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Question Number 38640 Answers: 0 Comments: 1

calculate Σ_(k=1) ^n k^4 interms of n.

$c a l c u l a t e \sum_{k = 1}^{n} k^{4} i n t e r m s o f n .$

Question Number 38636 Answers: 1 Comments: 0

Three variables u,v and w are related such that u varies directly as v and inversely as the square of w. If v increases by 15% and w decreased by 10%, find the percentage change in u.

$Three variables u, v and w are related such that$ $u varies directly as v and inversely as the square of$ $w . If v increases by 15 % and w decreased by 10 %,$ $find the percentage change in u .$

Question Number 38618 Answers: 1 Comments: 2

Question Number 38613 Answers: 1 Comments: 0

The radius of the largest circle which passes through (1,2) and (3,4) and lies completely in the first quadrant is A) 3 B) 2 C) (√6) D) 2(√5) I got the answer as 2 but the answer given is 2(√5).

$The radius of the largest circle which$ $passes through (1, 2) and (3, 4) and lies$ $completely in the first quadrant is$ $A) 3$ $B) 2$ $C) \sqrt{6}$ $D) 2 \sqrt{5}$ $I got the answer as 2 but the answer$ $given is 2 \sqrt{5} .$

Question Number 39491 Answers: 0 Comments: 0

Question Number 38600 Answers: 3 Comments: 1

Question Number 38593 Answers: 1 Comments: 3

Question Number 38587 Answers: 2 Comments: 2

solve for x: e^x + e^x^2 + e^x^3 = 3 + x + x^2 + x^3

$solve for x : e^{x} + e^{x^{2}} + e^{x^{3}} = 3 + x + x^{2} + x^{3}$

Question Number 38570 Answers: 0 Comments: 2

Question Number 38568 Answers: 0 Comments: 18

Find the area common to min{[x], [y] } =2 and max{[x], [y] } =4 . [x] denotes the greatest integer less than or equal to x.

$F i n d t h e a r e a c o m m o n t o$ $m i n {[x], [y]} = 2 a n d$ $m a x {[x], [y]} = 4 .$ $[x] d e n o t e s t h e g r e a t e s t i n t e g e r$ $l e s s t h a n o r e q u a l t o x .$

Question Number 38562 Answers: 1 Comments: 0

((√2) +i)(1−(√(2i)) )

$(\sqrt{2} + i) (1 - \sqrt{2 i})$

Question Number 38559 Answers: 1 Comments: 0

in a geometric series, the first term =a, common ratio=r. If S_n denotes the sum of the n terms and U_n =Σ_(n=1) ^n S_(n,) then rS_n +(1−r)U_(n ) equals to (a) 0 (b) n (c) na (d)nar

$i n a g e o m e t r i c s e r i e s, t h e f i r s t t e r m$ $= a, c o m m o n r a t i o = r . I f S_{n} d e n o t e s$ $t h e s u m o f t h e n t e r m s a n d U_{n} = \underset{n = 1}{\sum^{n}} S_{n,}$ $t h e n {r S}_{n} + (1 - r) U_{n} e q u a l s t o$ $(a) 0 (b) n (c) n a (d) n a r$

Question Number 38557 Answers: 1 Comments: 0

prove that ((2 cos 2^n θ + 1)/(2 cos θ + 1)) = (2 cos θ − 1)(2 cos 2θ − 1)(2 cos 2^2 θ− 1) ...(2 cos 2^(n − 1) θ − 1)

$p r o v e t h a t$ $\frac{2 \cos 2^{n} θ + 1}{2 \cos θ + 1} = (2 \cos θ - 1) (2 \cos 2 θ - 1) (2 \cos 2^{2} θ - 1)$ $. . . (2 \cos 2^{n - 1} θ - 1)$

Question Number 38536 Answers: 2 Comments: 0

∫_0 ^π (dx/(√(3−cos x)))=

$\int_{0}^{π} \frac{d x}{\sqrt{3 - \cos x}} =$

Question Number 38535 Answers: 0 Comments: 0

Given the function f(x) where f(x)= { ((∫x^2 + 1 ,for {x:x D(f) 2)),((∫x^3 − 1,for y = f′(x))) :} a) Evaluate f(2) if f(a)= 2 + a^(n−1) find the value of a hence the domain of f(x).

$G i v e n t h e f u n c t i o n$ $f (x) w h e r e$ $f (x) = {\begin{cases} \int x^{2} + 1, f o r {x : x D (f) 2 \\ \int x^{3} - 1, f o r y = f^{'} (x) \end{cases}$ $a) E v a l u a t e f (2)$ $i f f (a) = 2 + a^{n - 1}$ $f i n d t h e v a l u e o f a$ $h e n c e t h e d o m a i n o f f (x) .$