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Question Number 135361 Answers: 1 Comments: 0

f(x)=3x^2 +6x,[−1,5] find−the−average−value

$${f}\left({x}\right)=\mathrm{3}{x}^{\mathrm{2}} +\mathrm{6}{x},\left[−\mathrm{1},\mathrm{5}\right] \\ $$$${find}−{the}−{average}−{value} \\ $$$$ \\ $$

Question Number 135364 Answers: 0 Comments: 0

Question Number 135371 Answers: 0 Comments: 0

let f(x)=tan(2x) ddvelopp f at fourier serie

$${let}\:{f}\left({x}\right)={tan}\left(\mathrm{2}{x}\right) \\ $$$${ddvelopp}\:{f}\:{at}\:{fourier}\:{serie} \\ $$

Question Number 135354 Answers: 1 Comments: 0

Algebra A & B together can finish a work in 24 days, B & C in 30 days. If C is 20% more efficient than B, then how many days are required for A alone to finish the work?

$${Algebra} \\ $$A & B together can finish a work in 24 days, B & C in 30 days. If C is 20% more efficient than B, then how many days are required for A alone to finish the work?

Question Number 135352 Answers: 1 Comments: 0

Probability Urn I contains 5 red and 3 green balls. Urn II contains 2 red and 7 green balls. One balls is transferred (at random) from urn I to urn II . After stirring , 1 ball is chosen from urn II. What is probability that the (final) ball is green?

$$\underline{\mathrm{Probability}} \\ $$$$\mathrm{Urn}\:\mathrm{I}\:\mathrm{contains}\:\mathrm{5}\:\mathrm{red}\:\mathrm{and}\:\mathrm{3}\:\mathrm{green}\:\mathrm{balls}.\:\mathrm{Urn}\:\mathrm{II} \\ $$$$\mathrm{contains}\:\mathrm{2}\:\mathrm{red}\:\mathrm{and}\:\mathrm{7}\:\mathrm{green}\:\mathrm{balls}.\:\mathrm{One}\:\mathrm{balls} \\ $$$$\mathrm{is}\:\mathrm{transferred}\:\left(\mathrm{at}\:\mathrm{random}\right)\:\mathrm{from}\:\mathrm{urn}\:\mathrm{I}\:\mathrm{to}\:\mathrm{urn}\:\mathrm{II} \\ $$$$.\:\mathrm{After}\:\mathrm{stirring}\:,\:\mathrm{1}\:\mathrm{ball}\:\mathrm{is}\:\mathrm{chosen}\:\mathrm{from}\:\mathrm{urn}\:\mathrm{II}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{the}\:\left(\mathrm{final}\right)\:\mathrm{ball}\:\mathrm{is} \\ $$$$\mathrm{green}?\: \\ $$

Question Number 135350 Answers: 0 Comments: 1

Question Number 135348 Answers: 0 Comments: 0

An online trading company wants to offer discounts to customers. The company has recently emailed the discount codes to customers. New customers must have the code to be eligible but returning customers are not eligible for the discount. Let A − Returning Customer B − Discount Code (a) Draw a truth table to represent vwhen a customer has a discout (b) From your table in (a), produce a Boolean expression to represent discounted customer (Q) for the trading company.

$$\mathrm{An}\:\mathrm{online}\:\mathrm{trading}\:\mathrm{company}\:\mathrm{wants}\:\mathrm{to} \\ $$$$\mathrm{offer}\:\mathrm{discounts}\:\mathrm{to}\:\mathrm{customers}.\:\mathrm{The}\: \\ $$$$\mathrm{company}\:\mathrm{has}\:\mathrm{recently}\:\mathrm{emailed}\:\mathrm{the} \\ $$$$\mathrm{discount}\:\mathrm{codes}\:\mathrm{to}\:\mathrm{customers}.\:\mathrm{New}\: \\ $$$$\mathrm{customers}\:\mathrm{must}\:\mathrm{have}\:\mathrm{the}\:\mathrm{code}\:\mathrm{to}\:\mathrm{be}\: \\ $$$$\mathrm{eligible}\:\mathrm{but}\:\mathrm{returning}\:\mathrm{customers}\:\mathrm{are} \\ $$$$\mathrm{not}\:\mathrm{eligible}\:\mathrm{for}\:\mathrm{the}\:\mathrm{discount}. \\ $$$$\:\:\:\:\:\:{Let}\:\:\:{A}\:−\:{Returning}\:{Customer} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{B}\:−\:\:{Discount}\:{Code} \\ $$$$\left({a}\right)\:\mathrm{Draw}\:\mathrm{a}\:\mathrm{truth}\:\mathrm{table}\:\mathrm{to}\:\mathrm{represent} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{vwhen}\:\mathrm{a}\:\mathrm{customer}\:\mathrm{has}\:\mathrm{a}\:\mathrm{discout} \\ $$$$\left({b}\right)\:\mathrm{From}\:\mathrm{your}\:\mathrm{table}\:\mathrm{in}\:\left({a}\right),\:\mathrm{produce}\:\mathrm{a} \\ $$$$\:\:\:\:\:\:\:\mathrm{Boolean}\:\mathrm{expression}\:\mathrm{to}\:\mathrm{represent} \\ $$$$\:\:\:\:\:\:\:\mathrm{discounted}\:\mathrm{customer}\:\left({Q}\right)\:\mathrm{for}\:\mathrm{the} \\ $$$$\:\:\:\:\:\:\:\mathrm{trading}\:\mathrm{company}. \\ $$

Question Number 135342 Answers: 2 Comments: 1

Question Number 135338 Answers: 1 Comments: 0

What is the name of the hydrocarbon −CH_2 ?

