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Question Number 45429 Answers: 0 Comments: 0

a set containing (k+1) elements has 8 more subsets that of a set containing k elements. find the value of k

$$\mathrm{a}\:\mathrm{set}\:\mathrm{containing}\:\left(\boldsymbol{\mathrm{k}}+\mathrm{1}\right)\:\mathrm{elements} \\ $$$$\mathrm{has}\:\mathrm{8}\:\mathrm{more}\:\mathrm{subsets}\:\mathrm{that}\:\mathrm{of}\: \\ $$$$\mathrm{a}\:\mathrm{set}\:\mathrm{containing}\:\boldsymbol{\mathrm{k}}\:\mathrm{elements}. \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\boldsymbol{\mathrm{k}} \\ $$

Question Number 45427 Answers: 0 Comments: 4

Question Number 45422 Answers: 1 Comments: 0

Three consecutive terms of a G.P are the 3rd, 5th and 8th term of an A.P. Find the common ratio.

$$\mathrm{Three}\:\mathrm{consecutive}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{a}\:\mathrm{G}.\mathrm{P}\:\mathrm{are}\:\mathrm{the}\:\mathrm{3rd},\:\mathrm{5th}\:\mathrm{and}\:\mathrm{8th}\:\mathrm{term}\:\mathrm{of}\:\mathrm{an}\:\mathrm{A}.\mathrm{P}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{common}\:\mathrm{ratio}. \\ $$

Question Number 45417 Answers: 1 Comments: 0

Find image of plane x−y+z−3=0 in plane 2x+y−z+4=0 ?

$${Find}\:{image}\:{of}\:{plane}\:{x}−{y}+{z}−\mathrm{3}=\mathrm{0}\:{in}\: \\ $$$${plane}\:\mathrm{2}{x}+{y}−{z}+\mathrm{4}=\mathrm{0}\:? \\ $$

Question Number 45413 Answers: 2 Comments: 1

if y=((sin^(−1) x)/(√(1+x^2 ))) show that (dy/dx)(1+x^2 )+xy=1

$$\boldsymbol{\mathrm{if}}\:\boldsymbol{{y}}=\frac{\boldsymbol{\mathrm{sin}}^{−\mathrm{1}} \boldsymbol{{x}}}{\sqrt{\mathrm{1}+\boldsymbol{{x}}^{\mathrm{2}} }}\:\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}} \\ $$$$\frac{\boldsymbol{{dy}}}{\boldsymbol{{dx}}}\left(\mathrm{1}+\boldsymbol{{x}}^{\mathrm{2}} \right)+\boldsymbol{{xy}}=\mathrm{1} \\ $$

Question Number 45410 Answers: 1 Comments: 1

given the AP a,a +d ,a+2d,a+3d,... show that S_n = (n/2){(2a+(n−1)d}

$${given}\:{the}\:{AP} \\ $$$${a},{a}\:+{d}\:,{a}+\mathrm{2}{d},{a}+\mathrm{3}{d},... \\ $$$${show}\:{that}\: \\ $$$${S}_{{n}} =\:\frac{{n}}{\mathrm{2}}\left\{\left(\mathrm{2}{a}+\left({n}−\mathrm{1}\right){d}\right\}\right. \\ $$

Question Number 45399 Answers: 1 Comments: 0

using your knowlege on Arithmetic progressions, show that A= p(1+(r/(100)))^n

$${using}\:{your}\:{knowlege}\:{on}\:{Arithmetic}\:{progressions}, \\ $$$${show}\:{that}\:\:{A}=\:{p}\left(\mathrm{1}+\frac{{r}}{\mathrm{100}}\right)^{{n}} \\ $$

Question Number 45387 Answers: 0 Comments: 0

Question Number 45381 Answers: 0 Comments: 1

Question Number 45373 Answers: 1 Comments: 1

∫(t^3 /(1+t))dt=?

$$\int\frac{\mathrm{t}^{\mathrm{3}} }{\mathrm{1}+\mathrm{t}}\mathrm{dt}=? \\ $$

Question Number 45366 Answers: 2 Comments: 2

Question Number 45364 Answers: 1 Comments: 0

Find the sum of n terms: (1/(1.3)) + (1/(3.5)) + ... + (1/((2n − 1)(2n + 1))) = ?

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{n}\:\mathrm{terms}:\:\:\frac{\mathrm{1}}{\mathrm{1}.\mathrm{3}}\:+\:\frac{\mathrm{1}}{\mathrm{3}.\mathrm{5}}\:+\:...\:+\:\frac{\mathrm{1}}{\left(\mathrm{2n}\:−\:\mathrm{1}\right)\left(\mathrm{2n}\:+\:\mathrm{1}\right)}\:\:=\:? \\ $$

Question Number 45356 Answers: 1 Comments: 0

x=(1/(1+(1/(2+(1/(3+(1/(4+...))))))))=?

$${x}=\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}+\frac{\mathrm{1}}{\mathrm{3}+\frac{\mathrm{1}}{\mathrm{4}+...}}}}=? \\ $$

