Question and Answers Forum

All Questions Topic List

AllQuestion and Answers: Page 1839

Question Number 25728 Answers: 1 Comments: 3

Question Number 25726 Answers: 0 Comments: 1

x−3=11

$${x}−\mathrm{3}=\mathrm{11} \\ $$

Question Number 25702 Answers: 1 Comments: 1

Question Number 25700 Answers: 0 Comments: 1

Question Number 25689 Answers: 0 Comments: 0

Question Number 25684 Answers: 1 Comments: 0

For a geosynchronous satellite of mass m moving in a circular orbit around the earth at a constant speed v and an altitude h above the earth surface.Show the velocity v=(((GM_e )/(R_e +h)))^(1/2) . If the satellite above is synchronous how fast is it moving through space,taking the period to be 24hrs and M_e =mass of the satellite and is equal to 5.98×10^(24) kg

$${For}\:{a}\:{geosynchronous}\:{satellite}\:{of} \\ $$$${mass}\:{m}\:{moving}\:{in}\:{a}\:{circular} \\ $$$${orbit}\:{around}\:{the}\:{earth}\:{at}\:{a}\:{constant} \\ $$$${speed}\:{v}\:{and}\:{an}\:{altitude}\:{h}\:{above} \\ $$$${the}\:{earth}\:{surface}.{Show}\:{the} \\ $$$${velocity}\:{v}=\left(\frac{{GM}_{{e}} }{{R}_{{e}} +{h}}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} . \\ $$$$ \\ $$$${If}\:{the}\:{satellite}\:{above}\:{is}\:{synchronous} \\ $$$${how}\:{fast}\:{is}\:{it}\:{moving}\:{through} \\ $$$${space},{taking}\:{the}\:{period}\:{to}\:{be}\:\mathrm{24}{hrs} \\ $$$${and}\:{M}_{{e}} ={mass}\:{of}\:{the}\:{satellite}\:{and} \\ $$$${is}\:{equal}\:{to}\:\mathrm{5}.\mathrm{98}×\mathrm{10}^{\mathrm{24}} {kg} \\ $$

Question Number 25683 Answers: 0 Comments: 0

find the value of ∫_0 ^∞ sin(x^n )( 1 + x^2 )^(−1) dx

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:{sin}\left({x}^{{n}} \:\right)\left(\:\mathrm{1}\:+\:{x}^{\mathrm{2}} \right)^{−\mathrm{1}} {dx} \\ $$

Question Number 25682 Answers: 1 Comments: 0

we give ∫_0 ^∞ t^(a−1) (1 + t)^(−1) dt =π (sin(πa))^(−1) with 0<a<1 find the value of ∫_0 ^∞ (1 +x^(16) )^(−1) dx

$${we}\:{give}\:\int_{\mathrm{0}} ^{\infty} \:{t}^{{a}−\mathrm{1}} \left(\mathrm{1}\:+\:{t}\right)^{−\mathrm{1}} {dt}\:=\pi\:\left({sin}\left(\pi{a}\right)\right)^{−\mathrm{1}} \:{with}\:\mathrm{0}<{a}<\mathrm{1}\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\left(\mathrm{1}\:+{x}^{\mathrm{16}} \right)^{−\mathrm{1}} {dx} \\ $$

Question Number 25680 Answers: 0 Comments: 0

let p(X) = (1 +iX )^(n) − ( 1 − iX )^(n) if p(X ) =∝Σ ( X −xk) find xk and α

$${let}\:{p}\left({X}\right)\:=\:\left(\mathrm{1}\:+{iX}\:\overset{{n}} {\right)}\:−\:\left(\:\mathrm{1}\:−\:{iX}\:\overset{{n}} {\right)}\:\:{if}\:\:{p}\left({X}\:\right)\:=\propto\Sigma\:\left(\:{X}\:−{xk}\right)\:\:{find}\:{xk}\:{and}\:\alpha \\ $$

Question Number 25677 Answers: 0 Comments: 0

let 0<x<1 find the value of F(x) = ∫ ln (1+x cost)dt fromt=0 to t=pi

$${let}\:\mathrm{0}<{x}<\mathrm{1}\:\:{find}\:{the}\:{value}\:{of}\:{F}\left({x}\right)\:=\:\int\:\mathrm{ln}\:\left(\mathrm{1}+{x}\:{cost}\right){dt}\:{fromt}=\mathrm{0}\:{to}\:{t}={pi} \\ $$

