Question and Answers Forum

AllQuestion and Answers: Page 1030

Question Number 116742 Answers: 0 Comments: 0

the curve y=f(x) is rotated about the x−axis to form solid.the volume of this solid is 0.5π(a−2sina cosa) for the limit of 0≤x≤a. find the value of a

$${the}\:{curve}\:{y}={f}\left({x}\right)\:{is}\:{rotated}\:{about}\:{the} \\ $$$${x}−{axis}\:{to}\:{form}\:{solid}.{the}\:{volume}\:{of}\:{this} \\ $$$${solid}\:{is}\:\mathrm{0}.\mathrm{5}\pi\left({a}−\mathrm{2}{sina}\:{cosa}\right)\:{for}\:{the}\:{limit} \\ $$$${of}\:\mathrm{0}\leqslant{x}\leqslant{a}.\:{find}\:{the}\:{value}\:{of}\:{a} \\ $$$$ \\ $$

Question Number 116738 Answers: 1 Comments: 1

determine the area of the region bounded by y=(2x+6)^(0.5 ) and y=x−1

$${determine}\:{the}\:{area}\:{of}\:{the}\:{region}\:{bounded} \\ $$$${by}\:{y}=\left(\mathrm{2}{x}+\mathrm{6}\right)^{\mathrm{0}.\mathrm{5}\:} {and}\:{y}={x}−\mathrm{1} \\ $$

Question Number 116737 Answers: 1 Comments: 0

find the lenght of the function y=sinx for 0<x<π

$${find}\:{the}\:{lenght}\:{of}\:{the}\:{function}\:{y}={sinx}\: \\ $$$${for}\:\mathrm{0}<{x}<\pi \\ $$$$ \\ $$

Question Number 116710 Answers: 2 Comments: 0

Question Number 116701 Answers: 2 Comments: 2

∫ (dx/(x+x(√x))) =?

$$\int\:\frac{\mathrm{dx}}{\mathrm{x}+\mathrm{x}\sqrt{\mathrm{x}}}\:=? \\ $$

Question Number 116700 Answers: 1 Comments: 0

How many positive integral solutions does 3x+5y=300 have?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{positive}\:\mathrm{integral}\: \\ $$$$\mathrm{solutions}\:\mathrm{does}\:\mathrm{3x}+\mathrm{5y}=\mathrm{300}\:\mathrm{have}? \\ $$

Question Number 116695 Answers: 2 Comments: 0

Solving by Gaussian elimination using the following system of linear equation { ((x−3y−2z=6)),((2x−4y−3z=8)),((−3x+6y+8z=−5)) :}

$$\mathrm{Solving}\:\mathrm{by}\:\mathrm{Gaussian}\:\mathrm{elimination} \\ $$$$\mathrm{using}\:\mathrm{the}\:\mathrm{following}\:\mathrm{system}\:\mathrm{of} \\ $$$$\mathrm{linear}\:\mathrm{equation}\:\begin{cases}{\mathrm{x}−\mathrm{3y}−\mathrm{2z}=\mathrm{6}}\\{\mathrm{2x}−\mathrm{4y}−\mathrm{3z}=\mathrm{8}}\\{−\mathrm{3x}+\mathrm{6y}+\mathrm{8z}=−\mathrm{5}}\end{cases} \\ $$

Question Number 116687 Answers: 2 Comments: 0

Help please, to solve this ... If f(x)=1+x^2 for x∈[−2,2] and f(x)=5 otherwise. Then what is the value of ∫_(−2) ^(+2) f(2x^2 )dx?

$${Help}\:{please},\:{to}\:{solve}\:{this}\:... \\ $$$${If}\:{f}\left({x}\right)=\mathrm{1}+{x}^{\mathrm{2}} \:\:{for}\:{x}\in\left[−\mathrm{2},\mathrm{2}\right]\:{and}\: \\ $$$$\:\:\:\:\:\:{f}\left({x}\right)=\mathrm{5}\:\:\:\:\:\:\:\:{otherwise}. \\ $$$${Then}\:{what}\:{is}\:{the}\:{value}\:{of} \\ $$$$\int_{−\mathrm{2}} ^{+\mathrm{2}} {f}\left(\mathrm{2}{x}^{\mathrm{2}} \right){dx}? \\ $$$$ \\ $$

