Question and Answers Forum

AllQuestion and Answers: Page 1614

Question Number 40285 Answers: 3 Comments: 0

solve for 1 period sin (α/2) =sin 2α sin (β/3) =sin 3β cos (γ/2) =cos 2γ cos (δ/3) =cos 3δ tan (ε/2) =tan 2ε tan (ζ/3) =tan 3ζ

$$\mathrm{solve}\:\mathrm{for}\:\mathrm{1}\:\mathrm{period} \\ $$$$\mathrm{sin}\:\frac{\alpha}{\mathrm{2}}\:=\mathrm{sin}\:\mathrm{2}\alpha \\ $$$$\mathrm{sin}\:\frac{\beta}{\mathrm{3}}\:=\mathrm{sin}\:\mathrm{3}\beta \\ $$$$\mathrm{cos}\:\frac{\gamma}{\mathrm{2}}\:=\mathrm{cos}\:\mathrm{2}\gamma \\ $$$$\mathrm{cos}\:\frac{\delta}{\mathrm{3}}\:=\mathrm{cos}\:\mathrm{3}\delta \\ $$$$\mathrm{tan}\:\frac{\epsilon}{\mathrm{2}}\:=\mathrm{tan}\:\mathrm{2}\epsilon \\ $$$$\mathrm{tan}\:\frac{\zeta}{\mathrm{3}}\:=\mathrm{tan}\:\mathrm{3}\zeta \\ $$

Question Number 40284 Answers: 1 Comments: 0

How many permutation can be made using the word CANADA each of the six letter being used mixed in each permutation? In how many of these permutation will the three A′s be together? In how many will two A′s be together but not the three?

$${How}\:{many}\:{permutation}\:{can}\:{be}\:{made}\:{using}\:{the}\:{word} \\ $$$${CANADA}\:{each}\:{of}\:{the}\:{six}\:{letter}\:{being}\:{used}\:{mixed} \\ $$$${in}\:{each}\:{permutation}?\:\:{In}\:{how}\:{many}\:{of}\:{these} \\ $$$${permutation}\:{will}\:{the}\:{three}\:{A}'{s}\:{be}\:{together}?\:{In}\: \\ $$$${how}\:{many}\:{will}\:{two}\:{A}'{s}\:{be}\:{together}\:{but}\:{not}\:{the}\:{three}? \\ $$

Question Number 40283 Answers: 0 Comments: 0

There are four ladies and four gentlemen ready to play tennis.if there is only one tennis court readily available. In how many ways is it possible to arrange for one mixed double to be played (a lady and gentleman)?

$${There}\:{are}\:{four}\:{ladies}\:{and}\:{four}\:{gentlemen}\:{ready}\:{to}\:{play}\: \\ $$$${tennis}.{if}\:{there}\:{is}\:{only}\:{one}\:{tennis}\:{court}\:{readily} \\ $$$${available}.\:{In}\:{how}\:{many}\:{ways}\:{is}\:{it}\:{possible}\:{to}\:{arrange}\:{for}\:{one}\:{mixed}\:{double}\:{to}\:{be}\:{played} \\ $$$$\left({a}\:{lady}\:{and}\:{gentleman}\right)? \\ $$

Question Number 40277 Answers: 2 Comments: 0

Question Number 40276 Answers: 2 Comments: 0

Question Number 40271 Answers: 1 Comments: 0

Using Bionomial solve; Given that y = 3x and x increases at 2(1/2)%, find percentage increase in y.

$${Using}\:{Bionomial}\:{solve}; \\ $$$${Given}\:{that}\:\:{y}\:=\:\mathrm{3}{x}\:\:{and}\:{x}\:{increases} \\ $$$${at}\:\mathrm{2}\frac{\mathrm{1}}{\mathrm{2}}\%,\:{find}\:\:{percentage}\:{increase} \\ $$$${in}\:{y}. \\ $$

