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Question Number 83606    Answers: 1   Comments: 0

a car drives at a speed of 120 km/hr it starts to brake at a road mark A and passes a road mark B at a speed of 60 km/hr. acceleration is constant. the distance AB is 4 km. (1) calculate the acceleration (2) calculate the time between A and B (3) there are n reflector posts between A and B. calculate the speed of the car at each of them (find a function for the speed depending on the distance traveled)

$$\mathrm{a}\:\mathrm{car}\:\mathrm{drives}\:\mathrm{at}\:\mathrm{a}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{120}\:\mathrm{km}/\mathrm{hr} \\ $$$$\mathrm{it}\:\mathrm{starts}\:\mathrm{to}\:\mathrm{brake}\:\mathrm{at}\:\mathrm{a}\:\mathrm{road}\:\mathrm{mark}\:{A}\:\mathrm{and} \\ $$$$\mathrm{passes}\:\mathrm{a}\:\mathrm{road}\:\mathrm{mark}\:{B}\:\mathrm{at}\:\mathrm{a}\:\mathrm{speed}\:\mathrm{of} \\ $$$$\mathrm{60}\:\mathrm{km}/\mathrm{hr}.\:\mathrm{acceleration}\:\mathrm{is}\:\mathrm{constant}.\:\mathrm{the} \\ $$$$\mathrm{distance}\:{AB}\:\mathrm{is}\:\mathrm{4}\:\mathrm{km}. \\ $$$$\left(\mathrm{1}\right)\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{acceleration} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{time}\:\mathrm{between}\:{A}\:\mathrm{and}\:{B} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{there}\:\mathrm{are}\:{n}\:\mathrm{reflector}\:\mathrm{posts}\:\mathrm{between}\:{A} \\ $$$$\:\:\:\:\:\:\:\mathrm{and}\:{B}.\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{car}\:\mathrm{at} \\ $$$$\:\:\:\:\:\:\:\mathrm{each}\:\mathrm{of}\:\mathrm{them}\:\left(\mathrm{find}\:\mathrm{a}\:\mathrm{function}\:\mathrm{for}\:\mathrm{the}\right. \\ $$$$\left.\:\:\:\:\:\:\:\mathrm{speed}\:\mathrm{depending}\:\mathrm{on}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{traveled}\right) \\ $$

Question Number 83604    Answers: 0   Comments: 7

need help. When typing with microsoft word i face some difficulties like when typing lim_(x→0) f(x) it turns to lim_(x→0) f(x) and Σ_(r=0) ^n a_n turns to Σ_(r=0) ^n a_n please how do i rectify this problem? and any suggestion on a better application to type my maths papers? thanks in advance.

$$\mathrm{need}\:\mathrm{help}.\:\mathrm{When}\:\mathrm{typing}\:\mathrm{with}\:\mathrm{microsoft}\:\mathrm{word} \\ $$$$\mathrm{i}\:\mathrm{face}\:\mathrm{some}\:\mathrm{difficulties}\:\mathrm{like}\:\mathrm{when}\:\mathrm{typing}\: \\ $$$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{f}\left({x}\right)\:\mathrm{it}\:\mathrm{turns}\:\mathrm{to}\:\mathrm{lim}_{{x}\rightarrow\mathrm{0}} \:{f}\left({x}\right)\:\mathrm{and}\:\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}{a}_{{n}} \: \\ $$$$\mathrm{turns}\:\mathrm{to}\:\sum_{{r}=\mathrm{0}} ^{{n}} {a}_{{n}} \:\:\mathrm{please}\:\mathrm{how}\:\mathrm{do}\:\mathrm{i}\:\mathrm{rectify}\:\mathrm{this} \\ $$$$\mathrm{problem}?\:\mathrm{and}\:\mathrm{any}\:\mathrm{suggestion}\:\mathrm{on}\:\mathrm{a}\:\mathrm{better}\:\mathrm{application} \\ $$$$\mathrm{to}\:\mathrm{type}\:\mathrm{my}\:\mathrm{maths}\:\mathrm{papers}?\:\mathrm{thanks}\:\mathrm{in}\:\mathrm{advance}. \\ $$

