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Question Number 55621 Answers: 1 Comments: 0

The function pogof(x) = x^4 + 2x^3 + 2x^2 is divisible by the half of the function of p. Find g(x).

$$\mathrm{The}\:\mathrm{function}\:\:\:\mathrm{pogof}\left(\mathrm{x}\right)\:\:=\:\:\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{2x}^{\mathrm{3}} \:+\:\mathrm{2x}^{\mathrm{2}} \:\:\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{the}\:\:\mathrm{half}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{function}\:\mathrm{of}\:\:\mathrm{p}.\:\:\mathrm{Find}\:\:\mathrm{g}\left(\mathrm{x}\right). \\ $$

Question Number 55615 Answers: 1 Comments: 0

let F(α)=∫_α ^(1+α^2 ) ((sin(αx))/(1+αx^2 ))dx 1) calculate (dF/dα)(α) 2) calculate lim_(α→0) F(α)

$${let}\:{F}\left(\alpha\right)=\int_{\alpha} ^{\mathrm{1}+\alpha^{\mathrm{2}} } \:\:\frac{{sin}\left(\alpha{x}\right)}{\mathrm{1}+\alpha{x}^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\frac{{dF}}{{d}\alpha}\left(\alpha\right) \\ $$$$\left.\mathrm{2}\right)\:\:{calculate}\:{lim}_{\alpha\rightarrow\mathrm{0}} \:\:{F}\left(\alpha\right) \\ $$

Question Number 55613 Answers: 0 Comments: 5

Question Number 55592 Answers: 2 Comments: 1

lim_(x→π/3) ((cos x−sin (π/6))/((π/6)−(x/2)))=..

$$\underset{{x}\rightarrow\pi/\mathrm{3}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:{x}−\mathrm{sin}\:\frac{\pi}{\mathrm{6}}}{\frac{\pi}{\mathrm{6}}−\frac{{x}}{\mathrm{2}}}=.. \\ $$

Question Number 55587 Answers: 2 Comments: 0

If 12% of a number is equal to s, what is the e% of s? A. ((es)/(12)) B. ((es)/(88)) C. ((12s)/e) D. ((12e)/s)

$$\mathrm{If}\:\mathrm{12\%}\:\mathrm{of}\:\mathrm{a}\:\mathrm{number}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:{s}, \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:{e\%}\:\mathrm{of}\:{s}? \\ $$$$\mathrm{A}.\:\frac{{es}}{\mathrm{12}} \\ $$$$\mathrm{B}.\:\frac{{es}}{\mathrm{88}} \\ $$$$\mathrm{C}.\:\frac{\mathrm{12}{s}}{{e}} \\ $$$$\mathrm{D}.\:\frac{\mathrm{12}{e}}{{s}} \\ $$

Question Number 55583 Answers: 1 Comments: 0

Question Number 55606 Answers: 0 Comments: 0

Question Number 55597 Answers: 1 Comments: 0

(d^2 y/dx^2 )+6y((dy/dx))^2 =0 Please solve the differential eq.

$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+\mathrm{6}{y}\left(\frac{{dy}}{{dx}}\right)^{\mathrm{2}} =\mathrm{0} \\ $$$${Please}\:{solve}\:{the}\:{differential}\:{eq}. \\ $$

Question Number 55571 Answers: 0 Comments: 1

let u_n = ∫_(π/(n+1)) ^(π/n) (√(tan(x)))dx with n≥3 1) calculate U_n interms of n and calculate lim_(n→+∞ ) U_n 2) find nature of the serie Σ_(n≥3) U_n

$${let}\:{u}_{{n}} =\:\int_{\frac{\pi}{{n}+\mathrm{1}}} ^{\frac{\pi}{{n}}} \sqrt{{tan}\left({x}\right)}{dx}\:\:{with}\:{n}\geqslant\mathrm{3} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \:{interms}\:{of}\:{n}\:\:\:{and}\:{calculate}\:{lim}_{{n}\rightarrow+\infty\:\:} \:{U}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{nature}\:{of}\:{the}\:{serie}\:\sum_{{n}\geqslant\mathrm{3}} \:{U}_{{n}} \\ $$

Question Number 55561 Answers: 0 Comments: 3

Question Number 55560 Answers: 1 Comments: 0

Question Number 55557 Answers: 0 Comments: 0

Goodday great minds.Its been quite a while. Please can anyone recommend any site, app or video that can explain the elevation and 3d of shapes.Please I sincerely need your help. Thanks in advance.