Question Number 40270 Answers: 1 Comments: 0

calculate the area of one “leaf” of r=sin nθ n∈N

$$\mathrm{calculate}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{one}\:``\mathrm{leaf}''\:\mathrm{of} \\ $$$${r}=\mathrm{sin}\:{n}\theta \\ $$$${n}\in\mathbb{N} \\ $$

Question Number 40260 Answers: 0 Comments: 2

let f(x)=sin(2x) 1) find f^((n)) (x) and f^((n)) (0) 2) developp f at integr serie .

$${let}\:{f}\left({x}\right)={sin}\left(\mathrm{2}{x}\right) \\ $$$$\left.\mathrm{1}\right)\:{find}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$

Question Number 40251 Answers: 1 Comments: 0

1. ∫(dα/(sin 2α +tan 3α))=? 2. ∫(dβ/(cos 2β +cos 3β))=? 3. ∫(dγ/(sinh 2γ +tanh 3γ))=? 4. ∫(dδ/(cosh 2δ +cosh 3δ))=?

$$\mathrm{1}.\:\:\:\:\:\int\frac{{d}\alpha}{\mathrm{sin}\:\mathrm{2}\alpha\:+\mathrm{tan}\:\mathrm{3}\alpha}=? \\ $$$$\mathrm{2}.\:\:\:\:\:\int\frac{{d}\beta}{\mathrm{cos}\:\mathrm{2}\beta\:+\mathrm{cos}\:\mathrm{3}\beta}=? \\ $$$$\mathrm{3}.\:\:\:\:\:\int\frac{{d}\gamma}{\mathrm{sinh}\:\mathrm{2}\gamma\:+\mathrm{tanh}\:\mathrm{3}\gamma}=? \\ $$$$\mathrm{4}.\:\:\:\:\:\int\frac{{d}\delta}{\mathrm{cosh}\:\mathrm{2}\delta\:+\mathrm{cosh}\:\mathrm{3}\delta}=? \\ $$

Question Number 40255 Answers: 1 Comments: 2

Question Number 40254 Answers: 0 Comments: 3

sum of this series: 1.3.5+3.5.7+5.7.9+...up to n terms

$${sum}\:{of}\:{this}\:{series}: \\ $$$$\mathrm{1}.\mathrm{3}.\mathrm{5}+\mathrm{3}.\mathrm{5}.\mathrm{7}+\mathrm{5}.\mathrm{7}.\mathrm{9}+...{up}\:{to}\:{n}\:{terms} \\ $$

Question Number 40238 Answers: 2 Comments: 0

Question Number 40237 Answers: 1 Comments: 4

Mr Rag is a buisiness man in at the Sao Paolo main market. He took a loan of 200,000 bucks from a bank for 3 yrs at 3.5% per month. Find the compound interest.

$${Mr}\:{Rag}\:{is}\:{a}\:{buisiness}\:{man}\:{in} \\ $$$${at}\:{the}\:{Sao}\:{Paolo}\:{main}\:{market}. \\ $$$${He}\:{took}\:{a}\:{loan}\:{of}\:\mathrm{200},\mathrm{000}\:{bucks} \\ $$$${from}\:{a}\:{bank}\:{for}\:\mathrm{3}\:{yrs}\:{at}\:\mathrm{3}.\mathrm{5\%} \\ $$$${per}\:{month}.\:{Find}\:{the}\:\boldsymbol{{compound}} \\ $$$$\boldsymbol{{interest}}. \\ $$

Question Number 40236 Answers: 1 Comments: 0

if a b c are in H.P then prove that (a/(b+c)),(b/(c+a)),(c/(a+b)) arw also in H.P.

$${if}\:{a}\:{b}\:{c}\:{are}\:{in}\:{H}.{P}\:{then}\:{prove}\:{that}\:\frac{{a}}{{b}+{c}},\frac{{b}}{{c}+{a}},\frac{{c}}{{a}+{b}}\:\:{arw} \\ $$$${also}\:{in}\:{H}.{P}. \\ $$

Question Number 40231 Answers: 1 Comments: 0