Question and Answers Forum

the 15^(th) term of an AP is 34 the sum of the 94^(th) to 100^(th) term is 2000 find the 2^(nd) term and the mean from the sixth term to the 10^(th) term if the 100^(th) term is 360.

$$\:{the}\:\mathrm{15}^{{th}} \:{term}\:{of}\:{an}\:{AP}\:{is}\:\mathrm{34}\:{the}\: \\ $$$${sum}\:{of}\:{the}\:\mathrm{94}^{{th}} \:{to}\:\mathrm{100}^{{th}} \:{term}\:{is} \\ $$$$\mathrm{2000}\:{find}\:{the}\:\mathrm{2}^{{nd}} \:{term}\:{and}\:{the} \\ $$$${mean}\:{from}\:{the}\:{sixth}\:{term}\:{to}\:{the} \\ $$$$\mathrm{10}^{{th}} \:{term}\:{if}\:{the}\:\mathrm{100}^{{th}} \:{term}\:{is} \\ $$$$\:\mathrm{360}. \\ $$

Question Number 34205 Answers: 1 Comments: 1

Question Number 34206 Answers: 0 Comments: 1

Question Number 34202 Answers: 1 Comments: 0

find the gradient of the curve y=(1/x).

$$\:\:{find}\:{the}\:{gradient}\:{of}\:{the}\:{curve} \\ $$$$\:\:\:\:{y}=\frac{\mathrm{1}}{{x}}. \\ $$

Question Number 34196 Answers: 1 Comments: 2

Question Number 34186 Answers: 1 Comments: 1

Let x_1 = 0, x_2 = 1 and x_n = (1/2)(x_(n−1) + x_(n−2) ) Show that x_n = ((2^(n−1) + (−1)^n )/(3 . 2^(n−2) ))

$$\mathrm{Let}\:{x}_{\mathrm{1}} \:=\:\mathrm{0},\:{x}_{\mathrm{2}} \:=\:\mathrm{1}\:\mathrm{and}\:{x}_{{n}} \:=\:\frac{\mathrm{1}}{\mathrm{2}}\left({x}_{{n}−\mathrm{1}} \:+\:{x}_{{n}−\mathrm{2}} \right) \\ $$$$\mathrm{Show}\:\mathrm{that}\: \\ $$$${x}_{{n}} \:=\:\frac{\mathrm{2}^{{n}−\mathrm{1}} \:+\:\left(−\mathrm{1}\right)^{{n}} }{\mathrm{3}\:.\:\mathrm{2}^{{n}−\mathrm{2}} } \\ $$

Question Number 34184 Answers: 1 Comments: 1

if α and β are the roots of the equation 3x^2 + (x/2) − 4= 0 find p is α−β are the roots of x^2 −px + 7 =0

$$\:{if}\:\alpha\:{and}\:\beta\:{are}\:{the}\:{roots}\:{of}\:{the}\:{equation} \\ $$$$\mathrm{3}{x}^{\mathrm{2}} +\:\frac{{x}}{\mathrm{2}}\:−\:\mathrm{4}=\:\mathrm{0}\:{find}\:{p}\:{is}\:\alpha−\beta\:{are} \\ $$$${the}\:{roots}\:{of}\:\:{x}^{\mathrm{2}} −{px}\:+\:\mathrm{7}\:=\mathrm{0} \\ $$

Question Number 34182 Answers: 2 Comments: 0

resolve (x^3 /(x^6 −1)) into partial fraction

$${resolve}\:\frac{{x}^{\mathrm{3}} }{{x}^{\mathrm{6}} −\mathrm{1}}\:{into}\:{partial}\:{fraction} \\ $$

Question Number 34170 Answers: 1 Comments: 0

the distance from A to B is 44km the speed of a car is 2kms^(−1) find the term hence the amount of money needed to buy fuel if for every 6km 10 l of fuel is used which causes 600 box.

$${the}\:{distance}\:{from}\:{A}\:{to}\:{B}\:{is}\:\mathrm{44}{km} \\ $$$${the}\:{speed}\:{of}\:{a}\:{car}\:{is}\:\mathrm{2}{kms}^{−\mathrm{1}} \:{find}\: \\ $$$${the}\:{term}\:{hence}\:{the}\:{amount}\:{of}\: \\ $$$${money}\:{needed}\:{to}\:{buy}\:{fuel}\:{if}\:{for}\: \\ $$$${every}\:\mathrm{6}{km}\:\mathrm{10}\:{l}\:{of}\:{fuel}\:{is}\:{used}\:{which} \\ $$$${causes}\:\mathrm{600}\:{box}. \\ $$

Question Number 34169 Answers: 1 Comments: 0

if the sum S_4 of the first 4 terms of a G P is 24 and the sum S_6 of the first 6 terms is 30 find the first term and common ratio..

