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Question Number 94756    Answers: 0   Comments: 2

solution: Q1)a) n=((ln(m/m_0 ))/(ln0.5)) = ((ln(12/75))/(ln0.5)) =2.64 N=N_0 (0.5)^n = 6.02×10^(23) (0.5)^(2.64) = 9.66×10^(22) A=λN=1.5×10^(−4) × 9.66×10^(22) =1.45×10^(19) Bq

$$\left.{s}\left.{olution}:\:\mathrm{Q1}\right){a}\right)\:{n}=\frac{{ln}\left({m}/{m}_{\mathrm{0}} \right)}{{ln}\mathrm{0}.\mathrm{5}}\:=\:\frac{{ln}\left(\mathrm{12}/\mathrm{75}\right)}{{ln}\mathrm{0}.\mathrm{5}}\:=\mathrm{2}.\mathrm{64} \\ $$$${N}=\mathrm{N}_{\mathrm{0}} \left(\mathrm{0}.\mathrm{5}\right)^{{n}} \:=\:\mathrm{6}.\mathrm{02}×\mathrm{10}^{\mathrm{23}} \left(\mathrm{0}.\mathrm{5}\right)^{\mathrm{2}.\mathrm{64}} =\:\mathrm{9}.\mathrm{66}×\mathrm{10}^{\mathrm{22}} \\ $$$${A}=\lambda{N}=\mathrm{1}.\mathrm{5}×\mathrm{10}^{−\mathrm{4}} \:×\:\mathrm{9}.\mathrm{66}×\mathrm{10}^{\mathrm{22}} =\mathrm{1}.\mathrm{45}×\mathrm{10}^{\mathrm{19}} \:{Bq} \\ $$

Question Number 94752    Answers: 0   Comments: 1

Find the volume of the region bounded above by the surface z=x and below by the region x^2 +y^2 −2y=0 ? pleas sir can you help me becouse im very nedd ?

$${Find}\:{the}\:{volume}\:{of}\:{the}\:{region}\:{bounded}\:{above}\:{by}\:{the}\:{surface}\:{z}={x} \\ $$$${and}\:{below}\:{by}\:{the}\:{region}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{2}{y}=\mathrm{0}\:? \\ $$$${pleas}\:{sir}\:{can}\:{you}\:{help}\:{me}\:{becouse}\:{im}\:{very}\:{nedd}\:? \\ $$

Question Number 94742    Answers: 0   Comments: 1

Question Number 94739    Answers: 2   Comments: 2

Question Number 94735    Answers: 0   Comments: 9

∫((2t)/((1+t^4 )(1+t)))dt=?

$$\int\frac{\mathrm{2t}}{\left(\mathrm{1}+\mathrm{t}^{\mathrm{4}} \right)\left(\mathrm{1}+\mathrm{t}\right)}\mathrm{dt}=? \\ $$

Question Number 94753    Answers: 1   Comments: 0

Question Number 94730    Answers: 2   Comments: 0

Question Number 94723    Answers: 2   Comments: 0

lim_(x→0) ((∫_0 ^x^2 (√(4+t^3 )) dt)/x^2 ) ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\underset{\mathrm{0}} {\overset{{x}^{\mathrm{2}} } {\int}}\:\sqrt{\mathrm{4}+{t}^{\mathrm{3}} \:}\:{dt}}{{x}^{\mathrm{2}} }\:?\: \\ $$

Question Number 94718    Answers: 0   Comments: 4

∫ (√(tan x)) dx = ∫(((√(tan x))+(√(cot x)))/2) dx + ∫ (((√(tan x))−(√(cot x)))/2) dx =(1/((√2) ))∫ ((sin x+cos x)/(√(sin 2x))) dx + (1/((√2) ))∫ ((sin x−cos x)/(√(sin 2x))) dx = (1/((√2) ))∫ ((sin x+cos x)/(√(1−(sin x−cos x)^2 ))) dx + (1/(√2)) ∫ ((sin x−cos x)/(√((sin x+cos x)^2 −1))) dx = (1/((√2) ))∫ (dt/(√(1−t^2 ))) +(1/((√2) ))∫ ((−du)/(√(u^2 −1))) = (1/((√2) ))sin^(−1) (t) −(1/(√2)) ln(u+(√(u^2 −1))) +c = (1/(√2)) sin^(−1) (sin x−cos x)− (1/(√2)) ln (sin x+cos x+(√(sin 2x))) + c where t = sin x−cos x ; u = sin x+cos x