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{name}\:\mathrm{of}\:\mathrm{the}\:\mathrm{hydrocarbon}\:−\mathrm{CH}_{\mathrm{2}} ? \\ $$

Question Number 135335 Answers: 0 Comments: 0

Question Number 135326 Answers: 0 Comments: 0

Question Number 135313 Answers: 2 Comments: 0

Given f(x) = 5x+cos (3x) Find the value of (d/dx) [f^(−1) (1)]

$${Given}\:{f}\left({x}\right)\:=\:\mathrm{5}{x}+\mathrm{cos}\:\left(\mathrm{3}{x}\right) \\ $$$${Find}\:{the}\:{value}\:{of}\:\frac{{d}}{{dx}}\:\left[{f}^{−\mathrm{1}} \left(\mathrm{1}\right)\right] \\ $$

Question Number 135309 Answers: 1 Comments: 0

.... Nice Calculus .... prove that ::: 𝛗=∫_0 ^( ∞) ((sin(ksinα)x)/( (√x)))dx=(√(π/k)) sin((α/2))...

$$\:\:\:\:\:\:\:\:\:\:....\:\:\mathscr{N}{ice}\:\:\:\:\mathscr{C}{alculus}\:.... \\ $$$$\:\:\:\:\:\:\:\:{prove}\:\:{that}\:::: \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({ksin}\alpha\right){x}}{\:\sqrt{{x}}}{dx}=\sqrt{\frac{\pi}{{k}}}\:{sin}\left(\frac{\alpha}{\mathrm{2}}\right)... \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\: \\ $$

Question Number 135308 Answers: 1 Comments: 2

Question Number 135307 Answers: 0 Comments: 0

Question Number 135305 Answers: 1 Comments: 0

Question Number 135303 Answers: 2 Comments: 0

in how many ways can 10 people be seated in a round table if 3 persons want to seat consecutively?

$$ \\ $$in how many ways can 10 people be seated in a round table if 3 persons want to seat consecutively?

Question Number 135300 Answers: 3 Comments: 0

((√2) +(√3) +1)((√2) −(√3) +1)((√2) +(√3)−1)((√2)−(√3)−1)=?

$$\left(\sqrt{\mathrm{2}}\:+\sqrt{\mathrm{3}}\:+\mathrm{1}\right)\left(\sqrt{\mathrm{2}}\:−\sqrt{\mathrm{3}}\:+\mathrm{1}\right)\left(\sqrt{\mathrm{2}}\:+\sqrt{\mathrm{3}}−\mathrm{1}\right)\left(\sqrt{\mathrm{2}}−\sqrt{\mathrm{3}}−\mathrm{1}\right)=? \\ $$

Question Number 135298 Answers: 2 Comments: 0

Question Number 135285 Answers: 1 Comments: 0

pre−calculus if log_(48) ^(72) +log_(54) ^(12) =k then log_( 12) ^( 27) =???

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:{pre}−{calculus} \\ $$$$\:\:{if}\:\:\:\:\:\:\:{log}_{\mathrm{48}} ^{\mathrm{72}} +{log}_{\mathrm{54}} ^{\mathrm{12}} \:={k}\: \\ $$$$\:\:\:\:\:\:{then}\:\:{log}_{\:\mathrm{12}} ^{\:\mathrm{27}} \:\:=??? \\ $$$$\:\:\:\:\:\:\:\: \\ $$

Question Number 135284 Answers: 0 Comments: 3

2^x +4^x =9^x . Solve for x

$$\mathrm{2}^{{x}} +\mathrm{4}^{{x}} =\mathrm{9}^{{x}} .\:{Solve}\:{for}\:{x} \\ $$

Question Number 135259 Answers: 2 Comments: 0

∫(x^2 +3x)cos (x)dx

$$\int\left({x}^{\mathrm{2}} +\mathrm{3}{x}\right)\mathrm{cos}\:\left({x}\right){dx} \\ $$

Question Number 135257 Answers: 2 Comments: 1

∫t^7 ln(t)dt

$$\int{t}^{\mathrm{7}} {ln}\left({t}\right){dt} \\ $$

Question Number 135254 Answers: 2 Comments: 0

Question Number 135253 Answers: 0 Comments: 3

Question Number 135252 Answers: 1 Comments: 0

....advanced calculus.... first prove that:: 𝛗_1 =∫_0 ^( 1) ((ln(1−x)ln(1+x))/x)dx=((−5)/8) ζ(3) then conclude that: 𝛗_2 =∫_0 ^( 1) ((ln^2 (1+x))/x)dx=((ζ(3))/4) ....m.n...

$$\:\:\:\:\:\:\:\:\:....{advanced}\:\:\:\:{calculus}.... \\ $$$$\:\:\:\:{first}\:{prove}\:{that}::\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}_{\mathrm{1}} =\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left(\mathrm{1}−{x}\right){ln}\left(\mathrm{1}+{x}\right)}{{x}}{dx}=\frac{−\mathrm{5}}{\mathrm{8}}\:\zeta\left(\mathrm{3}\right) \\ $$$$\:\:\:\:\:{then}\:{conclude}\:{that}:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}_{\mathrm{2}} =\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}^{\mathrm{2}} \left(\mathrm{1}+{x}\right)}{{x}}{dx}=\frac{\zeta\left(\mathrm{3}\right)}{\mathrm{4}} \\ $$$$\:\:\:\:\:\:\:....{m}.{n}... \\ $$

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