Question and Answers Forum

AllQuestion and Answers: Page 1705

Question Number 32258 Answers: 2 Comments: 0

find ∫ (1/(2−x^2 )) dx

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

Question Number 32256 Answers: 0 Comments: 0

1)let a>0 and x>0 find lim _(x→a) ((e^(−ax^2 ) − e^(−xa^2 ) )/(a^x −x^a )) . 2)find lim_(x→2) ((e^(−2x^2 ) − e^(−4x) )/(2^x −x^2 )) .

$$\left.\mathrm{1}\right){let}\:{a}>\mathrm{0}\:{and}\:{x}>\mathrm{0}\:{find}\:{lim}\:_{{x}\rightarrow{a}} \:\frac{{e}^{−{ax}^{\mathrm{2}} } \:−\:{e}^{−{xa}^{\mathrm{2}} } }{{a}^{{x}} \:−{x}^{{a}} }\:. \\ $$$$\left.\mathrm{2}\right){find}\:{lim}_{{x}\rightarrow\mathrm{2}} \:\:\:\frac{{e}^{−\mathrm{2}{x}^{\mathrm{2}} } \:−\:{e}^{−\mathrm{4}{x}} }{\mathrm{2}^{{x}} \:−{x}^{\mathrm{2}} }\:. \\ $$

Question Number 32255 Answers: 0 Comments: 0

le x>0 and a>0 find lim_(x→a) ((log_a (x) −log_x (a))/(sinx −sina)) .

$${le}\:{x}>\mathrm{0}\:{and}\:{a}>\mathrm{0}\:{find}\:{lim}_{{x}\rightarrow{a}} \:\frac{{log}_{{a}} \:\left({x}\right)\:−{log}_{{x}} \left({a}\right)}{{sinx}\:−{sina}}\:\:. \\ $$

Question Number 32265 Answers: 0 Comments: 0

Question Number 32242 Answers: 1 Comments: 0

A company manufactures two types of products; X ($4.50 profit per item x) and Y ($3.00 profit per item y). These items are built using both machine time and manual labour. The X product requires 3 hours of machine time and two hours of manual labour. The Y product requires 3 hours of machine time and no manual labour. If the week′s supply of manual labour is limited to 8 hours and machine time to 15 hours, write down all inequalities involving x and y.

$$\mathrm{A}\:\mathrm{company}\:\mathrm{manufactures}\:\mathrm{two}\:\mathrm{types}\:\mathrm{of}\:\mathrm{products}; \\ $$$$\mathrm{X}\:\left(\$\mathrm{4}.\mathrm{50}\:\mathrm{profit}\:\mathrm{per}\:\mathrm{item}\:\mathrm{x}\right)\:\mathrm{and}\:\mathrm{Y}\:\left(\$\mathrm{3}.\mathrm{00}\:\mathrm{profit}\:\mathrm{per}\right. \\ $$$$\left.\mathrm{item}\:\mathrm{y}\right).\:\mathrm{These}\:\mathrm{items}\:\mathrm{are}\:\mathrm{built}\:\mathrm{using}\:\mathrm{both}\:\mathrm{machine} \\ $$$$\mathrm{time}\:\mathrm{and}\:\mathrm{manual}\:\mathrm{labour}.\:\mathrm{The}\:\mathrm{X}\:\mathrm{product}\:\mathrm{requires} \\ $$$$\mathrm{3}\:\mathrm{hours}\:\mathrm{of}\:\mathrm{machine}\:\mathrm{time}\:\mathrm{and}\:\mathrm{two}\:\mathrm{hours}\:\mathrm{of}\:\mathrm{manual} \\ $$$$\mathrm{labour}.\:\mathrm{The}\:\mathrm{Y}\:\mathrm{product}\:\mathrm{requires}\:\mathrm{3}\:\mathrm{hours}\:\mathrm{of}\:\mathrm{machine} \\ $$$$\mathrm{time}\:\mathrm{and}\:\mathrm{no}\:\mathrm{manual}\:\mathrm{labour}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{week}'\mathrm{s}\:\mathrm{supply}\:\mathrm{of}\: \\ $$$$\mathrm{manual}\:\mathrm{labour}\:\mathrm{is}\:\mathrm{limited}\:\mathrm{to}\:\mathrm{8}\:\mathrm{hours}\:\mathrm{and}\:\mathrm{machine} \\ $$$$\mathrm{time}\:\mathrm{to}\:\mathrm{15}\:\mathrm{hours},\:\mathrm{write}\:\mathrm{down}\:\mathrm{all}\:\mathrm{inequalities}\: \\ $$$$\mathrm{involving}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}. \\ $$

