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Question Number 209744 Answers: 4 Comments: 0

Question Number 209735 Answers: 3 Comments: 0

tan(3x) + tan(5x) = 2 Find: x = ?

$$\mathrm{tan}\left(\mathrm{3x}\right)\:\:+\:\:\mathrm{tan}\left(\mathrm{5x}\right)\:\:=\:\:\mathrm{2} \\ $$$$\mathrm{Find}:\:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$

Question Number 209732 Answers: 1 Comments: 0

Q) The collection A={12,13,15,18,23,24,25,26}& B⊆A if m,M ∈B ; m=min & M =max & nm=10k which number of B : 1)59 2)60 3)61 4)62

$$\left.{Q}\right)\:{The}\:{collection}\:{A}=\left\{\mathrm{12},\mathrm{13},\mathrm{15},\mathrm{18},\mathrm{23},\mathrm{24},\mathrm{25},\mathrm{26}\right\}\&\:{B}\subseteq{A} \\ $$$${if}\:\:{m},{M}\:\in{B}\:\:;\:{m}={min}\:\&\:{M}\:={max}\:\&\:\:{nm}=\mathrm{10}{k} \\ $$$${which}\:{number}\:{of}\:\:{B}\:: \\ $$$$\left.\mathrm{1}\left.\right)\left.\mathrm{5}\left.\mathrm{9}\:\:\:\:\:\:\:\mathrm{2}\right)\mathrm{60}\:\:\:\:\:\:\:\mathrm{3}\right)\mathrm{61}\:\:\:\:\:\:\mathrm{4}\right)\mathrm{62} \\ $$$$ \\ $$

Question Number 209719 Answers: 1 Comments: 0

If: 7^(243) = a...bc^(−) Find: b∙c = ?

$$\mathrm{If}: \\ $$$$\mathrm{7}^{\mathrm{243}} \:\:=\:\:\overline {\mathrm{a}...\mathrm{bc}} \\ $$$$\mathrm{Find}: \\ $$$$\mathrm{b}\centerdot\mathrm{c}\:=\:? \\ $$

Question Number 209718 Answers: 1 Comments: 0

Question Number 209712 Answers: 2 Comments: 3

Question Number 209709 Answers: 1 Comments: 0

∫(sinx+cosx)^(11) dx= ? help me please

$$ \\ $$$$\:\:\:\int\left({sinx}+{cosx}\right)^{\mathrm{11}} {dx}=\:? \\ $$$$\:\:\:{help}\:{me}\:{please} \\ $$

Question Number 209707 Answers: 0 Comments: 0

a,b ∈C : ab^− + b = 0 f : z′ = az^− + b such that f(M) = M′ 1. let z_A = z and z_(A′) = z′ and f(A) = A show that 2Re(b^− z) = bb^− (A is the set of invariant points and describes a line (△) ) 2. Deduce that (△) is a line with gradient u^( →) with affix z_u^→ = ib 3. show that (z_(MM ′) /z_u ) = ((bb^− − 2Re(bz^− ))/(ibb^− )) 4. show that 2Re(b^− z_0 ) = bb^_ where z_0 = ((z + z ′)/2) 5. Deduce that for M ∉ (△) , M is a perpendicular bisector of [MM ′]

