2}} w i t h n > 1$

Question Number 66461 Answers: 0 Comments: 0

x(n)=3n^2 −2n+7 find even and odd component

$x (n) = 3 n^{2} - 2 n + 7$ $f i n d e v e n a n d o d d c o m p o n e n t$

Question Number 66439 Answers: 0 Comments: 4

for a geometric series. can the sun to infinty use the two formulas S_∞ = (a/(1−r)) ∣r∣ <1 and S_∞ = (a/(r−1)) ∣r∣ > 1 ?? please i am getting confused on this.

$f o r a g e o m e t r i c s e r i e s .$ $c a n t h e s u n t o i n f i n t y u s e t h e t w o f o r m u l a s$ $S_{\infty} = \frac{a}{1 - r} ∣ r ∣ < 1 a n d S_{\infty} = \frac{a}{r - 1} ∣ r ∣ > 1 ? ? p l e a s e i a m g e t t i n g c o n f u s e d o n t h i s .$

Question Number 66421 Answers: 1 Comments: 0

show that for a given complex number z z^n = r^n (cosnθ + isinnθ)

$s h o w t h a t f o r a g i v e n c o m p l e x n u m b e r z$ $z^{n} = r^{n} (c o s n θ + i s i n n θ)$

Question Number 66420 Answers: 0 Comments: 3

solve the differential equation 2(d^2 y/dx^2 ) + (dy/dx) − e^(−x) = 4

$s o l v e t h e d i f f e r e n t i a l e q u a t i o n$ $2 \frac{d^{2} y}{{d x}^{2}} + \frac{d y}{d x} - e^{- x} = 4$

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