Question Number 32241 Answers: 0 Comments: 1

Question Number 32240 Answers: 1 Comments: 0

Question Number 32239 Answers: 1 Comments: 0

Find the sum of the coefficients of all the integral power of x in the expansion of (1+2(√x))^(40) .

$$\boldsymbol{{F}}{ind}\:{the}\:{sum}\:{of}\:{the}\:{coefficients} \\ $$$${of}\:{all}\:{the}\:{integral}\:{power}\:{of}\:{x}\:{in}\:{the} \\ $$$${expansion}\:{of}\:\left(\mathrm{1}+\mathrm{2}\sqrt{{x}}\right)^{\mathrm{40}} . \\ $$

Question Number 32237 Answers: 0 Comments: 0

Question Number 32236 Answers: 1 Comments: 0

Question Number 32233 Answers: 0 Comments: 1

A particle id moving in a circular path of radius a with constant velocity v.The center of cirvle marked by C.The angular momentum from the origin is.

$${A}\:{particle}\:{id}\:{moving}\:{in}\:{a}\:{circular} \\ $$$${path}\:{of}\:{radius}\:{a}\:{with}\:{constant} \\ $$$${velocity}\:{v}.{The}\:{center}\:{of}\:{cirvle} \\ $$$${marked}\:{by}\:{C}.{The}\:{angular}\:{momentum} \\ $$$${from}\:{the}\:{origin}\:{is}. \\ $$

Question Number 32220 Answers: 0 Comments: 3

Find the value of a for which the equation sin^4 x+asin^2 x+1=0 will have a solution.

$${Find}\:{the}\:{value}\:{of}\:{a}\:{for}\:{which}\:{the}\:{equation} \\ $$$$\mathrm{sin}\:^{\mathrm{4}} {x}+{a}\mathrm{sin}\:^{\mathrm{2}} {x}+\mathrm{1}=\mathrm{0}\:{will}\:{have}\:{a}\:{solution}. \\ $$

Question Number 32218 Answers: 1 Comments: 0

Question Number 32209 Answers: 1 Comments: 0

a boy rides his bicycle 10km at an average speed of 12 km/hr. and again travel 12 km at an average speed of 10 km/hr his average speed for dntire trip is approximately a)10.4km/hr b)10.8km/hr c)12.2km/hr d)11.2km/hr

$${a}\:{boy}\:{rides}\:{his}\:{bicycle}\:\mathrm{10}{km}\:{at}\:{an}\:{average}\:{speed}\:{of}\:\mathrm{12}\:{km}/{hr}. \\ $$$${and}\:{again}\:{travel}\:\mathrm{12}\:{km}\:{at}\:{an}\:{average}\:{speed}\:{of}\:\mathrm{10}\:{km}/{hr} \\ $$$${his}\:{average}\:{speed}\:{for}\:{dntire}\:{trip}\:{is}\:{approximately} \\ $$$$\left.{a}\right)\mathrm{10}.\mathrm{4}{km}/{hr} \\ $$$$\left.{b}\right)\mathrm{10}.\mathrm{8}{km}/{hr} \\ $$$$\left.{c}\right)\mathrm{12}.\mathrm{2}{km}/{hr} \\ $$$$\left.{d}\right)\mathrm{11}.\mathrm{2}{km}/{hr} \\ $$

Question Number 32208 Answers: 0 Comments: 0

Question Number 32207 Answers: 0 Comments: 0

mi servirebbe aiuto per capire come si puo ruotare la vista del sofware per un ragazzo DISABILE. Grazie.