Question Number 83603    Answers: 0   Comments: 4

∫ (dx/(1−2cos x))

$$\int\:\frac{\mathrm{dx}}{\mathrm{1}−\mathrm{2cos}\:\mathrm{x}} \\ $$

Question Number 83599    Answers: 0   Comments: 0

Question Number 83597    Answers: 0   Comments: 1

∫_0 ^2 (3x^2 −4x+2)dx

$$\int_{\mathrm{0}} ^{\mathrm{2}} \left(\mathrm{3}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{2}\right){dx} \\ $$

Question Number 83591    Answers: 0   Comments: 1

3x^2 −x+(t^2 −4t+3) = 0 has a roots sin α and cos α. find (√(t^2 −4t+5))

$$\mathrm{3x}^{\mathrm{2}} −\mathrm{x}+\left(\mathrm{t}^{\mathrm{2}} −\mathrm{4t}+\mathrm{3}\right)\:=\:\mathrm{0} \\ $$$$\mathrm{has}\:\mathrm{a}\:\mathrm{roots}\:\mathrm{sin}\:\alpha\:\mathrm{and}\:\mathrm{cos}\:\alpha. \\ $$$$\mathrm{find}\:\sqrt{\mathrm{t}^{\mathrm{2}} −\mathrm{4t}+\mathrm{5}} \\ $$

Question Number 83590    Answers: 0   Comments: 3

transform the ellipse (x^2 /a^2 )+(y^2 /b^2 )=1 to the polar equation r= ((a(1−e^2 ))/(1+ecosθ)) a: semimajor axis e: eccentricity

$${transform}\:{the}\:{ellipse}\:\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{1}\:{to} \\ $$$${the}\:{polar}\:{equation}\:{r}=\:\frac{{a}\left(\mathrm{1}−{e}^{\mathrm{2}} \right)}{\mathrm{1}+{ecos}\theta} \\ $$$${a}:\:{semimajor}\:{axis} \\ $$$${e}:\:{eccentricity} \\ $$

Question Number 83587    Answers: 0   Comments: 2

lim_(x→0) ((3sin πx−sin 3πx)/x^3 )

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{3sin}\:\pi\mathrm{x}−\mathrm{sin}\:\mathrm{3}\pi\mathrm{x}}{\mathrm{x}^{\mathrm{3}} } \\ $$

Question Number 83582    Answers: 0   Comments: 0

Given A = 580^o find sin ((A/2)) in term sin (A)

$$\mathrm{Given}\:\mathrm{A}\:=\:\mathrm{580}^{\mathrm{o}} \\ $$$$\mathrm{find}\:\mathrm{sin}\:\left(\frac{\mathrm{A}}{\mathrm{2}}\right)\:\mathrm{in}\:\mathrm{term}\:\mathrm{sin}\:\left(\mathrm{A}\right) \\ $$

Question Number 83570    Answers: 2   Comments: 3

Find the locus of a point which moves such that its distance from the line y = 4 is a constant k.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:\mathrm{a}\:\mathrm{point}\:\mathrm{which}\:\mathrm{moves}\:\mathrm{such}\:\mathrm{that}\:\mathrm{its} \\ $$$$\mathrm{distance}\:\mathrm{from}\:\mathrm{the}\:\mathrm{line}\:\:\:\mathrm{y}\:\:=\:\:\mathrm{4}\:\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{constant}\:\:\:\mathrm{k}. \\ $$

Question Number 83569    Answers: 0   Comments: 1

calculate ∫_1 ^(+∞) (dx/(x^4 (3x−1)^5 ))

$${calculate}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{{dx}}{{x}^{\mathrm{4}} \left(\mathrm{3}{x}−\mathrm{1}\right)^{\mathrm{5}} } \\ $$