$${a},{b}\:\in\mathbb{C}\::\:{a}\overset{−} {{b}}\:+\:{b}\:=\:\mathrm{0}\:{f}\::\:{z}'\:=\:{a}\overset{−} {{z}}\:+\:{b}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:{such}\:{that}\:{f}\left({M}\right)\:=\:{M}' \\ $$$$\mathrm{1}.\:{let}\:{z}_{{A}} \:=\:{z}\:{and}\:{z}_{{A}'} \:=\:{z}'\:{and}\:{f}\left({A}\right)\:=\:{A} \\ $$$${show}\:{that}\:\mathrm{2}{Re}\left(\overset{−} {{b}z}\right)\:=\:{b}\overset{−} {{b}} \\ $$$$\left({A}\:{is}\:{the}\:{set}\:{of}\:{invariant}\:{points}\:{and}\right. \\ $$$$\left.\:{describes}\:{a}\:{line}\:\left(\bigtriangleup\right)\:\right) \\ $$$$\mathrm{2}.\:{Deduce}\:{that}\:\left(\bigtriangleup\right)\:{is}\:{a}\:{line}\:{with}\: \\ $$$${gradient}\:\overset{\:\rightarrow} {{u}}\:{with}\:{affix}\:{z}_{\overset{\rightarrow} {{u}}} \:=\:{ib} \\ $$$$\mathrm{3}.\:{show}\:{that}\:\frac{{z}_{{MM}\:'} }{{z}_{{u}} }\:=\:\frac{{b}\overset{−} {{b}}\:−\:\mathrm{2}{Re}\left({b}\overset{−} {{z}}\right)}{{ib}\overset{−} {{b}}} \\ $$$$\mathrm{4}.\:{show}\:{that}\:\mathrm{2}{Re}\left(\overset{−} {{b}z}_{\mathrm{0}} \right)\:=\:{b}\overset{\_} {{b}}\:{where} \\ $$$$\:{z}_{\mathrm{0}} \:=\:\frac{{z}\:+\:{z}\:'}{\mathrm{2}} \\ $$$$\mathrm{5}.\:{Deduce}\:{that}\:{for}\:{M}\:\notin\:\left(\bigtriangleup\right)\:,\:{M}\:{is}\: \\ $$$${a}\:{perpendicular}\:{bisector}\:{of}\:\left[{MM}\:'\right] \\ $$

Question Number 209706 Answers: 2 Comments: 0

find the sum of sin^2 1°+sin^2 2°+...+sin^2 60°=?

$${find}\:{the}\:{sum}\:{of}\: \\ $$$$\mathrm{sin}^{\mathrm{2}} \:\mathrm{1}°+\mathrm{sin}^{\mathrm{2}} \:\mathrm{2}°+...+\mathrm{sin}^{\mathrm{2}} \:\mathrm{60}°=? \\ $$

Question Number 209695 Answers: 1 Comments: 0

If: (a + b)∙(√2) = 7∙(a−b−4) Find: (2a + b) = ?

$$\mathrm{If}: \\ $$$$\left(\mathrm{a}\:+\:\mathrm{b}\right)\centerdot\sqrt{\mathrm{2}}\:=\:\mathrm{7}\centerdot\left(\mathrm{a}−\mathrm{b}−\mathrm{4}\right) \\ $$$$\mathrm{Find}: \\ $$$$\left(\mathrm{2a}\:+\:\mathrm{b}\right)\:=\:? \\ $$

Question Number 209694 Answers: 1 Comments: 0

x^2 +xy+y^2 =α^2 y^2 +yz+z^2 =β^2 z^2 +zx+x^2 =α^2 +β^2 Find x+y+z for x, y, z ∈R^+

$${x}^{\mathrm{2}} +{xy}+{y}^{\mathrm{2}} =\alpha^{\mathrm{2}} \\ $$$${y}^{\mathrm{2}} +{yz}+{z}^{\mathrm{2}} =\beta^{\mathrm{2}} \\ $$$${z}^{\mathrm{2}} +{zx}+{x}^{\mathrm{2}} =\alpha^{\mathrm{2}} +\beta^{\mathrm{2}} \\ $$$$\mathrm{Find}\:{x}+{y}+{z}\:\mathrm{for}\:{x},\:{y},\:{z}\:\in\mathbb{R}^{+} \\ $$

Question Number 209691 Answers: 0 Comments: 0

∫(2x^(3x^2 +4x−7) )(log _2 (x^2 +3x−7))e^(x^2 +3x−5) dx=?

