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Question Number 40058 Answers: 2 Comments: 0

Question Number 40057 Answers: 1 Comments: 0

Mike and Stev had 620 bucks each to spend . Mike used all his money to buy 3pens and 4books,while Stev bought 4pens and 3books and had a balance of 50 bucks.Find the cost of a pen and book.

$${Mike}\:{and}\:{Stev}\:{had}\:\mathrm{620}\:{bucks} \\ $$$${each}\:{to}\:{spend}\:.\:{Mike}\:{used}\:{all} \\ $$$${his}\:{money}\:{to}\:{buy}\:\mathrm{3}{pens}\:{and}\: \\ $$$$\mathrm{4}{books},{while}\:{Stev}\:{bought}\: \\ $$$$\mathrm{4}{pens}\:{and}\:\mathrm{3}{books}\:{and}\:{had}\:{a} \\ $$$${balance}\:{of}\:\mathrm{50}\:{bucks}.{Find} \\ $$$${the}\:{cost}\:{of}\:{a}\:{pen}\:{and}\:{book}. \\ $$$$ \\ $$

Question Number 40055 Answers: 1 Comments: 0

A boy starts from a point A and moves on a bearing of 20° to a point B which is 5km from A.He then changes his course to a bearing of 11° and moves to a point C which is 12km from B. Find the distance and bearing from C to A.

$${A}\:{boy}\:{starts}\:{from}\:{a}\:{point}\:{A} \\ $$$${and}\:{moves}\:{on}\:{a}\:{bearing}\:{of} \\ $$$$\mathrm{20}°\:{to}\:{a}\:{point}\:{B}\:{which}\:{is} \\ $$$$\mathrm{5}{km}\:{from}\:{A}.{He}\:{then}\:{changes} \\ $$$${his}\:{course}\:{to}\:{a}\:{bearing}\:{of}\: \\ $$$$\mathrm{11}°\:{and}\:{moves}\:{to}\:{a}\:{point}\:{C}\:{which}\:{is} \\ $$$$\mathrm{12}{km}\:{from}\:{B}. \\ $$$${Find}\:{the}\:{distance}\:{and}\:{bearing} \\ $$$${from}\:{C}\:{to}\:{A}. \\ $$$$ \\ $$

Question Number 40054 Answers: 0 Comments: 0

3 boys X,Y,and Z are standing 3 metres north of each other if X and Z are both 1.5m tall and Y is 2m tall. Find a) the bearing from each of the boys b) the bearing if Y moves to the left.

$$\mathrm{3}\:{boys}\:{X},{Y},{and}\:{Z}\:{are}\:{standing} \\ $$$$\mathrm{3}\:{metres}\:{north}\:{of}\:{each}\:{other} \\ $$$${if}\:{X}\:{and}\:{Z}\:{are}\:{both}\:\mathrm{1}.\mathrm{5}{m}\:{tall} \\ $$$${and}\:{Y}\:{is}\:\mathrm{2}{m}\:{tall}. \\ $$$${Find} \\ $$$$\left.{a}\right)\:{the}\:{bearing}\:{from}\:{each}\:{of} \\ $$$${the}\:{boys} \\ $$$$\left.{b}\right)\:{the}\:{bearing}\:{if}\:{Y}\:{moves} \\ $$$${to}\:{the}\:{left}. \\ $$

Question Number 40140 Answers: 1 Comments: 1

calculate ∫_0 ^(π/2) ((sin(x)dx)/(cos^2 x +a^2 sin^2 x))dx

$${calculate}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{sin}\left({x}\right){dx}}{{cos}^{\mathrm{2}} {x}\:+{a}^{\mathrm{2}} \:{sin}^{\mathrm{2}} {x}}{dx} \\ $$

Question Number 40052 Answers: 2 Comments: 0

f ′(x)=g(x) and g ′(x)=−f(x) for all real x andf(5)=2=f ′(5) then f^2 (10)+g^2 (10) is (a) 2 (b) 4 (c) 8 (d) none

$${f}\:'\left({x}\right)={g}\left({x}\right)\:{and}\:\:{g}\:'\left({x}\right)=−{f}\left({x}\right)\:{for} \\ $$$${all}\:{real}\:\:{x}\:\:{andf}\left(\mathrm{5}\right)=\mathrm{2}={f}\:'\left(\mathrm{5}\right)\:{then} \\ $$$${f}^{\mathrm{2}} \left(\mathrm{10}\right)+{g}^{\mathrm{2}} \left(\mathrm{10}\right)\:{is} \\ $$$$\left({a}\right)\:\:\:\mathrm{2}\:\:\:\:\:\left({b}\right)\:\:\:\mathrm{4}\:\:\:\:\:\left({c}\right)\:\:\:\:\mathrm{8}\:\:\:\:\:\left({d}\right)\:{none} \\ $$