Question Number 116685 Answers: 1 Comments: 0

Given the equality: 1+3+5+...+(2p+1)=(p+1)^(2 ) p ∈ N^∗ Show this equality is true when we replace p by p+1

$$\mathrm{Given}\:\mathrm{the}\:\mathrm{equality}: \\ $$$$\mathrm{1}+\mathrm{3}+\mathrm{5}+...+\left(\mathrm{2p}+\mathrm{1}\right)=\left(\mathrm{p}+\mathrm{1}\right)^{\mathrm{2}\:} \:\:\:\mathrm{p}\:\in\:\mathbb{N}^{\ast} \\ $$$$ \\ $$$$\mathrm{Show}\:\mathrm{this}\:\mathrm{equality}\:\mathrm{is}\:\mathrm{true}\:\mathrm{when} \\ $$$$\mathrm{we}\:\mathrm{replace}\:\mathrm{p}\:\mathrm{by}\:\mathrm{p}+\mathrm{1} \\ $$

Question Number 116683 Answers: 2 Comments: 0

Given 1+3+5+7=16 we know that 16=4^2 and 4 is the half of 8 which is the successor of 7. conjecture the result of this sum: 1+3+5+7+...+25

$$\mathrm{Given}\:\mathrm{1}+\mathrm{3}+\mathrm{5}+\mathrm{7}=\mathrm{16}\:\:\:\mathrm{we}\:\mathrm{know}\:\mathrm{that} \\ $$$$\mathrm{16}=\mathrm{4}^{\mathrm{2}} \:\:\mathrm{and}\:\mathrm{4}\:\mathrm{is}\:\mathrm{the}\:\mathrm{half}\:\mathrm{of}\:\mathrm{8}\:\mathrm{which}\:\mathrm{is}\:\mathrm{the}\: \\ $$$$\mathrm{successor}\:\mathrm{of}\:\mathrm{7}. \\ $$$$ \\ $$$$\mathrm{conjecture}\:\mathrm{the}\:\mathrm{result}\:\mathrm{of}\:\mathrm{this}\:\mathrm{sum}: \\ $$$$\mathrm{1}+\mathrm{3}+\mathrm{5}+\mathrm{7}+...+\mathrm{25} \\ $$

Question Number 116674 Answers: 2 Comments: 1

Question Number 116672 Answers: 2 Comments: 0

... nice calculus ... prove that : I = ∫_0 ^( 1) ((π/4) −Arctan(x))(dx/(1−x^2 )) = (G/2) ✓ G is catalan constant ... M.N.1970

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:...\:\:\:{nice}\:\:{calculus}\:... \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{prove}\:\:{that}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \left(\frac{\pi}{\mathrm{4}}\:\:−\mathscr{A}{rctan}\left({x}\right)\right)\frac{{dx}}{\mathrm{1}−{x}^{\mathrm{2}} }\:=\:\frac{\mathrm{G}}{\mathrm{2}}\:\:\checkmark\:\:\:\: \\ $$$$\:\:\:\:\:\:\: \\ $$$$\mathrm{G}\:{is}\:\:\:{catalan}\:\:{constant}\:... \\ $$$$\:\:\:\:\:\:\:\mathscr{M}.\mathscr{N}.\mathrm{1970} \\ $$$$ \\ $$$$ \\ $$$$\:\:\: \\ $$

Question Number 116669 Answers: 1 Comments: 1

Question Number 116667 Answers: 1 Comments: 0

... nice calculus... very nice integral:: demonstrate::: Ω = ∫_0 ^( 1) ((1−x)/((1+x+x^2 +x^3 )log(x))) dx=^(???) log((√(1/2))) .m.n.1970.