$$\:{if}\:{the}\:{sum}\:{S}_{\mathrm{4}} \:{of}\:{the}\:{first}\:\mathrm{4}\:{terms} \\ $$$${of}\:{a}\:{G}\:{P}\:{is}\:\mathrm{24}\:{and}\:{the}\:{sum}\:{S}_{\mathrm{6}} \:{of}\: \\ $$$${the}\:{first}\:\mathrm{6}\:{terms}\:{is}\:\mathrm{30}\:{find}\:{the}\: \\ $$$${first}\:{term}\:{and}\:{common}\:{ratio}.. \\ $$

Question Number 34160 Answers: 1 Comments: 3

prove that lim_(x→0^+ ) ln x∙ln (1+x)=lim_(x→1) ln x∙ln (1+x)

$${prove}\:{that} \\ $$$$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}ln}\:{x}\centerdot\mathrm{ln}\:\left(\mathrm{1}+{x}\right)=\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}ln}\:{x}\centerdot\mathrm{ln}\:\left(\mathrm{1}+{x}\right) \\ $$

Question Number 34159 Answers: 1 Comments: 1

let S=1+2+...+2018 compute S(mod 2)+S(mod8)+S(mod2018)

$${let}\:{S}=\mathrm{1}+\mathrm{2}+...+\mathrm{2018} \\ $$$${compute}\:{S}\left(\mathrm{mod}\:\mathrm{2}\right)+{S}\left(\mathrm{mod8}\right)+{S}\left(\mathrm{mod2018}\right) \\ $$

Question Number 34142 Answers: 0 Comments: 1

what is the derivative of (x+3)(x^2 + 5) and find the n sequence of Σ_(r=n+1 ) ^(2n) (4r^3 −3)

$${what}\:{is}\:{the}\:{derivative}\:{of}\: \\ $$$$\:\:\:\:\:\left(\boldsymbol{{x}}+\mathrm{3}\right)\left(\boldsymbol{{x}}^{\mathrm{2}} +\:\mathrm{5}\right) \\ $$$${and}\:{find}\:{the}\:{n}\:{sequence}\:{of}\: \\ $$$$\:\:\:\underset{{r}={n}+\mathrm{1}\:} {\overset{\mathrm{2}{n}} {\sum}}\:\:\left(\mathrm{4}{r}^{\mathrm{3}} −\mathrm{3}\right) \\ $$

Question Number 34140 Answers: 2 Comments: 0

what is the remainder when 767^(1009) is divided by 25

$${what}\:{is}\:{the}\:{remainder}\:{when} \\ $$$$\mathrm{767}^{\mathrm{1009}} \:{is}\:{divided}\:{by}\:\mathrm{25} \\ $$

Question Number 34139 Answers: 2 Comments: 0

What is the remainder when 17^(200) is divided by 18

$${What}\:{is}\:{the}\:{remainder}\:{when} \\ $$$$\mathrm{17}^{\mathrm{200}} \:{is}\:{divided}\:{by}\:\mathrm{18} \\ $$

Question Number 34129 Answers: 2 Comments: 2

find the value of ∫_0 ^1 ln(x)ln(1+x)dx .

$${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({x}\right){ln}\left(\mathrm{1}+{x}\right){dx}\:. \\ $$

Question Number 34126 Answers: 0 Comments: 0

let give n natural integr not o calculate A_n = ∫_0 ^∞ (dx/(Π_(k=1) ^n (x^2 +k))) .

$${let}\:{give}\:{n}\:{natural}\:{integr}\:{not}\:{o} \\ $$$${calculate}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\prod_{{k}=\mathrm{1}} ^{{n}} \left({x}^{\mathrm{2}} \:+{k}\right)}\:. \\ $$

Question Number 34119 Answers: 3 Comments: 0

if u and v are real valued functions of x, then (d/dx)((u/v))= A. ((v(du/dx)− u(dv/dx))/u^2 ) B. ((v(du/dx)− u(dv/dx))/u^2 ) C. ((v(du/dx)−u (dv/dx))/v^2 ) D. ((u(dv/dx) − v(du/dx))/v^2 )

$${if}\:{u}\:{and}\:{v}\:{are}\:{real}\:{valued}\:{functions} \\ $$$${of}\:{x},\:{then}\:\:\frac{{d}}{{dx}}\left(\frac{{u}}{{v}}\right)= \\ $$$${A}.\:\frac{{v}\frac{{du}}{{dx}}−\:{u}\frac{{dv}}{{dx}}}{{u}^{\mathrm{2}} }\:\:\:\:\:\:\:\:{B}.\:\:\frac{{v}\frac{{du}}{{dx}}−\:{u}\frac{{dv}}{{dx}}}{{u}^{\mathrm{2}} } \\ $$$${C}.\:\frac{{v}\frac{{du}}{{dx}}−{u}\:\frac{{dv}}{{dx}}}{{v}^{\mathrm{2}} }\:\:\:\:\:\:\:\:\:\:{D}.\:\frac{{u}\frac{{dv}}{{dx}}\:−\:{v}\frac{{du}}{{dx}}}{{v}^{\mathrm{2}} } \\ $$

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