Question Number 83565    Answers: 1   Comments: 4

Question Number 83559    Answers: 1   Comments: 1

Question Number 83558    Answers: 0   Comments: 4

Question Number 83556    Answers: 2   Comments: 0

find the value of (b) wich makes the line y=b divide the tow funtions into tow equal parts 1) f(x)=9−x^2 , g(x)=0 2)f(x)=9−∣x∣ , g(x)=0

$${find}\:{the}\:{value}\:{of}\:\:\left({b}\right)\:{wich}\:{makes}\:{the} \\ $$$${line}\:{y}={b}\:{divide}\:{the}\:{tow}\:{funtions}\:{into} \\ $$$${tow}\:{equal}\:{parts} \\ $$$$ \\ $$$$\left.\mathrm{1}\right)\:{f}\left({x}\right)=\mathrm{9}−{x}^{\mathrm{2}} \:,\:{g}\left({x}\right)=\mathrm{0} \\ $$$$ \\ $$$$\left.\mathrm{2}\right){f}\left({x}\right)=\mathrm{9}−\mid{x}\mid\:,\:{g}\left({x}\right)=\mathrm{0} \\ $$

Question Number 83554    Answers: 1   Comments: 0

Question Number 83543    Answers: 1   Comments: 2

Question Number 83542    Answers: 2   Comments: 0

Question Number 83539    Answers: 0   Comments: 3

what is range of function f(x) = (x/(√(x^2 −1)))?

$$\mathrm{what}\:\mathrm{is}\:\mathrm{range}\:\mathrm{of}\:\mathrm{function}\: \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{x}}{\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}}? \\ $$

Question Number 83621    Answers: 2   Comments: 1

∣ x+(1/x)∣ < 4 find the solution

$$\mid\:{x}+\frac{\mathrm{1}}{{x}}\mid\:<\:\mathrm{4}\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{solution} \\ $$

Question Number 83524    Answers: 2   Comments: 2

Question Number 83521    Answers: 0   Comments: 1

∫((√(sin(x)))/(sin^2 (x)+1)) dx

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

Question Number 83520    Answers: 1   Comments: 0

closest distance point (6,9) to curve y = x^2 −12x+32 . mister w your method can be applied to this problem?

$$\mathrm{closest}\:\mathrm{distance}\:\mathrm{point}\:\left(\mathrm{6},\mathrm{9}\right)\: \\ $$$$\mathrm{to}\:\mathrm{curve}\:\mathrm{y}\:=\:\mathrm{x}^{\mathrm{2}} −\mathrm{12x}+\mathrm{32}\:. \\ $$$$\mathrm{mister}\:\mathrm{w}\:\mathrm{your}\:\mathrm{method}\:\mathrm{can}\:\mathrm{be}\: \\ $$$$\mathrm{applied}\:\mathrm{to}\:\mathrm{this}\:\mathrm{problem}? \\ $$

Question Number 83513    Answers: 0   Comments: 2

If m tan (θ−30^o ) = n tan (θ+12^o ) prove that cos 2θ = ((m+n)/(2(m−n)))

$$\mathrm{If}\:\mathrm{m}\:\mathrm{tan}\:\left(\theta−\mathrm{30}^{\mathrm{o}} \right)\:=\:\mathrm{n}\:\mathrm{tan}\:\left(\theta+\mathrm{12}^{\mathrm{o}} \right) \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{cos}\:\mathrm{2}\theta\:=\:\frac{\mathrm{m}+\mathrm{n}}{\mathrm{2}\left(\mathrm{m}−\mathrm{n}\right)} \\ $$

Question Number 83512    Answers: 1   Comments: 0

find the solution ((4x^2 )/((1−(√(2x+1)))^2 )) < 2x+9

$$\mathrm{find}\:\mathrm{the}\:\mathrm{solution}\: \\ $$$$\frac{\mathrm{4x}^{\mathrm{2}} }{\left(\mathrm{1}−\sqrt{\mathrm{2x}+\mathrm{1}}\right)^{\mathrm{2}} }\:<\:\mathrm{2x}+\mathrm{9} \\ $$

Question Number 83511    Answers: 1   Comments: 0

find minimum value of ∣x−y∣ +(√((x−3)^2 +(y+1)^2 ))

$$\mathrm{find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\mid\mathrm{x}−\mathrm{y}\mid\:+\sqrt{\left(\mathrm{x}−\mathrm{3}\right)^{\mathrm{2}} +\left(\mathrm{y}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

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