Question Number 25676 Answers: 0 Comments: 0

find the value of ∫_0 ^∞ sin(x^ n )/x^ 2 + 1 dx

$$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{value}}\:\boldsymbol{{of}}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\boldsymbol{{sin}}\left(\hat {\boldsymbol{{x}}}{n}\:\right)/\hat {{x}}\mathrm{2}\:+\:\mathrm{1}\:{dx} \\ $$

Question Number 25675 Answers: 1 Comments: 1

Question Number 25667 Answers: 0 Comments: 2

Deepak srarts a work and work for 12 days and find he has ompleted 10% less work which he had to finish in order to complete the work in 24 days,^ so he ask Rahman to join him to finish the work on time . If Rahman work half day only for the remaining days. Find the efficiency of Rahman is what percent less then the efficiency of Deepak ?

$$\mathrm{Deepak}\:\mathrm{srarts}\:\mathrm{a}\:\mathrm{work}\:\mathrm{and}\:\mathrm{work}\:\mathrm{for}\:\mathrm{12} \\ $$$$\mathrm{days}\:\mathrm{and}\:\mathrm{find}\:\mathrm{he}\:\mathrm{has}\:\mathrm{ompleted}\:\mathrm{10\%}\: \\ $$$$\mathrm{less}\:\mathrm{work}\:\mathrm{which}\:\mathrm{he}\:\mathrm{had}\:\mathrm{to}\:\mathrm{finish}\:\mathrm{in}\: \\ $$$$\mathrm{order}\:\mathrm{to}\:\mathrm{complete}\:\mathrm{the}\:\mathrm{work}\:\mathrm{in}\:\mathrm{24}\:\mathrm{days}\bar {,} \\ $$$$\mathrm{so}\:\mathrm{he}\:\mathrm{ask}\:\mathrm{Rahman}\:\mathrm{to}\:\mathrm{join}\:\mathrm{him}\:\mathrm{to}\:\mathrm{finish} \\ $$$$\mathrm{the}\:\mathrm{work}\:\mathrm{on}\:\mathrm{time}\:.\:\mathrm{If}\:\mathrm{Rahman}\:\mathrm{work}\: \\ $$$$\mathrm{half}\:\mathrm{day}\:\mathrm{only}\:\mathrm{for}\:\mathrm{the}\:\mathrm{remaining}\:\mathrm{days}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{efficiency}\:\mathrm{of}\:\mathrm{Rahman}\:\mathrm{is}\:\mathrm{what} \\ $$$$\mathrm{percent}\:\mathrm{less}\:\mathrm{then}\:\mathrm{the}\:\mathrm{efficiency}\:\mathrm{of} \\ $$$$\mathrm{Deepak}\:? \\ $$

Question Number 27181 Answers: 0 Comments: 1

find the value of ∫_0 ^(∝ ) ((ln(1+t^2 ))/(1−t^2 )) dt

$${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\propto\:} \frac{{ln}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}{\mathrm{1}−{t}^{\mathrm{2}} }\:{dt} \\ $$

Question Number 27180 Answers: 0 Comments: 1

find the value of ∫∫_D (x^2 /y^2 ) dxdy with D ={(x ,y)∈R^2 / 1≤x≤2 and (1/x)≤y≤ x }.

$${find}\:{the}\:{value}\:{of}\:\:\int\int_{{D}} \:\:\frac{{x}^{\mathrm{2}} }{{y}^{\mathrm{2}} }\:{dxdy}\:\:{with} \\ $$$${D}\:=\left\{\left({x}\:,{y}\right)\in\mathbb{R}^{\mathrm{2}} \:/\:\:\:\mathrm{1}\leqslant{x}\leqslant\mathrm{2}\:\:{and}\:\:\frac{\mathrm{1}}{{x}}\leqslant{y}\leqslant\:{x}\:\:\right\}. \\ $$

Question Number 25660 Answers: 0 Comments: 1

Question Number 25656 Answers: 0 Comments: 3

trace the curve y^2 (x+1)=x^2 (3−x) clearly stating all the properties used for tracing.

$${trace}\:{the}\:{curve}\: \\ $$$${y}^{\mathrm{2}} \left({x}+\mathrm{1}\right)={x}^{\mathrm{2}} \left(\mathrm{3}−{x}\right) \\ $$$${clearly}\:{stating}\:{all}\:{the}\:{properties}\:{used} \\ $$$${for}\:{tracing}. \\ $$

Question Number 25655 Answers: 0 Comments: 0

use lagranges mean value theorem to prove that x<sin^(−1) x<(x/(√(1−x^2 ))),0<x<1.