$${mi}\:{servirebbe}\:{aiuto}\:{per}\:{capire}\:{come}\:{si}\:{puo}\:{ruotare}\: \\ $$$${la}\:{vista}\:{del}\:{sofware}\:{per}\:{un}\:{ragazzo}\:{DISABILE}.\:{Grazie}. \\ $$$$ \\ $$$$ \\ $$

Question Number 32206 Answers: 0 Comments: 0

Find Σ_(k=1) ^∞ (∫_(k−1) ^k x^(−x) dx) .

$$\mathrm{Find}\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\underset{\mathrm{k}−\mathrm{1}} {\overset{\mathrm{k}} {\int}}\mathrm{x}^{−\mathrm{x}} \:\mathrm{dx}\right)\:. \\ $$$$ \\ $$

Question Number 32203 Answers: 0 Comments: 5

Number of solutions of the equation z^3 +(([3(z^− )^2 ])/(∣z∣))=0 where z is a complex no.

$$\boldsymbol{{N}}{umber}\:{of}\:{solutions}\:{of}\:{the}\:{equation} \\ $$$${z}^{\mathrm{3}} +\frac{\left[\mathrm{3}\left(\overset{−} {{z}}\right)^{\mathrm{2}} \right]}{\mid{z}\mid}=\mathrm{0}\:{where}\:{z}\:{is}\:{a}\:{complex}\:{no}. \\ $$

Question Number 32191 Answers: 1 Comments: 1

Question Number 32211 Answers: 1 Comments: 1

Question Number 32184 Answers: 1 Comments: 0

If one vertex of the triangle having maximum area that can be inscribed in the circle ∣z−i∣=5 is 3−3i, then find other vertices of triangle.

$$\boldsymbol{{I}}{f}\:{one}\:{vertex}\:{of}\:{the}\:{triangle}\:{having} \\ $$$${maximum}\:{area}\:{that}\:{can}\:{be}\:{inscribed} \\ $$$${in}\:{the}\:{circle}\:\mid\boldsymbol{{z}}−\boldsymbol{{i}}\mid=\mathrm{5}\:{is}\:\mathrm{3}−\mathrm{3}\boldsymbol{{i}},\:{then} \\ $$$${find}\:{other}\:{vertices}\:{of}\:{triangle}. \\ $$

Question Number 32181 Answers: 1 Comments: 1

Intercept made by the circle zz^− +a^− z+az^− +r=0 on the real axis on complex plane is :−

$$\boldsymbol{{I}}{ntercept}\:{made}\:{by}\:{the}\:{circle}\: \\ $$$$\boldsymbol{{z}}\overset{−} {\boldsymbol{{z}}}+\overset{−} {\boldsymbol{{a}z}}+\boldsymbol{{a}}\overset{−} {\boldsymbol{{z}}}+\boldsymbol{{r}}=\mathrm{0}\:\boldsymbol{{o}}{n}\:{the}\:{real}\:{axis}\:{on} \\ $$$${complex}\:{plane}\:{is}\::− \\ $$

Question Number 32163 Answers: 0 Comments: 0

If the corrdinater of the verticle of an eqvilateral triangle with length x are (x_(1+) y_1 ),(y_1 +y_2 ) and (x_3 ,y_3 ) then ( determinant (((x_1 y_1 2)),((x_2 y_2 2)),((x_3 y_3 2))))^2 =3a^4 ?

