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Question Number 146487 Answers: 0 Comments: 0

Cube ABCD.EFGH has side length a. Point P lies on AC such that AP : PC = 3 : 1 Through P a line l parallel to BD is drawn such that l each intersect BC at X and CD at Y. If AC and BD intersect at O find the distance between XY with OG!

$$ \\ $$$$\mathrm{Cube}\:\mathrm{ABCD}.\mathrm{EFGH}\:\mathrm{has}\:\mathrm{side}\:\mathrm{length}\:\mathrm{a}. \\ $$$$\mathrm{P}{o}\mathrm{int}\:\mathrm{P}\:\mathrm{lies}\:\mathrm{on}\:\mathrm{AC}\:\mathrm{such}\:\mathrm{that}\:\mathrm{AP}\::\:\mathrm{PC}\:=\:\mathrm{3}\::\:\mathrm{1}\:\mathrm{Through}\:\mathrm{P}\:\mathrm{a}\:\mathrm{line}\:\mathrm{l}\:\mathrm{parallel}\:\mathrm{to}\:\mathrm{BD}\:\mathrm{is} \\ $$$$\mathrm{dr}{a}\mathrm{wn}\:\mathrm{such}\:\mathrm{that}\:\mathrm{l}\:\mathrm{each}\:\mathrm{intersect}\:\mathrm{BC}\:\mathrm{at}\: \\ $$$$\mathrm{X}\:\mathrm{and}\:\mathrm{CD}\:\mathrm{at}\:\mathrm{Y}.\:\mathrm{If}\:\mathrm{AC}\:\mathrm{and}\:\mathrm{BD}\: \\ $$$$\mathrm{intersect}\:\mathrm{at}\:\mathrm{O}\:\mathrm{find}\:\mathrm{the}\:\mathrm{distance}\: \\ $$$$\mathrm{between}\:\mathrm{XY}\:\mathrm{with}\:\mathrm{OG}! \\ $$

Question Number 146497 Answers: 1 Comments: 0

f(x)=(2/x)∫_0 ^x (t^2 /( (√(1+t^2 ))))dt calculate lim_(x→0) f(x)

$$\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{2}}{\mathrm{x}}\int_{\mathrm{0}} ^{\mathrm{x}} \:\:\frac{\mathrm{t}^{\mathrm{2}} }{\:\sqrt{\mathrm{1}+\mathrm{t}^{\mathrm{2}} }}\mathrm{dt}\:\:\mathrm{calculate}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \mathrm{f}\left(\mathrm{x}\right) \\ $$

Question Number 146472 Answers: 0 Comments: 1

Question Number 146467 Answers: 2 Comments: 0

if ((√3)/2) + (1/2) i find z^(11) = ?

$${if}\:\:\:\:\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\:\boldsymbol{{i}}\:\:\:\:{find}\:\:\:\boldsymbol{{z}}^{\mathrm{11}} \:=\:? \\ $$

Question Number 146470 Answers: 1 Comments: 0

if 4a=7b=2c and dcm(a;b;c)=3 find a+b+c=?

$${if}\:\:\:\mathrm{4}{a}=\mathrm{7}{b}=\mathrm{2}{c}\:\:{and}\:\:\:\boldsymbol{{dcm}}\left({a};{b};{c}\right)=\mathrm{3} \\ $$$${find}\:\:\:{a}+{b}+{c}=? \\ $$

Question Number 146465 Answers: 1 Comments: 0

arccos(cos 9) = ?

$${arccos}\left({cos}\:\mathrm{9}\right)\:=\:? \\ $$

Question Number 147762 Answers: 0 Comments: 0

how to minimalize t? ∫_x_2 ^x_1 ((√(1+(y(x)′)^2 ))/( (√(x^2 +y(x)^2 ))∙c_1 +c_0 ))Δx=t

$${how}\:{to}\:{minimalize}\:{t}? \\ $$$$\underset{{x}_{\mathrm{2}} } {\overset{{x}_{\mathrm{1}} } {\int}}\frac{\sqrt{\mathrm{1}+\left({y}\left({x}\right)'\right)^{\mathrm{2}} }}{\:\sqrt{{x}^{\mathrm{2}} +{y}\left({x}\right)^{\mathrm{2}} }\centerdot{c}_{\mathrm{1}} +{c}_{\mathrm{0}} }\Delta{x}={t} \\ $$$$ \\ $$

Question Number 146459 Answers: 1 Comments: 0

if x^2 =y^3 find log_x x(√y) = ?

$${if}\:\:\:{x}^{\mathrm{2}} ={y}^{\mathrm{3}} \:\:\:{find}\:\:\:\:{log}_{\boldsymbol{{x}}} {x}\sqrt{{y}}\:=\:?\:\:\: \\ $$