$$\:\:\:\:\:\:\:\:\:\:\:\:...\:\:\:{nice}\:\:{calculus}... \\ $$$$ \\ $$$$\:\:\:\:\:\:{very}\:{nice}\:\:{integral}:: \\ $$$$\:\:\:\:\:\:\:{demonstrate}::: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{1}−{x}}{\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} +{x}^{\mathrm{3}} \right){log}\left({x}\right)}\:{dx}\overset{???} {=}{log}\left(\sqrt{\frac{\mathrm{1}}{\mathrm{2}}}\right) \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:.{m}.{n}.\mathrm{1970}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\: \\ $$

Question Number 116666 Answers: 1 Comments: 0

Question Number 116763 Answers: 0 Comments: 1

∫(dx/( ((1+x^3 ))^(1/3) ))=?

$$ \\ $$$$\:\:\:\:\:\int\frac{{dx}}{\:\sqrt[{\mathrm{3}}]{\mathrm{1}+{x}^{\mathrm{3}} }}=? \\ $$

Question Number 116759 Answers: 2 Comments: 0

Question Number 116658 Answers: 2 Comments: 2

Question Number 116717 Answers: 2 Comments: 0

∫xdx

$$\int{xdx} \\ $$

Question Number 116725 Answers: 4 Comments: 3

what the value of log _(10) (−1) in complex number

$$\mathrm{what}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{log}\:_{\mathrm{10}} \left(−\mathrm{1}\right)\:\mathrm{in}\: \\ $$$$\mathrm{complex}\:\mathrm{number} \\ $$

Question Number 116722 Answers: 1 Comments: 0

find the range of values of k for which the equation e^x −5=k has no solution

$${find}\:{the}\:{range}\:{of}\:{values}\:{of}\:{k}\:{for} \\ $$$${which}\:{the}\:{equation}\:{e}^{{x}} −\mathrm{5}={k}\:{has}\:{no} \\ $$$${solution} \\ $$

Question Number 116641 Answers: 1 Comments: 0

Question Number 116633 Answers: 1 Comments: 0

Question Number 116630 Answers: 3 Comments: 0

Given cosec x + cot x = p , find the value of cosec x =?

$$\mathrm{Given}\:\mathrm{cosec}\:\mathrm{x}\:+\:\mathrm{cot}\:\mathrm{x}\:=\:\mathrm{p}\:,\:\mathrm{find}\:\mathrm{the}\: \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{cosec}\:\mathrm{x}\:=? \\ $$

Question Number 116627 Answers: 2 Comments: 0

... nice calculus... please evaluate :: Φ = (((∫_0 ^( (π/2)) ((e^x +e^(−x) )/(sin(x)+cos(x)))dx)^2 )/((∫_0 ^( (π/2)) (e^x /(sin(x)+cos(x)))dx)(∫_0 ^( (π/2)) (e^(−x) /(sin(x)+cos(x)))dx))) =??? m.n.1970

$$\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:...\:\:{nice}\:\:\:{calculus}... \\ $$$$ \\ $$$$\:\:\:\:\:\:{please}\:\:\:{evaluate}\::: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Phi\:=\:\frac{\left(\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{{e}^{{x}} +{e}^{−{x}} }{{sin}\left({x}\right)+{cos}\left({x}\right)}{dx}\right)^{\mathrm{2}} }{\left(\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{{e}^{{x}} }{{sin}\left({x}\right)+{cos}\left({x}\right)}{dx}\right)\left(\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{{e}^{−{x}} }{{sin}\left({x}\right)+{cos}\left({x}\right)}{dx}\right)}\:=???\:\:\:\: \\ $$$$ \\ $$$$\:\:\:\:{m}.{n}.\mathrm{1970} \\ $$$$ \\ $$

Question Number 116626 Answers: 2 Comments: 0

Π_(n=1) ^∞ (((a^2 n^2 )/((an)^2 −1))))=???

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\frac{{a}^{\mathrm{2}} {n}^{\mathrm{2}} }{\left.\left({an}\right)^{\mathrm{2}} −\mathrm{1}\right)}\right)=??? \\ $$$$ \\ $$

Pg 1025 Pg 1026 Pg 1027 Pg 1028 Pg 1029 Pg 1030 Pg 1031 Pg 1032 Pg 1033 Pg 1034

Contact: info@tinkutara.com