$${If}\:{the}\:{corrdinater}\:{of}\:{the}\:{verticle}\:{of}\:{an} \\ $$$${eqvilateral}\:{triangle}\:{with}\:{length}\:{x}\:{are} \\ $$$$\left({x}_{\mathrm{1}+} {y}_{\mathrm{1}} \right),\left({y}_{\mathrm{1}} +{y}_{\mathrm{2}} \right)\:{and}\:\left({x}_{\mathrm{3}} ,{y}_{\mathrm{3}} \right)\:{then} \\ $$$$\left(\begin{vmatrix}{{x}_{\mathrm{1}} \:\:\:{y}_{\mathrm{1}} \:\:\:\mathrm{2}}\\{{x}_{\mathrm{2}} \:\:\:{y}_{\mathrm{2}} \:\:\:\mathrm{2}}\\{{x}_{\mathrm{3}} \:\:\:{y}_{\mathrm{3}} \:\:\:\mathrm{2}}\end{vmatrix}\right)^{\mathrm{2}} =\mathrm{3}{a}^{\mathrm{4}} ? \\ $$

Question Number 32161 Answers: 1 Comments: 0

Let a function F :R→R be defined by f(x)=1+ax,α≠ 0 for all X ∈ R. Show that f is invertible and find its inverse function.Also find the value (s) of α if inverse of f is itself

$${Let}\:{a}\:{function}\:{F}\::{R}\rightarrow{R}\:{be}\:{defined}\:{by} \\ $$$${f}\left({x}\right)=\mathrm{1}+{ax},\alpha\neq\:\mathrm{0}\:{for}\:{all}\:{X}\:\in\:{R}.\:{Show} \\ $$$${that}\:{f}\:{is}\:{invertible}\:{and}\:{find}\:{its}\:{inverse} \\ $$$${function}.{Also}\:{find}\:{the}\:{value}\:\left({s}\right)\:{of}\:\alpha \\ $$$${if}\:{inverse}\:{of}\:{f}\:{is}\:{itself} \\ $$

Question Number 32160 Answers: 1 Comments: 0

If z=cosθ+isinθ is a root of equation a_0 z^n +a_1 z^(n−1) +a_2 z^(n−2) +.....+a_(n−1) z+a_n =0 then prove that: i) a_0 +a_1 cos θ+a_2 cos 2θ+.....+a_n cos nθ=0 ii) a_1 sin θ + a_2 sin 2θ+....+a_n sin nθ=0.

$$\boldsymbol{{I}}{f}\:{z}={cos}\theta+{isin}\theta\:{is}\:{a}\:{root}\:{of}\:{equation} \\ $$$${a}_{\mathrm{0}} {z}^{{n}} +{a}_{\mathrm{1}} {z}^{{n}−\mathrm{1}} +{a}_{\mathrm{2}} {z}^{{n}−\mathrm{2}} +.....+{a}_{{n}−\mathrm{1}} {z}+{a}_{{n}} =\mathrm{0} \\ $$$${then}\:{prove}\:{that}: \\ $$$$\left.{i}\right)\:{a}_{\mathrm{0}} +{a}_{\mathrm{1}} \mathrm{cos}\:\theta+{a}_{\mathrm{2}} \mathrm{cos}\:\mathrm{2}\theta+.....+{a}_{{n}} \mathrm{cos}\:{n}\theta=\mathrm{0} \\ $$$$\left.{ii}\right)\:{a}_{\mathrm{1}} \mathrm{sin}\:\theta\:+\:{a}_{\mathrm{2}} \mathrm{sin}\:\mathrm{2}\theta+....+{a}_{{n}} \mathrm{sin}\:{n}\theta=\mathrm{0}. \\ $$

Question Number 32159 Answers: 1 Comments: 2

Express the following in a+ib form: (((cos x+isin x)(cos y+isin y))/((cosa+isin a)(cosb+isinb))).

$$\boldsymbol{{E}}{xpress}\:{the}\:{following}\:{in}\:{a}+{ib}\:{form}: \\ $$$$\frac{\left(\mathrm{cos}\:{x}+{i}\mathrm{sin}\:{x}\right)\left(\mathrm{cos}\:{y}+{i}\mathrm{sin}\:{y}\right)}{\left({cosa}+{i}\mathrm{sin}\:{a}\right)\left({cosb}+{isinb}\right)}. \\ $$

Pg 1700 Pg 1701 Pg 1702 Pg 1703 Pg 1704 Pg 1705 Pg 1706 Pg 1707 Pg 1708 Pg 1709

Contact: info@tinkutara.com