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AlgebraQuestion and Answers: Page 221

Question Number 123626 Answers: 0 Comments: 0

Question Number 123595 Answers: 0 Comments: 1

For real numbers (a/b/c) define s_n =a^n +b^n +c^n Suppose s_1 =2 s_2 =6 and s_(3 ) =14.Prove that ∣s_n ^2 −s_(n−1) s_(n+1) ∣=8=holds ∀ n>1

$F o r r e a l n u m b e r s (a / b / c) d e f i n e s_{n} = a^{n} + b^{n} + c^{n}$ $S u p p o s e s_{1} = 2 s_{2} = 6 a n d s_{3} = 14 . P r o v e t h a t$ $∣ s_{n}^{2} - s_{n - 1} s_{n + 1} ∣= 8 = h o l d s \forall n > 1$

Question Number 123591 Answers: 0 Comments: 2

Question Number 123576 Answers: 1 Comments: 2

Question Number 123574 Answers: 1 Comments: 0

Question Number 123548 Answers: 1 Comments: 1

a man 6 ft tall walks at a rate of 7 ft/sec away from a lamppost that is 14 ft hight. at what rate is the lenght of his shadow charging when he is 30 ft away from the lamppost

$a m a n 6 f t t a l l w a l k s a t a r a t e$ $o f 7 f t / s e c a w a y f r o m a l a m p p o s t$ $t h a t i s 14 f t h i g h t .$ $a t w h a t r a t e i s t h e l e n g h t o f h i s$ $s h a d o w c h a r g i n g w h e n h e i s 30 f t$ $a w a y f r o m t h e l a m p p o s t$

Question Number 123510 Answers: 0 Comments: 0

sorry −(π/2)

$s o r r y - \frac{π}{2}$

Question Number 123509 Answers: 1 Comments: 0

∫_(−(π/)2) ^(π/2) ∣cosx∣=?

$\underset{- \frac{π}{} 2}{\int^{\frac{π}{2}}} ∣ c o s x ∣= ?$

Question Number 123426 Answers: 0 Comments: 5

find the radii of all circles with center C tangenting the curve h C= ((5),(1) ) h: x^2 −y^2 =1

$find the radii of all circles with center C$ $tangenting the curve h$ $C = (\begin{matrix} 5 \\ 1 \end{matrix})$ $h : x^{2} - y^{2} = 1$

Question Number 123409 Answers: 1 Comments: 0

x^4 +12x−5=0 show that the sum of two roots of the equation is 2

$x^{4} + 12 x - 5 = 0 s h o w t h a t t h e s u m o f t w o r o o t s$ $o f t h e e q u a t i o n i s 2$

Question Number 123362 Answers: 1 Comments: 0

Question Number 123265 Answers: 2 Comments: 2

Question Number 123175 Answers: 1 Comments: 0

Show by recurrence that ∀ n ∈ N, Σ_(k=0 ) ^(n−1) q^k =((q^n −1)/(q−1))

$S h o w b y r e c u r r e n c e t h a t$ $\forall n \in N, \sum_{k = 0}^{n - 1} q^{k} = \frac{q^{n} - 1}{q - 1}$

Question Number 123114 Answers: 2 Comments: 2

Is there any solution(s)?? { ((36x^2 y−27y^3 =8)),((4x^3 −27xy^2 =4)) :} please....

$I s t h e r e a n y s o l u t i o n (s) ? ?$ ${\begin{cases} 36 x^{2} y - 27 y^{3} = 8 \\ 4 x^{3} - 27 {x y}^{2} = 4 \end{cases}$ $p l e a s e . . . .$

Question Number 123108 Answers: 0 Comments: 2

Question Number 123053 Answers: 0 Comments: 0

Find all P(x) with real coefficients such that P(x^2 +x+1) divides P(x^3 −1)

$F i n d a l l P (x) w i t h r e a l c o e f f i c i e n t s s u c h t h a t$ $P (x^{2} + x + 1) d i v i d e s P (x^{3} - 1)$

Question Number 123039 Answers: 1 Comments: 0

{ ((3^x +9^(2y) =27)),((2^x +4^(−y) =2^(−3) )) :} x=? y=?

${\begin{cases} 3^{x} + 9^{2 y} = 27 \\ 2^{x} + 4^{- y} = 2^{- 3} \end{cases}$ $x = ? y = ?$

Question Number 123062 Answers: 1 Comments: 0

Erica′s age is 8 years and her mother is 42. In how many years time will the mother be 3 times as old as her daughter?

${Erica}^{'} s age is 8 years and her mother is 42 .$ $In how many years time will the mother be$ $3 times as old as her daughter ?$

Question Number 123025 Answers: 1 Comments: 4

Question Number 123024 Answers: 1 Comments: 0

Question Number 122957 Answers: 1 Comments: 1

Question Number 122950 Answers: 0 Comments: 1

(√(1+(√(1+2(√(3+...(√(1+2014+(√(1+2015.2016)))))))))) = ?

$\sqrt{1 + \sqrt{1 + 2 \sqrt{3 + . . . \sqrt{1 + 2014 + \sqrt{1 + 2015.2016}}}}} = ?$

Question Number 122897 Answers: 2 Comments: 0

Question Number 122883 Answers: 4 Comments: 2

Σ_1 ^∞ (((sin (x))/x))=?

$\sum_{1}^{\infty} (\frac{\sin (x)}{x}) = ?$

Question Number 122860 Answers: 1 Comments: 0

Question Number 122861 Answers: 0 Comments: 3

is there a formula for this? Σ_(n=0) ^∞ (1/(n^2 +an+b))

$is there a formula for this ?$ $\underset{n = 0}{\sum^{\infty}} \frac{1}{n^{2} + a n + b}$

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