Question Number 146457 Answers: 2 Comments: 1

Question Number 146455 Answers: 1 Comments: 0

Given that F(x) = ∫_0 ^x (t^2 /( (√(t^2 +1))))dt Show that F(x) is an increasing function

$$\mathrm{Given}\:\mathrm{that}\:\:{F}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{{x}} \frac{{t}^{\mathrm{2}} }{\:\sqrt{{t}^{\mathrm{2}} +\mathrm{1}}}{dt}\: \\ $$$$\:\mathrm{Show}\:\mathrm{that}\:{F}\left({x}\right)\:\mathrm{is}\:\mathrm{an}\:\mathrm{increasing}\:\mathrm{function} \\ $$

Question Number 147769 Answers: 0 Comments: 0

Question Number 147768 Answers: 1 Comments: 0

Question Number 146444 Answers: 0 Comments: 0

Question Number 146442 Answers: 2 Comments: 0

(d/dn)∣_(n=1) H_n =?

$$\frac{\mathrm{d}}{\mathrm{dn}}\mid_{\mathrm{n}=\mathrm{1}} \mathrm{H}_{\mathrm{n}} =? \\ $$

Question Number 146436 Answers: 2 Comments: 0

((sin^2 25 - sin^2 5)/(sin 20)) = ?

$$\frac{{sin}^{\mathrm{2}} \:\mathrm{25}\:-\:{sin}^{\mathrm{2}} \:\mathrm{5}}{{sin}\:\mathrm{20}}\:=\:? \\ $$

Question Number 146440 Answers: 1 Comments: 0

Question Number 146429 Answers: 1 Comments: 1

Σ_(n=1) ^∞ (n∙ln((2n+1)/(2n−1))−1)=?

$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\mathrm{n}\centerdot\mathrm{ln}\frac{\mathrm{2n}+\mathrm{1}}{\mathrm{2n}−\mathrm{1}}−\mathrm{1}\right)=? \\ $$

Question Number 146425 Answers: 1 Comments: 2

4 people took the elevator to the first floor of the 6 - storey building. Find the probability that they fall on different floors.

$$\mathrm{4}\:{people}\:{took}\:{the}\:{elevator}\:{to}\:{the}\:{first} \\ $$$${floor}\:{of}\:{the}\:\mathrm{6}\:-\:{storey}\:{building}.\:{Find} \\ $$$${the}\:{probability}\:{that}\:{they}\:{fall}\:{on} \\ $$$${different}\:{floors}. \\ $$

Question Number 147666 Answers: 0 Comments: 0

6bhh bnn77 chb65b fbb7(√) m977 tgvn

$$\mathrm{6bhh} \\ $$$$\mathrm{bnn77} \\ $$$$\mathrm{chb65b} \\ $$$$\mathrm{fbb7}\sqrt{} \\ $$$$\mathrm{m977} \\ $$$$\mathrm{tgvn} \\ $$

Question Number 146420 Answers: 0 Comments: 0

Question Number 146411 Answers: 1 Comments: 1

prove 197 prime number

$${prove}\:\mathrm{197}\:{prime}\:{number} \\ $$

Question Number 146408 Answers: 3 Comments: 3

find 3x≊4( mod 5)

$${find}\:\mathrm{3}{x}\approxeq\mathrm{4}\left(\:{mod}\:\mathrm{5}\right) \\ $$

Question Number 146404 Answers: 1 Comments: 1

trigonometry

$$\:\mathrm{trigonometry} \\ $$

Question Number 146403 Answers: 0 Comments: 1

let f(x,y)=((x^5 y^2 )/(10)) then find D_u f(−5,−3) in the direction of the vector <0,−2>?

$${let}\:{f}\left({x},{y}\right)=\frac{{x}^{\mathrm{5}} {y}^{\mathrm{2}} }{\mathrm{10}}\:{then}\:{find}\: \\ $$$${D}_{{u}} {f}\left(−\mathrm{5},−\mathrm{3}\right)\:{in}\:{the}\:{direction}\:{of}\: \\ $$$${the}\:{vector}\:<\mathrm{0},−\mathrm{2}>? \\ $$

Question Number 146401 Answers: 0 Comments: 1

(dy/dx)(x!)

$$\frac{{dy}}{{dx}}\left({x}!\right) \\ $$

Question Number 146386 Answers: 2 Comments: 0

if (8/(3^x + 2^(−x) )) = ((27)/(3^(−x) + 2^x )) find 2x+1=?

$${if}\:\:\:\frac{\mathrm{8}}{\mathrm{3}^{\boldsymbol{{x}}} \:+\:\mathrm{2}^{−\boldsymbol{{x}}} }\:=\:\frac{\mathrm{27}}{\mathrm{3}^{−\boldsymbol{{x}}} \:+\:\mathrm{2}^{\boldsymbol{{x}}} } \\ $$$${find}\:\:\:\mathrm{2}{x}+\mathrm{1}=? \\ $$

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