Question Number 45353 Answers: 1 Comments: 3

Prove that p(n)=((a_1 +a_2 +...+a_n )/n) ≥^n (√(a_1 a_2 ...a_n )) ∀ n ∈N

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{p}\left(\mathrm{n}\right)=\frac{\boldsymbol{\mathrm{a}}_{\mathrm{1}} +\boldsymbol{\mathrm{a}}_{\mathrm{2}} +...+\boldsymbol{\mathrm{a}}_{\mathrm{n}} }{\mathrm{n}}\:\geqslant\:^{\mathrm{n}} \sqrt{\boldsymbol{\mathrm{a}}_{\mathrm{1}} \boldsymbol{\mathrm{a}}_{\mathrm{2}} ...\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} } \\ $$$$\forall\:\mathrm{n}\:\in\boldsymbol{\mathrm{N}} \\ $$

Question Number 45352 Answers: 1 Comments: 0

Question Number 45346 Answers: 1 Comments: 2

Question Number 45334 Answers: 1 Comments: 0

Question Number 45327 Answers: 2 Comments: 0

Question Number 45316 Answers: 1 Comments: 0

I heard this sum can be close using the Digamma function. Please help me use it. i don′t know it. sum of nth term: (1/(1.2.3)) + (1/(4.5.6)) + (1/(7.8.9)) + ...

$$\mathrm{I}\:\mathrm{heard}\:\mathrm{this}\:\mathrm{sum}\:\mathrm{can}\:\mathrm{be}\:\mathrm{close}\:\mathrm{using}\:\mathrm{the}\:\mathrm{Digamma}\:\mathrm{function}. \\ $$$$\mathrm{Please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{use}\:\mathrm{it}.\:\mathrm{i}\:\mathrm{don}'\mathrm{t}\:\mathrm{know}\:\mathrm{it}.\:\:\: \\ $$$$\:\:\:\mathrm{sum}\:\mathrm{of}\:\mathrm{nth}\:\mathrm{term}:\:\:\:\frac{\mathrm{1}}{\mathrm{1}.\mathrm{2}.\mathrm{3}}\:+\:\frac{\mathrm{1}}{\mathrm{4}.\mathrm{5}.\mathrm{6}}\:+\:\frac{\mathrm{1}}{\mathrm{7}.\mathrm{8}.\mathrm{9}}\:+\:...\: \\ $$

Question Number 45314 Answers: 1 Comments: 0

solve for x 10^x =x^(50)

$$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{{x}} \\ $$$$\mathrm{10}^{\boldsymbol{{x}}} =\boldsymbol{{x}}^{\mathrm{50}} \\ $$

Question Number 45313 Answers: 1 Comments: 1

Question Number 45291 Answers: 1 Comments: 0

How many possible triple of (a,b,c) ∈ integers so that : ∣ a + b ∣ + c = 19 ab + ∣ c ∣ = 97

$${How}\:\:{many}\:\:{possible}\:\:{triple}\:\:{of}\:\:\left({a},{b},{c}\right)\:\:\in\:\:{integers}\:\:{so}\:\:{that}\:\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mid\:{a}\:+\:{b}\:\mid\:+\:{c}\:\:=\:\:\mathrm{19} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{ab}\:+\:\mid\:{c}\:\mid\:\:=\:\:\mathrm{97} \\ $$

Question Number 45284 Answers: 1 Comments: 2

Question Number 45281 Answers: 1 Comments: 2

Question Number 45283 Answers: 1 Comments: 0

if x=1+a+a^2 +a^3 +……… y=1+b+b^2 +b^3 +……… prove that 1+ab+a^2 b^2 +a^3 b^3 +………=((xy)/(x+y−1))

$$\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{x}}=\mathrm{1}+\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\boldsymbol{\mathrm{a}}^{\mathrm{3}} +\ldots\ldots\ldots \\ $$$$\:\:\:\:\boldsymbol{\mathrm{y}}=\mathrm{1}+\boldsymbol{\mathrm{b}}+\boldsymbol{\mathrm{b}}^{\mathrm{2}} +\boldsymbol{\mathrm{b}}^{\mathrm{3}} +\ldots\ldots\ldots \\ $$$$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}} \\ $$$$\mathrm{1}+\boldsymbol{\mathrm{ab}}+\boldsymbol{\mathrm{a}}^{\mathrm{2}} \boldsymbol{\mathrm{b}}^{\mathrm{2}} +\boldsymbol{\mathrm{a}}^{\mathrm{3}} \boldsymbol{\mathrm{b}}^{\mathrm{3}} +\ldots\ldots\ldots=\frac{\boldsymbol{\mathrm{xy}}}{\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}−\mathrm{1}} \\ $$

Question Number 45280 Answers: 2 Comments: 0

solve the simultaneous equation a)sin(x+y)=(1/((√2) )) cos2x=((-1 )/2) for x and y ranging from 0 to 360 inclusive b)if siny+cosx=x show that (d^2 y/dx^(2 ) ) =(x/((2−x^2 )^(3/2) ))

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