$$\int\:\sqrt{\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}\:= \\ $$$$\int\frac{\sqrt{\mathrm{tan}\:\mathrm{x}}+\sqrt{\mathrm{cot}\:\mathrm{x}}}{\mathrm{2}}\:\mathrm{dx}\:+\:\int\:\frac{\sqrt{\mathrm{tan}\:\mathrm{x}}−\sqrt{\mathrm{cot}\:\mathrm{x}}}{\mathrm{2}}\:\mathrm{dx} \\ $$$$=\frac{\mathrm{1}}{\sqrt{\mathrm{2}}\:}\int\:\frac{\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}}{\sqrt{\mathrm{sin}\:\mathrm{2x}}}\:\mathrm{dx}\:+\:\frac{\mathrm{1}}{\sqrt{\mathrm{2}}\:}\int\:\frac{\mathrm{sin}\:\mathrm{x}−\mathrm{cos}\:\mathrm{x}}{\sqrt{\mathrm{sin}\:\mathrm{2x}}}\:\mathrm{dx} \\ $$$$=\:\frac{\mathrm{1}}{\sqrt{\mathrm{2}}\:}\int\:\frac{\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}}{\sqrt{\mathrm{1}−\left(\mathrm{sin}\:\mathrm{x}−\mathrm{cos}\:\mathrm{x}\right)^{\mathrm{2}} }}\:\mathrm{dx}\:+\: \\ $$$$\frac{\mathrm{1}}{\sqrt{\mathrm{2}}}\:\int\:\frac{\mathrm{sin}\:\mathrm{x}−\mathrm{cos}\:\mathrm{x}}{\sqrt{\left(\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}\right)^{\mathrm{2}} −\mathrm{1}}}\:\mathrm{dx}\: \\ $$$$=\:\frac{\mathrm{1}}{\sqrt{\mathrm{2}}\:}\int\:\frac{\mathrm{dt}}{\sqrt{\mathrm{1}−\mathrm{t}^{\mathrm{2}} }}\:+\frac{\mathrm{1}}{\sqrt{\mathrm{2}}\:}\int\:\frac{−\mathrm{du}}{\sqrt{\mathrm{u}^{\mathrm{2}} −\mathrm{1}}} \\ $$$$=\:\frac{\mathrm{1}}{\sqrt{\mathrm{2}}\:}\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{t}\right)\:−\frac{\mathrm{1}}{\sqrt{\mathrm{2}}}\:\mathrm{ln}\left(\mathrm{u}+\sqrt{\mathrm{u}^{\mathrm{2}} −\mathrm{1}}\right)\:+\mathrm{c} \\ $$$$=\:\frac{\mathrm{1}}{\sqrt{\mathrm{2}}}\:\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{sin}\:\mathrm{x}−\mathrm{cos}\:\mathrm{x}\right)− \\ $$$$\frac{\mathrm{1}}{\sqrt{\mathrm{2}}}\:\mathrm{ln}\:\left(\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}+\sqrt{\mathrm{sin}\:\mathrm{2x}}\right)\:+\:\mathrm{c}\: \\ $$$$\mathrm{where}\:\mathrm{t}\:=\:\mathrm{sin}\:\mathrm{x}−\mathrm{cos}\:\mathrm{x}\:;\: \\ $$$$\mathrm{u}\:=\:\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}\: \\ $$

Question Number 94710    Answers: 1   Comments: 2

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Question Number 94705    Answers: 0   Comments: 1

a set X had one more subset than set Y. If X has 8 more subsets than Y. Find the number if element in the set X.

$$\mathrm{a}\:\mathrm{set}\:\mathrm{X}\:\mathrm{had}\:\mathrm{one}\:\mathrm{more}\:\mathrm{subset}\:\mathrm{than}\:\mathrm{set}\:\mathrm{Y}. \\ $$$$\mathrm{If}\:\mathrm{X}\:\mathrm{has}\:\mathrm{8}\:\mathrm{more}\:\mathrm{subsets}\:\mathrm{than}\:\mathrm{Y}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{if}\:\mathrm{element}\:\mathrm{in}\:\mathrm{the}\:\mathrm{set}\:\mathrm{X}. \\ $$

Question Number 94701    Answers: 0   Comments: 3

what is the volume of x^2 +y^2 +z^2 =2

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} =\mathrm{2} \\ $$$$ \\ $$

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Find the supremum and infimum of A = { n ∣ 3 + (2/n) , n ∈ R }

$${Find}\:\:{the}\:\:{supremum}\:\:{and}\:\:{infimum}\:\:{of}\:\: \\ $$$${A}\:\:=\:\:\left\{\:{n}\:\mid\:\:\mathrm{3}\:+\:\frac{\mathrm{2}}{{n}}\:\:,\:\:{n}\:\in\:\:\mathbb{R}\:\:\right\} \\ $$

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