Question Number 40048 Answers: 0 Comments: 2

Question Number 40047 Answers: 0 Comments: 0

let S_n = Σ_(k=0) ^n (((−1)^k )/(2k+1)) 1) give S_n interms of H_n 2)find lim_(n→+∞) S_n 3) let W_n = Σ_(k=0) ^n (((−1)^k )/(4k^2 −1)) find W_n interms of H_n calculate lim_(n→+∞) W_n

$${let}\:{S}_{{n}} \:=\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\frac{\left(−\mathrm{1}\right)^{{k}} }{\mathrm{2}{k}+\mathrm{1}} \\ $$$$\left.\mathrm{1}\right)\:{give}\:{S}_{{n}} \:{interms}\:{of}\:{H}_{{n}} \\ $$$$\left.\mathrm{2}\right){find}\:{lim}_{{n}\rightarrow+\infty} {S}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{let}\:{W}_{{n}} =\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\frac{\left(−\mathrm{1}\right)^{{k}} }{\mathrm{4}{k}^{\mathrm{2}} −\mathrm{1}} \\ $$$${find}\:{W}_{{n}} \:\:{interms}\:{of}\:{H}_{{n}} \\ $$$${calculate}\:{lim}_{{n}\rightarrow+\infty} \:{W}_{{n}} \\ $$

Question Number 40046 Answers: 0 Comments: 2

let S_n = Σ_(k=2) ^n (((−1)^k )/(k^2 −1)) 1) calculate S_n interms of H_n ( H_n =Σ_(k=1) ^n (1/k)) 2) find lim_(n→+∞) S_n

$${let}\:{S}_{{n}} =\:\sum_{{k}=\mathrm{2}} ^{{n}} \:\:\frac{\left(−\mathrm{1}\right)^{{k}} }{{k}^{\mathrm{2}} −\mathrm{1}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\:{S}_{{n}} \:\:{interms}\:{of}\:{H}_{{n}} \\ $$$$\left(\:{H}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{S}_{{n}} \\ $$$$ \\ $$

Question Number 40044 Answers: 0 Comments: 2

let f(t) = ∫_0 ^(π/2) ln( cosx +t sinx) 1) calculate f(0) 2) calculate f^′ (t) then find a simple form of f(t) 3) calculate ∫_0 ^(π/2) ln(cosx +2 sinx)dx 4) calculate ∫_0 ^(π/2) ln((√3)cosx +sinx)dx

$${let}\:{f}\left({t}\right)\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\:{cosx}\:+{t}\:{sinx}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}^{'} \left({t}\right)\:{then}\:{find}\:\:{a}\:{simple}\:{form}\:{of}\:{f}\left({t}\right) \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left({cosx}\:+\mathrm{2}\:{sinx}\right){dx} \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\sqrt{\mathrm{3}}{cosx}\:+{sinx}\right){dx} \\ $$

Question Number 40043 Answers: 1 Comments: 0

find the value of ∫_(−1) ^(+∞) (√(x+1))e^(−x) dx

$${find}\:\:{the}\:{value}\:{of}\:\:\int_{−\mathrm{1}} ^{+\infty} \:\:\sqrt{{x}+\mathrm{1}}{e}^{−{x}} \:{dx} \\ $$$$ \\ $$$$ \\ $$

Question Number 40042 Answers: 0 Comments: 0

1) find the roots of p(x)=(1+ix +x^2 )^n −(1−ix+x^2 )^n with n integr natural 2) factorize p(x) inside C(x) 3) give p(x) at form Σ a_p x^p

$$\left.\mathrm{1}\right)\:{find}\:{the}\:{roots}\:{of}\:\: \\ $$$${p}\left({x}\right)=\left(\mathrm{1}+{ix}\:+{x}^{\mathrm{2}} \right)^{{n}} −\left(\mathrm{1}−{ix}+{x}^{\mathrm{2}} \right)^{{n}} \:{with}\:{n}\:{integr} \\ $$$${natural} \\ $$$$\left.\mathrm{2}\right)\:{factorize}\:{p}\left({x}\right)\:{inside}\:\:{C}\left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{give}\:{p}\left({x}\right)\:{at}\:{form}\:\:\Sigma\:{a}_{{p}} {x}^{{p}} \\ $$

Question Number 40040 Answers: 0 Comments: 1

let A_n = ∫_0 ^n e^(−n( x+2−[x])) dx with n integr natural 1) calculate A_n 2) find lim_(n→+∞) A_n 3) study the convergence of Σ_n A_n

$${let}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{{n}} \:\:{e}^{−{n}\left(\:{x}+\mathrm{2}−\left[{x}\right]\right)} {dx}\:\:{with}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{study}\:{the}\:{convergence}\:{of}\:\:\:\sum_{{n}} {A}_{{n}} \\ $$

Question Number 40037 Answers: 1 Comments: 0

Question Number 40031 Answers: 1 Comments: 1

Question Number 40023 Answers: 2 Comments: 0

Question Number 40022 Answers: 0 Comments: 2

To the developer Tinku Tara: Dear sir, can you please make it possible again that a posted image can be updated (changed) through the “edit post” function. This was possible in the past. But it is now not possible for unknown reasons. Thank you!

$${To}\:{the}\:{developer}\:{Tinku}\:{Tara}: \\ $$$${Dear}\:{sir}, \\ $$$${can}\:{you}\:{please}\:{make}\:{it}\:{possible}\:{again} \\ $$$${that}\:{a}\:{posted}\:{image}\:{can}\:{be}\:{updated} \\ $$$$\left({changed}\right)\:{through}\:{the}\:``{edit}\:{post}'' \\ $$$${function}. \\ $$$${This}\:{was}\:{possible}\:{in}\:{the}\:{past}.\:{But}\:{it}\:{is} \\ $$$${now}\:{not}\:{possible}\:{for}\:{unknown}\:{reasons}. \\ $$$${Thank}\:{you}! \\ $$

Question Number 40012 Answers: 1 Comments: 0