$${Goodday}\:{great}\:{minds}.{Its}\:{been}\:{quite}\:{a} \\ $$$${while}.\:{Please}\:{can}\:{anyone}\:{recommend} \\ $$$${any}\:{site},\:{app}\:{or}\:{video}\:{that}\:{can}\:{explain}\:{the} \\ $$$${elevation}\:{and}\:\mathrm{3}{d}\:{of}\:{shapes}.{Please}\:{I} \\ $$$${sincerely}\:{need}\:{your}\:{help}. \\ $$$$ \\ $$$${Thanks}\:{in}\:{advance}. \\ $$

Question Number 55539 Answers: 2 Comments: 2

Question Number 55577 Answers: 1 Comments: 1

Question Number 55576 Answers: 0 Comments: 0

An aeroplane has an air speed of 120kmh^(−1) and flies on a course of bearing S60°E. A wind is blowing steadily at 30kmh^(−1) from a bearing of N60°E. Find; i. the ground speed of the aeroplane ii. the path of the aeroplane

$$\mathrm{An}\:\mathrm{aeroplane}\:\mathrm{has}\:\mathrm{an}\:\mathrm{air}\:\mathrm{speed}\:\mathrm{of}\: \\ $$$$\mathrm{120kmh}^{−\mathrm{1}} \:\mathrm{and}\:\mathrm{flies}\:\mathrm{on}\:\mathrm{a}\:\mathrm{course}\:\mathrm{of} \\ $$$$\mathrm{bearing}\:\mathrm{S60}°\mathrm{E}.\:\mathrm{A}\:\mathrm{wind}\:\mathrm{is}\:\mathrm{blowing}\:\mathrm{steadily} \\ $$$$\mathrm{at}\:\mathrm{30kmh}^{−\mathrm{1}} \:\mathrm{from}\:\mathrm{a}\:\mathrm{bearing}\:\mathrm{of}\:\mathrm{N60}°\mathrm{E}. \\ $$$$\mathrm{Find}; \\ $$$$\mathrm{i}.\:\mathrm{the}\:\mathrm{ground}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{aeroplane} \\ $$$$\mathrm{ii}.\:\mathrm{the}\:\mathrm{path}\:\mathrm{of}\:\mathrm{the}\:\mathrm{aeroplane} \\ $$

Question Number 55534 Answers: 1 Comments: 0

A dish of mixed nut contains cashew and peanut . then two ounces of peanut are added to the dish making the new mixture of 20% cashew. Sara like cashew so she added 2 ounces of them to the dish. The mixture in the dish is now 33.33%. Cashews. what percentage of the origional mixture of nut was cashew? this was the correct question please help

$${A}\:{dish}\:{of}\:{mixed}\:{nut}\:{contains}\:{cashew} \\ $$$${and}\:{peanut}\:.\:{then}\:{two}\:{ounces}\:{of}\: \\ $$$${peanut}\:{are}\:{added}\:{to}\:{the}\:{dish}\:{making} \\ $$$${the}\:{new}\:{mixture}\:{of}\:\mathrm{20\%}\:{cashew}.\: \\ $$$${Sara}\:{like}\:{cashew}\:{so}\:{she}\:{added}\: \\ $$$$\mathrm{2}\:{ounces}\:{of}\:{them}\:{to}\:{the}\:{dish}.\:{The} \\ $$$${mixture}\:{in}\:{the}\:{dish}\:{is}\:{now}\:\:\mathrm{33}.\mathrm{33\%}.\: \\ $$$${Cashews}.\:{what}\:{percentage}\:{of}\:{the}\: \\ $$$${origional}\:{mixture}\:{of}\:{nut}\:{was}\:\: \\ $$$${cashew}?\:{this}\:{was}\:{the}\:{correct}\:{question} \\ $$$${please}\:{help} \\ $$

Question Number 55526 Answers: 1 Comments: 1

If ∫_(−1) ^4 f(x) dx = 4 and ∫_2 ^4 (3−f(x))dx=7, then ∫_( 2) ^(−1) f(x) dx =

$$\mathrm{If}\:\underset{−\mathrm{1}} {\overset{\mathrm{4}} {\int}}\:{f}\left({x}\right)\:{dx}\:=\:\mathrm{4}\:\mathrm{and}\:\underset{\mathrm{2}} {\overset{\mathrm{4}} {\int}}\:\left(\mathrm{3}−{f}\left({x}\right)\right){dx}=\mathrm{7}, \\ $$$$\mathrm{then}\:\:\underset{\:\mathrm{2}} {\overset{−\mathrm{1}} {\int}}\:{f}\left({x}\right)\:{dx}\:= \\ $$

Question Number 55520 Answers: 3 Comments: 2

How can solve ∫(√)tan(x)dx ?

