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AllQuestion and Answers: Page 1958

Question Number 9844    Answers: 1   Comments: 0

Question Number 9839    Answers: 0   Comments: 1

Question Number 9838    Answers: 0   Comments: 5

Where is YOZIA since this days. is being long i saw his chat here.

$$\mathrm{Where}\:\mathrm{is}\:\mathrm{YOZIA}\:\mathrm{since}\:\mathrm{this}\:\mathrm{days}. \\ $$$$\mathrm{is}\:\mathrm{being}\:\mathrm{long}\:\mathrm{i}\:\mathrm{saw}\:\mathrm{his}\:\mathrm{chat}\:\mathrm{here}. \\ $$

Question Number 9837    Answers: 0   Comments: 0

∫_0 ^1 e^x^2 dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{e}^{\mathrm{x}^{\mathrm{2}} } \mathrm{dx} \\ $$

Question Number 9836    Answers: 0   Comments: 3

Prove that. ∣z_1 + z_2 ∣ ≤ ∣z_1 ∣ ∣z_2 ∣

$$\mathrm{Prove}\:\mathrm{that}. \\ $$$$\mid\mathrm{z}_{\mathrm{1}} \:+\:\mathrm{z}_{\mathrm{2}} \mid\:\leqslant\:\mid\mathrm{z}_{\mathrm{1}} \mid\:\mid\mathrm{z}_{\mathrm{2}} \mid \\ $$

Question Number 9831    Answers: 1   Comments: 0

Question Number 9827    Answers: 1   Comments: 0

(7 − 4(√3))^(x^2 − 4x + 3) + (7 + 4(√3))^(x^2 − 4x + 3) = 14

$$\left(\mathrm{7}\:−\:\mathrm{4}\sqrt{\mathrm{3}}\right)^{\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{4x}\:+\:\mathrm{3}} \:+\:\left(\mathrm{7}\:+\:\mathrm{4}\sqrt{\mathrm{3}}\right)^{\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{4x}\:+\:\mathrm{3}} \:=\:\mathrm{14} \\ $$

Question Number 9824    Answers: 1   Comments: 0

Question Number 9822    Answers: 1   Comments: 0

Question Number 9821    Answers: 0   Comments: 1

Question Number 9818    Answers: 0   Comments: 1

Question Number 9817    Answers: 0   Comments: 0

Question Number 9813    Answers: 1   Comments: 0

From the top of a tower 80m high, a student observe that the angle of depression of the top of a vertical pole A is 45° and the angle of depression of point B on the pole is 60°. if O is the foot of the pole and OB = 20m. Find the distance between A and B. leaving your answer in surd form.

$$\mathrm{From}\:\mathrm{the}\:\mathrm{top}\:\mathrm{of}\:\mathrm{a}\:\mathrm{tower}\:\mathrm{80m}\:\mathrm{high},\:\mathrm{a}\:\mathrm{student} \\ $$$$\mathrm{observe}\:\mathrm{that}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{depression}\:\mathrm{of}\:\mathrm{the}\:\mathrm{top}\: \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{vertical}\:\mathrm{pole}\:\mathrm{A}\:\mathrm{is}\:\mathrm{45}°\:\mathrm{and}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{of}\: \\ $$$$\mathrm{depression}\:\mathrm{of}\:\mathrm{point}\:\mathrm{B}\:\mathrm{on}\:\mathrm{the}\:\mathrm{pole}\:\mathrm{is}\:\mathrm{60}°. \\ $$$$\mathrm{if}\:\mathrm{O}\:\mathrm{is}\:\mathrm{the}\:\mathrm{foot}\:\mathrm{of}\:\mathrm{the}\:\mathrm{pole}\:\mathrm{and}\:\mathrm{OB}\:=\:\mathrm{20m}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}. \\ $$$$\mathrm{leaving}\:\mathrm{your}\:\mathrm{answer}\:\mathrm{in}\:\mathrm{surd}\:\mathrm{form}. \\ $$

Question Number 9804    Answers: 0   Comments: 1

Express f(x)=x^t e^x as a series

$$\mathrm{Express}\:{f}\left({x}\right)={x}^{{t}} {e}^{{x}} \:\mathrm{as}\:\mathrm{a}\:\mathrm{series} \\ $$

Question Number 9800    Answers: 1   Comments: 2

is there a value for tg^2 (π/4) ?

$$\mathrm{is}\:\mathrm{there}\:\mathrm{a}\:\mathrm{value}\:\mathrm{for}\:\mathrm{tg}^{\mathrm{2}} \frac{\pi}{\mathrm{4}}\:\:? \\ $$

Question Number 9792    Answers: 1   Comments: 0

If one zero of the quadratic polynomial x^2 +7x +k is 2 then find the value of k

$$\mathrm{If}\:\mathrm{one}\:\mathrm{zero}\:\mathrm{of}\:\mathrm{the}\:\mathrm{quadratic}\:\mathrm{polynomial} \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{7x}\:+\mathrm{k}\:\mathrm{is}\:\mathrm{2}\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{k} \\ $$

Question Number 9790    Answers: 0   Comments: 3

prove by mathematical induction n! ≤ n^n

$$\mathrm{prove}\:\mathrm{by}\:\mathrm{mathematical}\:\mathrm{induction} \\ $$$$\mathrm{n}!\:\leqslant\:\mathrm{n}^{\mathrm{n}} \\ $$

Question Number 9788    Answers: 0   Comments: 0

∫_( 0) ^(π/2) (1/(1+tan^3 x)) dx =

$$\:\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{tan}^{\mathrm{3}} {x}}\:{dx}\:= \\ $$