$${use}\:{lagranges}\:{mean}\:{value}\:{theorem}\:{to} \\ $$$${prove}\:{that}\: \\ $$$${x}<{sin}^{−\mathrm{1}} {x}<\frac{{x}}{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }},\mathrm{0}<{x}<\mathrm{1}. \\ $$

Question Number 25718 Answers: 0 Comments: 8

Question Number 25723 Answers: 0 Comments: 0

Given a_1 , a_2 , ..., a_n are non−negative integers and satisfy (1/2^a_1 ) + (1/2^a_2 ) + ... + (1/2^a_n ) = (1/3^a_1 ) + (2/3^a_2 ) + ... + (n/3^a_n ) = 1 If n is positive integer, find all possible solution of n

$$\mathrm{Given}\:{a}_{\mathrm{1}} ,\:{a}_{\mathrm{2}} ,\:...,\:{a}_{{n}} \:\mathrm{are}\:\mathrm{non}−\mathrm{negative} \\ $$$$\mathrm{integers}\:\mathrm{and}\:\mathrm{satisfy} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}^{{a}_{\mathrm{1}} } }\:+\:\frac{\mathrm{1}}{\mathrm{2}^{{a}_{\mathrm{2}} } }\:+\:...\:+\:\frac{\mathrm{1}}{\mathrm{2}^{{a}_{{n}} } }\:=\:\frac{\mathrm{1}}{\mathrm{3}^{{a}_{\mathrm{1}} } }\:+\:\frac{\mathrm{2}}{\mathrm{3}^{{a}_{\mathrm{2}} } }\:+\:...\:+\:\frac{{n}}{\mathrm{3}^{{a}_{{n}} } }\:=\:\mathrm{1}\: \\ $$$$\mathrm{If}\:{n}\:\mathrm{is}\:\mathrm{positive}\:\mathrm{integer},\:\mathrm{find}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{solution} \\ $$$$\mathrm{of}\:{n}\: \\ $$

Question Number 25638 Answers: 0 Comments: 1

Question Number 25635 Answers: 0 Comments: 1

let f be the function defined on [−1,1] by f(x)={ { ((−1,if x is rational)),((1,if x is irrational.)) :} find U(P,f) and L(P,f).f is integrable or not ?

$${let}\:{f}\:{be}\:{the}\:{function}\:{defined}\:{on} \\ $$$$\left[−\mathrm{1},\mathrm{1}\right]\:{by} \\ $$$${f}\left({x}\right)=\left\{\begin{cases}{−\mathrm{1},{if}\:{x}\:{is}\:{rational}}\\{\mathrm{1},{if}\:{x}\:{is}\:{irrational}.}\end{cases}\right. \\ $$$${find}\:{U}\left({P},{f}\right)\:{and}\:{L}\left({P},{f}\right).{f}\:{is}\:{integrable} \\ $$$${or}\:{not}\:? \\ $$

Question Number 25634 Answers: 1 Comments: 0

find the equation of the tangent to the curve (√x)+(√y)=(√a) at any point (x,y)on it.

$${find}\:{the}\:{equation}\:{of}\:{the}\:{tangent}\:{to}\: \\ $$$${the}\:{curve}\:\sqrt{{x}}+\sqrt{{y}}=\sqrt{{a}}\:{at}\:{any}\:{point} \\ $$$$\left({x},{y}\right){on}\:{it}. \\ $$

Question Number 25630 Answers: 1 Comments: 0

Question Number 25628 Answers: 0 Comments: 0

Question Number 25623 Answers: 1 Comments: 0

solve for A and B if 2A+B [((6 3)),((6 −2)) ] and 3A+2B [((1 0)),((0 5)) ]

$${solve}\:{for}\:{A}\:{and}\:{B}\:{if}\:\mathrm{2}{A}+{B}\:\begin{bmatrix}{\mathrm{6}\:\:\:\mathrm{3}}\\{\mathrm{6}\:\:−\mathrm{2}}\end{bmatrix} \\ $$$${and}\:\mathrm{3}{A}+\mathrm{2}{B}\:\begin{bmatrix}{\mathrm{1}\:\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\:\mathrm{5}}\end{bmatrix} \\ $$

Pg 1834 Pg 1835 Pg 1836 Pg 1837 Pg 1838 Pg 1839 Pg 1840 Pg 1841 Pg 1842 Pg 1843

Contact: info@tinkutara.com