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AlgebraQuestion and Answers: Page 348

Question Number 25533 Answers: 1 Comments: 0

Three sets of beans l, m, and n are sold for5 for $5.00, $15.00 and $17.50 respectively per kg. If they are mixed in the ratio of 1:3:2, what is the cost per kg of the mixture?×

$${Three}\:{sets}\:{of}\:{beans}\:{l},\:{m},\:{and}\:{n}\:{are}\:{sold}\:{for}\mathrm{5} \\ $$$${for}\:\$\mathrm{5}.\mathrm{00},\:\$\mathrm{15}.\mathrm{00}\:{and}\:\$\mathrm{17}.\mathrm{50}\:{respectively} \\ $$$${per}\:{kg}.\:{If}\:{they}\:{are}\:{mixed}\:{in}\:{the}\:{ratio}\:{of} \\ $$$$\mathrm{1}:\mathrm{3}:\mathrm{2},\:{what}\:{is}\:{the}\:{cost}\:{per}\:{kg}\:{of}\:{the}\:{mixture}?× \\ $$

Question Number 25482 Answers: 1 Comments: 3

Question Number 25457 Answers: 1 Comments: 0

Question Number 25444 Answers: 1 Comments: 8

Question Number 25425 Answers: 0 Comments: 0

Sum of series 1 + 2x + 7x^2 + 20x^3 + ... up to n terms when x = −1 is

$$\mathrm{Sum}\:\mathrm{of}\:\mathrm{series}\:\mathrm{1}\:+\:\mathrm{2}{x}\:+\:\mathrm{7}{x}^{\mathrm{2}} \:+\:\mathrm{20}{x}^{\mathrm{3}} \:+\:... \\ $$$$\mathrm{up}\:\mathrm{to}\:{n}\:\mathrm{terms}\:\mathrm{when}\:{x}\:=\:−\mathrm{1}\:\mathrm{is} \\ $$

Question Number 25462 Answers: 1 Comments: 0

Let S_n , n = 1, 2, 3... be the sum of infinite geometric series whose first term is n and the common ratio is (1/(n + 1)). Then lim_(n→∞) ((S_1 S_n + S_2 S_(n−1) + S_3 S_(n−2) ... + S_n S_1 )/(S_1 ^2 + S_2 ^2 + ... + S_n ^2 )) is

$$\mathrm{Let}\:{S}_{{n}} ,\:{n}\:=\:\mathrm{1},\:\mathrm{2},\:\mathrm{3}...\:\mathrm{be}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of} \\ $$$$\mathrm{infinite}\:\mathrm{geometric}\:\mathrm{series}\:\mathrm{whose}\:\mathrm{first} \\ $$$$\mathrm{term}\:\mathrm{is}\:{n}\:\mathrm{and}\:\mathrm{the}\:\mathrm{common}\:\mathrm{ratio}\:\mathrm{is} \\ $$$$\frac{\mathrm{1}}{{n}\:+\:\mathrm{1}}.\:\mathrm{Then} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{{S}_{\mathrm{1}} {S}_{{n}} \:+\:{S}_{\mathrm{2}} {S}_{{n}−\mathrm{1}} \:+\:{S}_{\mathrm{3}} {S}_{{n}−\mathrm{2}} \:...\:+\:{S}_{{n}} {S}_{\mathrm{1}} }{{S}_{\mathrm{1}} ^{\mathrm{2}} \:+\:{S}_{\mathrm{2}} ^{\mathrm{2}} \:+\:...\:+\:{S}_{{n}} ^{\mathrm{2}} } \\ $$$$\mathrm{is} \\ $$

Question Number 25480 Answers: 0 Comments: 0

Question Number 25390 Answers: 1 Comments: 0

sin 90

$$\mathrm{sin}\:\mathrm{90} \\ $$

Question Number 25381 Answers: 1 Comments: 0

The first term of a sequence is 1, the second is 2 and every term is the sum of the two preceding terms. The n^(th) term is.

$$\mathrm{The}\:\mathrm{first}\:\mathrm{term}\:\mathrm{of}\:\mathrm{a}\:\mathrm{sequence}\:\mathrm{is}\:\mathrm{1},\:\mathrm{the} \\ $$$$\mathrm{second}\:\mathrm{is}\:\mathrm{2}\:\mathrm{and}\:\mathrm{every}\:\mathrm{term}\:\mathrm{is}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{two}\:\mathrm{preceding}\:\mathrm{terms}.\:\mathrm{The}\:{n}^{\mathrm{th}} \:\mathrm{term} \\ $$$$\mathrm{is}. \\ $$

Question Number 25378 Answers: 1 Comments: 0

If log x, log y, log z (x,y,z > 1) are in GP then 2x+log(bx), 3x+log(by), 4x+log(bz) are in A.P. True/False?

$${If}\:\mathrm{log}\:{x},\:\mathrm{log}\:{y},\:\mathrm{log}\:{z}\:\left({x},{y},{z}\:>\:\mathrm{1}\right)\:{are}\:{in} \\ $$$${GP}\:{then}\:\mathrm{2}{x}+\mathrm{log}\left({bx}\right),\:\mathrm{3}{x}+\mathrm{log}\left({by}\right), \\ $$$$\mathrm{4}{x}+\mathrm{log}\left({bz}\right)\:{are}\:{in}\:{A}.{P}. \\ $$$$\boldsymbol{{True}}/\boldsymbol{{False}}? \\ $$