Question Number 9784    Answers: 0   Comments: 4

For (x+y)^n :n∈Z (x+y)^n =Σ_(u=0) ^n ((n),(u) ) x^(n−u) y^n Is there a generalization for when n is non integer? e.g. (x+y)^(1/n) :n^(−1) ∉Z

$$\mathrm{For}\:\left({x}+{y}\right)^{{n}} :{n}\in\mathbb{Z} \\ $$$$\left({x}+{y}\right)^{{n}} =\underset{{u}=\mathrm{0}} {\overset{{n}} {\sum}}\begin{pmatrix}{{n}}\\{{u}}\end{pmatrix}\:{x}^{{n}−{u}} {y}^{{n}} \\ $$$$\: \\ $$$$\mathrm{Is}\:\mathrm{there}\:\mathrm{a}\:\mathrm{generalization}\:\mathrm{for}\:\mathrm{when} \\ $$$${n}\:\mathrm{is}\:\mathrm{non}\:\mathrm{integer}? \\ $$$$\: \\ $$$$\mathrm{e}.\mathrm{g}.\:\:\:\:\left({x}+{y}\right)^{\mathrm{1}/{n}} :{n}^{−\mathrm{1}} \notin\mathbb{Z} \\ $$

Question Number 9782    Answers: 0   Comments: 0

∫ ((sin^4 (x))/(sin^3 (x) + cos^4 (x))) dx

$$\int\:\:\frac{\mathrm{sin}^{\mathrm{4}} \left(\mathrm{x}\right)}{\mathrm{sin}^{\mathrm{3}} \left(\mathrm{x}\right)\:+\:\mathrm{cos}^{\mathrm{4}} \left(\mathrm{x}\right)}\:\mathrm{dx} \\ $$

Question Number 9779    Answers: 1   Comments: 0

Question Number 9778    Answers: 0   Comments: 0

find the relation between a,b, and c if the root of equatio ax^3 +bx^2 +cx=0 are in (i)GP (ii)Ap

$${find}\:{the}\:{relation}\:{between}\:{a},{b},\:{and}\:{c} \\ $$$${if}\:{the}\:{root}\:{of}\:{equatio}\:\:{ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} \:+{cx}=\mathrm{0} \\ $$$${are}\:{in} \\ $$$$\left({i}\right){GP} \\ $$$$\left({ii}\right){Ap} \\ $$$$ \\ $$

Question Number 9776    Answers: 1   Comments: 0

A plant group of company is to convey a machinery from city X with co ordinate (300,200) to city Z with co ordinate (700,900). The machinery can be air lifted at a cost of #9 per kilometer or through city Y with co ordinate (700,200) by an articulated truck at a cost of #7 per kilometer. Determine the route that is least expensive.

$$\mathrm{A}\:\mathrm{plant}\:\mathrm{group}\:\mathrm{of}\:\mathrm{company}\:\mathrm{is}\:\mathrm{to}\:\mathrm{convey}\:\mathrm{a}\: \\ $$$$\mathrm{machinery}\:\mathrm{from}\:\mathrm{city}\:\mathrm{X}\:\mathrm{with}\:\mathrm{co}\:\mathrm{ordinate} \\ $$$$\left(\mathrm{300},\mathrm{200}\right)\:\mathrm{to}\:\mathrm{city}\:\mathrm{Z}\:\mathrm{with}\:\mathrm{co}\:\mathrm{ordinate}\:\left(\mathrm{700},\mathrm{900}\right). \\ $$$$\mathrm{The}\:\mathrm{machinery}\:\mathrm{can}\:\mathrm{be}\:\mathrm{air}\:\mathrm{lifted}\:\mathrm{at}\:\mathrm{a}\:\mathrm{cost}\:\mathrm{of} \\ $$$$#\mathrm{9}\:\mathrm{per}\:\mathrm{kilometer}\:\mathrm{or}\:\mathrm{through}\:\mathrm{city}\:\mathrm{Y}\:\mathrm{with} \\ $$$$\mathrm{co}\:\mathrm{ordinate}\:\left(\mathrm{700},\mathrm{200}\right)\:\mathrm{by}\:\mathrm{an}\:\mathrm{articulated}\:\mathrm{truck} \\ $$$$\mathrm{at}\:\mathrm{a}\:\mathrm{cost}\:\mathrm{of}\:#\mathrm{7}\:\mathrm{per}\:\mathrm{kilometer}.\: \\ $$$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{route}\:\mathrm{that}\:\mathrm{is}\:\mathrm{least}\:\mathrm{expensive}. \\ $$

Question Number 9769    Answers: 0   Comments: 1

Question Number 9768    Answers: 1   Comments: 0

lim_(x→0) ((sin3xcos3x−sin3x)/(2x^2 tan2xcos(1/2)x))=...?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin3}{x}\mathrm{cos3}{x}−\mathrm{sin3}{x}}{\mathrm{2}{x}^{\mathrm{2}} \mathrm{tan2}{x}\mathrm{cos}\frac{\mathrm{1}}{\mathrm{2}}{x}}=...? \\ $$

Question Number 9765    Answers: 1   Comments: 0

The gravitational force of attraction between two spherical bodies having equal densities is increase by −−−−− ? if the radius of each of the bodies is doubled.

$$\mathrm{The}\:\mathrm{gravitational}\:\mathrm{force}\:\mathrm{of}\:\mathrm{attraction}\:\mathrm{between} \\ $$$$\mathrm{two}\:\mathrm{spherical}\:\mathrm{bodies}\:\mathrm{having}\:\mathrm{equal}\:\mathrm{densities} \\ $$$$\mathrm{is}\:\mathrm{increase}\:\mathrm{by}\:−−−−−\:? \\ $$$$\mathrm{if}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{each}\:\mathrm{of}\:\mathrm{the}\:\mathrm{bodies}\:\mathrm{is}\:\mathrm{doubled}. \\ $$

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