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Question Number 106695 Answers: 1 Comments: 0

#bobhans# 3^x −2^(x+1) ≤ (√(2.9^x −10.6^x +2^(2x+3) )) find the solution set

$$\:\:\:\:#\mathrm{bobhans}# \\ $$$$\mathrm{3}^{\mathrm{x}} −\mathrm{2}^{\mathrm{x}+\mathrm{1}} \:\leqslant\:\sqrt{\mathrm{2}.\mathrm{9}^{\mathrm{x}} −\mathrm{10}.\mathrm{6}^{\mathrm{x}} +\mathrm{2}^{\mathrm{2x}+\mathrm{3}} } \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{set} \\ $$

Question Number 106694 Answers: 3 Comments: 0

Question Number 106691 Answers: 2 Comments: 0

determine using laplce transformation this integrale ∫_0 ^(+∞) ((tsin(tx))/(a^2 +t^(2 ) ))dt

$$\boldsymbol{{determine}}\:\boldsymbol{{using}}\:\:\boldsymbol{{laplce}}\:\boldsymbol{{transformation}}\:\boldsymbol{{this}} \\ $$$$\boldsymbol{{integrale}}\: \\ $$$$\:\:\int_{\mathrm{0}} ^{+\infty} \frac{\boldsymbol{{tsin}}\left(\boldsymbol{{tx}}\right)}{\boldsymbol{{a}}^{\mathrm{2}} +\boldsymbol{{t}}^{\mathrm{2}\:} }\boldsymbol{{dt}} \\ $$

Question Number 106690 Answers: 1 Comments: 0

this question was repeatd six times in a various exams between 1971 to 2001. if C_0 ,C_1 ,C_2 .......,C_n are the coefficients in the expansion of (1+x)^n then c_0 +2C_1 +3C_2 ........(n+1)C_n =?

$${this}\:{question}\:{was}\:{repeatd}\:{six}\:{times} \\ $$$${in}\:{a}\:{various}\:{exams}\:{between}\:\mathrm{1971}\:{to}\:\mathrm{2001}. \\ $$$${if}\:{C}_{\mathrm{0}} ,{C}_{\mathrm{1}} ,{C}_{\mathrm{2}} .......,{C}_{{n}} \:{are}\:{the}\:{coefficients} \\ $$$${in}\:{the}\:{expansion}\:{of}\:\left(\mathrm{1}+{x}\right)^{{n}} \:{then} \\ $$$${c}_{\mathrm{0}} +\mathrm{2}{C}_{\mathrm{1}} +\mathrm{3}{C}_{\mathrm{2}} ........\left({n}+\mathrm{1}\right){C}_{{n}} =? \\ $$

Question Number 106688 Answers: 0 Comments: 0

Σ_(k=0) ^∞ (((−1)^n )/((2n+1)!))z^(2n−14) =?

$$\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)!}{z}^{\mathrm{2}{n}−\mathrm{14}} =? \\ $$

Question Number 106683 Answers: 0 Comments: 0

Prove that ∫_0 ^π ln(1−2αcost+α^2 )dt=2πlnα

$$\mathrm{Prove}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\pi} \mathrm{ln}\left(\mathrm{1}−\mathrm{2}\alpha\mathrm{cost}+\alpha^{\mathrm{2}} \right)\mathrm{dt}=\mathrm{2}\pi\mathrm{ln}\alpha \\ $$

Question Number 106677 Answers: 3 Comments: 0

Question Number 106666 Answers: 2 Comments: 2

In 2x+3y=8 and 5x+Ky=3, find the value of K so that the given system of equation has infinte solution.

$$\mathrm{In}\:\mathrm{2}{x}+\mathrm{3}{y}=\mathrm{8}\:\mathrm{and}\:\:\mathrm{5}{x}+{Ky}=\mathrm{3},\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:{K}\:\mathrm{so}\:\mathrm{that}\:\mathrm{the}\:\mathrm{given}\:\mathrm{system} \\ $$$$\mathrm{of}\:\mathrm{equation}\:\mathrm{has}\:\mathrm{infinte}\:\mathrm{solution}. \\ $$

Question Number 106665 Answers: 1 Comments: 0

Find a fourth proportional to 3, 12 and 15

$$\:\mathrm{Find}\:\mathrm{a}\:\mathrm{fourth}\:\mathrm{proportional}\:\mathrm{to} \\ $$$$\:\mathrm{3},\:\mathrm{12}\:\mathrm{and}\:\mathrm{15} \\ $$

Question Number 106664 Answers: 3 Comments: 0

Factorise: x^6 + 64y^6

$$\mathrm{Factorise}:\:\:\:{x}^{\mathrm{6}} \:+\:\mathrm{64}{y}^{\mathrm{6}} \\ $$

Question Number 106663 Answers: 2 Comments: 0

Question Number 106662 Answers: 1 Comments: 0

Question Number 106661 Answers: 0 Comments: 0

sin x(1/(cos x))= ((sin x)/(cos x))=tan x

$$\mathrm{sin}\:{x}\frac{\mathrm{1}}{\mathrm{cos}\:{x}}=\:\frac{\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}=\mathrm{tan}\:{x} \\ $$

Question Number 106659 Answers: 1 Comments: 0

How many terms has the polynomial; (X_1 +2X_2 −X_3 +34)^(10) ?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{terms}\:\mathrm{has}\:\mathrm{the}\:\mathrm{polynomial}; \\ $$$$\left(\mathrm{X}_{\mathrm{1}} +\mathrm{2X}_{\mathrm{2}} −\mathrm{X}_{\mathrm{3}} +\mathrm{34}\right)^{\mathrm{10}} \:? \\ $$