$${How}\:{can}\:{solve}\:\int\sqrt{}\mathrm{tan}\left({x}\right){dx}\:? \\ $$

Question Number 55502 Answers: 2 Comments: 1

Question Number 55501 Answers: 0 Comments: 5

Roots of x^3 +px+q=0 are x = u+v u^3 , v^3 are roots of z^2 −α^3 z+β^6 =0 ((d^2 (y/x))/dx^2 )∣_(x=α) =0 , (dy/dx)∣_(x=β) =0 . I have noticed long way back, please hunt why (how come) ?

$${Roots}\:{of}\:{x}^{\mathrm{3}} +{px}+{q}=\mathrm{0} \\ $$$${are}\:\:{x}\:=\:{u}+{v} \\ $$$${u}^{\mathrm{3}} ,\:{v}^{\mathrm{3}} \:{are}\:{roots}\:{of} \\ $$$$\:\:\:\:\:\:\:{z}^{\mathrm{2}} −\alpha^{\mathrm{3}} {z}+\beta^{\mathrm{6}} =\mathrm{0} \\ $$$$\:\:\:\frac{{d}^{\mathrm{2}} \left({y}/{x}\right)}{{dx}^{\mathrm{2}} }\mid_{{x}=\alpha} =\mathrm{0}\:\:,\:\frac{{dy}}{{dx}}\mid_{{x}=\beta} =\mathrm{0}\:. \\ $$$${I}\:{have}\:{noticed}\:{long}\:{way}\:{back}, \\ $$$${please}\:{hunt}\:{why}\:\left({how}\:{come}\right)\:? \\ $$

Question Number 55493 Answers: 0 Comments: 6

Find intgral of tan x by parts ∫tan x dx pls help me (i am a newbie in calculus)

$${Find}\:{intgral}\:{of}\:\mathrm{tan}\:{x}\:{by}\:{parts} \\ $$$$\int{tan}\:{x}\:{dx}\:\:\:{pls}\:{help}\:{me}\:\:\left({i}\:{am}\:{a}\:{newbie}\:{in}\:{calculus}\right) \\ $$

Question Number 55491 Answers: 1 Comments: 0

Question Number 55482 Answers: 1 Comments: 0

A group of n students are numbered continously from first sdtudent as 1,2,3,...... If 1101 digits had to be used in all,what is the number of students in the group

$${A}\:{group}\:{of}\:{n}\:{students}\:{are}\:{numbered} \\ $$$${continously}\:{from}\:{first}\:{sdtudent}\:{as}\:\mathrm{1},\mathrm{2},\mathrm{3},...... \\ $$$${If}\:\mathrm{1101}\:{digits}\:{had}\:{to}\:{be}\:{used}\:{in}\:{all},{what}\:{is}\:{the}\: \\ $$$${number}\:{of}\:{students}\:{in}\:{the}\:{group} \\ $$

Question Number 55476 Answers: 1 Comments: 0

4 metal rods of length 78 cm,104 cm,117cm, a.nd 169 cm are to be cut into parts of equal length Each length must be as long as possible What is the maximum number of pieces that can be cut?

$$\mathrm{4}\:{metal}\:{rods}\:{of}\:{length}\:\mathrm{78}\:{cm},\mathrm{104}\:{cm},\mathrm{117}{cm}, \\ $$$${a}.{nd}\:\mathrm{169}\:{cm}\:{are}\:{to}\:{be}\:{cut}\:{into}\:{parts}\:{of}\:{equal}\:{length} \\ $$$${Each}\:{length}\:{must}\:{be}\:{as}\:{long}\:{as}\:{possible} \\ $$$${What}\:{is}\:{the}\:{maximum}\:{number}\:{of}\:{pieces} \\ $$$${that}\:{can}\:{be}\:{cut}? \\ $$

Question Number 55475 Answers: 1 Comments: 0

Find the equation of the plane passing through the points (1,0,0) and (0,1,0) and makes an angle of (π/4) with the plane x+y = 3

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{plane} \\ $$$$\mathrm{passing}\:\mathrm{through}\:\mathrm{the}\:\mathrm{points} \\ $$$$\left(\mathrm{1},\mathrm{0},\mathrm{0}\right)\:\mathrm{and}\:\left(\mathrm{0},\mathrm{1},\mathrm{0}\right)\:\mathrm{and}\:\mathrm{makes} \\ $$$$\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\:\frac{\pi}{\mathrm{4}}\:\mathrm{with}\:\mathrm{the}\:\mathrm{plane} \\ $$$$\mathrm{x}+\mathrm{y}\:=\:\mathrm{3} \\ $$

Question Number 55473 Answers: 0 Comments: 1

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