$$\:\:\:\int\left(\mathrm{2x}^{\mathrm{3x}^{\mathrm{2}} +\mathrm{4x}−\mathrm{7}} \right)\left(\mathrm{log}\:_{\mathrm{2}} \:\left(\mathrm{x}^{\mathrm{2}} +\mathrm{3x}−\mathrm{7}\right)\right)\mathrm{e}^{\mathrm{x}^{\mathrm{2}} +\mathrm{3x}−\mathrm{5}} \:\mathrm{dx}=? \\ $$

Question Number 209687 Answers: 3 Comments: 0

Question Number 209685 Answers: 1 Comments: 0

Question Number 209672 Answers: 2 Comments: 0

Question Number 209671 Answers: 2 Comments: 0

5x+3x=10

$$\mathrm{5}{x}+\mathrm{3}{x}=\mathrm{10} \\ $$

Question Number 209670 Answers: 2 Comments: 0

find the sum of sin^2 (1)+...+sin^2 (90)

$${find}\:{the}\:{sum}\:{of}\:{sin}^{\mathrm{2}} \left(\mathrm{1}\right)+...+{sin}^{\mathrm{2}} \left(\mathrm{90}\right) \\ $$

Question Number 209662 Answers: 1 Comments: 0

∫(1/(sin^2 x(1+cos^2 x)))dx

$$\int\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{2}} {x}\left(\mathrm{1}+\mathrm{cos}^{\mathrm{2}} {x}\right)}{dx} \\ $$

Question Number 209659 Answers: 3 Comments: 0

Question Number 209656 Answers: 2 Comments: 0

2cos^2 x−3cosx+sinx+1=0 help

$$ \\ $$$$\:\:\:\mathrm{2}{cos}^{\mathrm{2}} {x}−\mathrm{3}{cosx}+{sinx}+\mathrm{1}=\mathrm{0} \\ $$$$\:\:\:{help} \\ $$$$ \\ $$

Question Number 209650 Answers: 0 Comments: 1

if the acceleration is constant, what will be the average and instantaneous accelerations?

$${if}\:{the}\:{acceleration}\:{is}\:{constant},\:{what}\: \\ $$$${will}\:{be}\:{the}\:{average}\:{and}\:{instantaneous} \\ $$$${accelerations}? \\ $$

Question Number 209639 Answers: 1 Comments: 1

Question Number 209637 Answers: 1 Comments: 8

Question Number 209633 Answers: 2 Comments: 0

Question Number 209630 Answers: 1 Comments: 0

If A varies as r^2 and V varies as r^3 find percentage increase in A and V if r is increased by 20%

$$\:\:{If}\:{A}\:\:{varies}\:{as}\:{r}^{\mathrm{2}} \:{and}\:{V}\:\:{varies}\:{as}\:{r}^{\mathrm{3}} \\ $$$$\:{find}\:{percentage}\:{increase}\:{in}\:{A}\:{and}\:{V} \\ $$$$\:{if}\:\:{r}\:{is}\:{increased}\:{by}\:\mathrm{20\%} \\ $$

Question Number 209631 Answers: 0 Comments: 0

Let u_n be a set satisfying u_1 =1 & u_(n+1) =u_n +((ln n)/u_n ) , ∀ n ≥1 1. Prove that u_(2023) >(√(2023.ln 2023)). 2. Find: lim_(n→∞) ((u_n .ln n)/n).

$$\mathrm{Let}\:{u}_{{n}} \:\mathrm{be}\:\mathrm{a}\:\mathrm{set}\:\mathrm{satisfying}\:{u}_{\mathrm{1}} =\mathrm{1}\:\&\:{u}_{{n}+\mathrm{1}} ={u}_{{n}} +\frac{\mathrm{ln}\:{n}}{{u}_{{n}} }\:\:,\:\forall\:{n}\:\geqslant\mathrm{1} \\ $$$$\mathrm{1}.\:\mathrm{Prove}\:\mathrm{that}\:{u}_{\mathrm{2023}} >\sqrt{\mathrm{2023}.\mathrm{ln}\:\mathrm{2023}}. \\ $$$$\mathrm{2}.\:\mathrm{Find}:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{{u}_{{n}} .\mathrm{ln}\:{n}}{{n}}. \\ $$

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