Question Number 106654 Answers: 1 Comments: 0

Question Number 106648 Answers: 0 Comments: 1

App Updates: Please update to latest version of app 2.132. It fixes some bugs and characters drawing is also improved so characters will now appear smooth. Download from playstore.

$$\mathrm{App}\:\mathrm{Updates}: \\ $$$$\mathrm{Please}\:\mathrm{update}\:\mathrm{to}\:\mathrm{latest}\:\mathrm{version}\:\mathrm{of} \\ $$$$\mathrm{app}\:\mathrm{2}.\mathrm{132}.\:\mathrm{It}\:\mathrm{fixes}\:\mathrm{some}\:\mathrm{bugs}\:\mathrm{and} \\ $$$$\mathrm{characters}\:\mathrm{drawing}\:\mathrm{is}\:\mathrm{also}\:\mathrm{improved} \\ $$$$\mathrm{so}\:\mathrm{characters}\:\mathrm{will}\:\mathrm{now}\:\mathrm{appear}\:\mathrm{smooth}. \\ $$$$\mathrm{Download}\:\mathrm{from}\:\mathrm{playstore}. \\ $$

Question Number 106653 Answers: 0 Comments: 7

30+144+420+960+1890+3360+...n

$$\mathrm{30}+\mathrm{144}+\mathrm{420}+\mathrm{960}+\mathrm{1890}+\mathrm{3360}+...{n} \\ $$

Question Number 106644 Answers: 0 Comments: 0

Let P(x) be a polynomial of degree n with real coefficients. Prove that Σ_(k=0) ^n ((P^((k)) (0))/((k+1)!))=Σ_(k=0) ^n (((−1)^k P^((k)) (1))/((k+1)!))

$$\mathrm{Let}\:\mathrm{P}\left(\mathrm{x}\right)\:\mathrm{be}\:\mathrm{a}\:\mathrm{polynomial}\:\mathrm{of}\:\mathrm{degree}\:\mathrm{n} \\ $$$$\mathrm{with}\:\mathrm{real}\:\mathrm{coefficients}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{P}^{\left(\mathrm{k}\right)} \left(\mathrm{0}\right)}{\left(\mathrm{k}+\mathrm{1}\right)!}=\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\frac{\left(−\mathrm{1}\right)^{\mathrm{k}} \mathrm{P}^{\left(\mathrm{k}\right)} \left(\mathrm{1}\right)}{\left(\mathrm{k}+\mathrm{1}\right)!} \\ $$$$ \\ $$

Question Number 106637 Answers: 1 Comments: 0

@JS@ The quartic equation x^4 +2x^3 +14x+15=0 has one root equal to 1+2i . Find the other three roots.

$$\:\:\:\:\:\:@\mathrm{JS}@ \\ $$$$\mathrm{The}\:\mathrm{quartic}\:\mathrm{equation}\:\mathrm{x}^{\mathrm{4}} +\mathrm{2x}^{\mathrm{3}} +\mathrm{14x}+\mathrm{15}=\mathrm{0} \\ $$$$\mathrm{has}\:\mathrm{one}\:\mathrm{root}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{1}+\mathrm{2i}\:.\:\mathrm{Find} \\ $$$$\mathrm{the}\:\mathrm{other}\:\mathrm{three}\:\mathrm{roots}.\: \\ $$

Question Number 106633 Answers: 3 Comments: 0

^(@bemath@) lim_(x→0) (((√(1+2sin x)) −(√(1−4sin 4x)))/(4x))

$$\:\:\:\:\:\:\:\overset{@\mathrm{bemath}@} {\:} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{1}+\mathrm{2sin}\:\mathrm{x}}\:−\sqrt{\mathrm{1}−\mathrm{4sin}\:\mathrm{4x}}}{\mathrm{4x}} \\ $$

Question Number 106630 Answers: 2 Comments: 0

Find n in this equation: (−2)^n = 4096

$${Find}\:{n}\:{in}\:{this}\:{equation}: \\ $$$$\left(−\mathrm{2}\right)^{{n}} \:=\:\mathrm{4096} \\ $$

Question Number 106628 Answers: 0 Comments: 0

(((p−1))/p) where p=prime no. Remainder will always be (p−1) or −1 Que. find Remainder ((1!+2!+3!+........................1000!)/(10)) Que. ((1!+2!+3!+........................1000!)/(12)) Que. ((1!+2!+3!+........................1000!)/9) Que. What id the unit digit of below expression 1!+2!+3!+4!+......................1000! ANS. If we divide some number by 100,then remainder is last 2digit similary 1000----Last 3digit 10000 last 4 digit 100000 last 5 digits [(((1+2+3+4+0+0+0+..........+0)/(10))),() ] R=3 unit digit =3

Question Number 106614 Answers: 3 Comments: 0

_(@bemath@) lim_(x→0) ((((1+3sin x ))^(1/3) −((1+sin 3x))^(1/3) )/(2x)) =?

$$\:\:\:\:\:\underset{@\mathrm{bemath}@} {\:} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\sqrt[{\mathrm{3}}]{\mathrm{1}+\mathrm{3sin}\:\mathrm{x}\:}\:−\sqrt[{\mathrm{3}}]{\mathrm{1}+\mathrm{sin}\:\mathrm{3x}}}{\mathrm{2x}}\:=?\: \\ $$

Question Number 106655 Answers: 0 Comments: 1

Question Number 106609 Answers: 1 Comments: 1

Prove that (1−sin^2 θ)sec^2 θ=1

$${Prove}\:{that} \\ $$$$\left(\mathrm{1}−{sin}^{\mathrm{2}} \theta\right){sec}^{\mathrm{2}} \theta=\mathrm{1} \\ $$

Question Number 106604 Answers: 7 Comments: 1

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