Question Number 25317 Answers: 2 Comments: 0

solvd for x:((√(2+(√3))))^x +((√(2−(√3))))^x =4

$${solvd}\:{for}\:{x}:\left(\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}\right)^{{x}} +\left(\sqrt{\mathrm{2}−\sqrt{\mathrm{3}}}\right)^{{x}} =\mathrm{4} \\ $$

Question Number 25283 Answers: 2 Comments: 1

Question Number 25246 Answers: 1 Comments: 0

8x^(3/(2n)) −8x^((−3)/(2n)) =63

$$\mathrm{8x}^{\frac{\mathrm{3}}{\mathrm{2n}}} −\mathrm{8x}^{\frac{−\mathrm{3}}{\mathrm{2n}}} \:=\mathrm{63} \\ $$

Question Number 25278 Answers: 0 Comments: 4

Find the number of solutions of log∣x∣ = e^x

$${Find}\:{the}\:{number}\:{of}\:{solutions}\:{of} \\ $$$$\mathrm{log}\mid{x}\mid\:=\:{e}^{{x}} \\ $$

Question Number 25226 Answers: 1 Comments: 0

Show that if x=3−(√3).Show that x^2 +((36)/x^2 )=24

$${Show}\:{that}\:{if}\:{x}=\mathrm{3}−\sqrt{\mathrm{3}}.{Show}\:{that}\:{x}^{\mathrm{2}} +\frac{\mathrm{36}}{{x}^{\mathrm{2}} }=\mathrm{24} \\ $$

Question Number 25215 Answers: 0 Comments: 1

Question Number 25173 Answers: 1 Comments: 0

Show that for all nεN−{0} 7^(2n+1) +1 is an integer multiple of 8.

$${Show}\:{that}\:{for}\:{all}\:{n}\epsilon{N}−\left\{\mathrm{0}\right\}\: \\ $$$$\mathrm{7}^{\mathrm{2}{n}+\mathrm{1}} +\mathrm{1}\:{is}\:{an}\:{integer}\:\:{multiple}\:{of} \\ $$$$\mathrm{8}. \\ $$

Question Number 25171 Answers: 1 Comments: 0

100n>n^2 for integral n>100

$$\mathrm{100}{n}>{n}^{\mathrm{2}} \:{for}\:{integral}\:{n}>\mathrm{100} \\ $$$$ \\ $$

Question Number 25170 Answers: 2 Comments: 2

prove that n^2 >n−5 for integral n≥3

$${prove}\:{that}\:{n}^{\mathrm{2}} >{n}−\mathrm{5}\:{for}\:{integral}\: \\ $$$${n}\geqslant\mathrm{3}\: \\ $$

Question Number 25122 Answers: 0 Comments: 1

3_C_1 + 4_C_2 + 5_C_3 +...........+ 49_C_(47) = ? where n_C_r = ((n!)/(r!×(n−r)!)) .

$$\:\mathrm{3}_{{C}_{\mathrm{1}} } \:+\:\mathrm{4}_{{C}_{\mathrm{2}} } \:+\:\mathrm{5}_{{C}_{\mathrm{3}} } \:+...........+\:\mathrm{49}_{{C}_{\mathrm{47}} } \:=\:? \\ $$$${where}\:{n}_{{C}_{{r}} } \:=\:\frac{{n}!}{{r}!×\left({n}−{r}\right)!}\:. \\ $$

Question Number 25114 Answers: 0 Comments: 1

Question Number 25113 Answers: 0 Comments: 1

Question Number 25112 Answers: 0 Comments: 1

Question Number 25088 Answers: 1 Comments: 1

Q...((x+7)/(x+4))>1, x∈R

$$ \\ $$$$ \\ $$$$ \\ $$$${Q}...\frac{{x}+\mathrm{7}}{{x}+\mathrm{4}}>\mathrm{1},\:\:\:\:\:{x}\in{R} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 25085 Answers: 1 Comments: 0

If a_n −a_(n−1) =1 for every positive integer greater than 1, then a_1 +a_2 +a_3 +...a_(100) equals (1) 5000 . a_1 (2) 5050 . a_1 (3) 5051 . a_1 (3) 5052 . a_2

$${If}\:{a}_{{n}} −{a}_{{n}−\mathrm{1}} =\mathrm{1}\:{for}\:{every}\:{positive} \\ $$$${integer}\:{greater}\:{than}\:\mathrm{1},\:{then}\:{a}_{\mathrm{1}} +{a}_{\mathrm{2}} +{a}_{\mathrm{3}} \\ $$$$+...{a}_{\mathrm{100}} \:{equals} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{5000}\:.\:{a}_{\mathrm{1}} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{5050}\:.\:{a}_{\mathrm{1}} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{5051}\:.\:{a}_{\mathrm{1}} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{5052}\:.\:{a}_{\mathrm{2}} \\ $$

Question Number 25074 Answers: 0 Comments: 1

Pg 343 Pg 344 Pg 345 Pg 346 Pg 347 Pg 348 Pg 349 Pg 350 Pg 351 Pg 352

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