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Question Number 206558    Answers: 1   Comments: 0

Question Number 206557    Answers: 1   Comments: 0

Question Number 206554    Answers: 2   Comments: 0

Question Number 206550    Answers: 1   Comments: 0

calcul Residus de f en o f(z)=((ze^z )/((z−1)^2 ))

$${calcul}\:\:{Residus}\:{de}\:{f}\:{en}\:{o} \\ $$$${f}\left({z}\right)=\frac{{ze}^{{z}} }{\left({z}−\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 206549    Answers: 2   Comments: 2

∫_0 ^(+∞) (e^(−x^2 ) /((x^2 +(1/2))^2 ))dx

$$\int_{\mathrm{0}} ^{+\infty} \frac{{e}^{−{x}^{\mathrm{2}} } }{\left({x}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 206543    Answers: 1   Comments: 0

Question Number 206542    Answers: 1   Comments: 0

Question Number 206541    Answers: 1   Comments: 0

Question Number 206537    Answers: 1   Comments: 0

∫((x^4 −1)/(x^2 (√(x^4 +x^2 +1))))dx

$$\int\frac{{x}^{\mathrm{4}} −\mathrm{1}}{{x}^{\mathrm{2}} \sqrt{{x}^{\mathrm{4}} +{x}^{\mathrm{2}} +\mathrm{1}}}{dx} \\ $$

Question Number 206536    Answers: 1   Comments: 1

⋖ ♠[2^x sin ((√(4−2^(x+2) )) )

$$\:\:\:\:\underline{\underbrace{\lessdot}\cancel{} }\underbrace{\nsupseteqq\spadesuit\left[}\mathrm{2}^{{x}} \:\mathrm{sin}\:\left(\sqrt{\mathrm{4}−\mathrm{2}^{{x}+\mathrm{2}} }\:\right)\right. \\ $$

Question Number 206532    Answers: 3   Comments: 0

Find the nth term of the sequence 0,3,8,15,24,......

$${Find}\:{the}\:{nth}\:{term}\:{of}\:{the}\:{sequence} \\ $$$$\mathrm{0},\mathrm{3},\mathrm{8},\mathrm{15},\mathrm{24},...... \\ $$

Question Number 206522    Answers: 1   Comments: 0

Question Number 206514    Answers: 0   Comments: 0

In this covid −19 pandemic, it is known that are 5,667,355 confirmed cases out of 273,500,000 in X country population based WHO. One of the equipment to test the covid−19 is GeNose C19−S developed by UGM. GeNose C19−S is a rapid screening equipment for Sars−CoV2 virus infection through the breath of Covid −19 patient . It is claim that the sensivity of the test is 0,90 that is, if a person has the disease, then the probability that the diagnostic blood test comes back positive is 0,90. In addition , the specificity of the test is 0,95, i.e if a person is free the disease, then the probability that the diagnostic test comes back negative is 0,95. Let D and H is the event that a randomly selected individual has the disease and disease−free (healty), respectively. a. What is the positive predictive value of the GeNose C19−S test? That is, given that the blood test is positive for disease, what is the probability that person actually has the disease? b. If the doctor perfoms the test for the second time , taking P(D) equals to the value of probability you obtained from part a), determine the update positive predictive value of the test.

$$\:{In}\:{this}\:{covid}\:−\mathrm{19}\:{pandemic},\:{it}\:{is}\: \\ $$$$\:{known}\:{that}\:{are}\:\mathrm{5},\mathrm{667},\mathrm{355}\:{confirmed}\: \\ $$$$\:{cases}\:{out}\:{of}\:\mathrm{273},\mathrm{500},\mathrm{000}\:{in}\:{X}\:{country} \\ $$$$\:{population}\:{based}\:{WHO}.\: \\ $$$$\:{One}\:{of}\:{the}\:{equipment}\:{to}\:{test}\:{the} \\ $$$$\:{covid}−\mathrm{19}\:{is}\:{GeNose}\:{C}\mathrm{19}−{S}\:{developed} \\ $$$$\:{by}\:{UGM}.\:{GeNose}\:{C}\mathrm{19}−{S}\:{is}\:{a}\:{rapid} \\ $$$$\:{screening}\:{equipment}\:{for}\:{Sars}−{CoV}\mathrm{2} \\ $$$$\:{virus}\:{infection}\:{through}\:{the}\:{breath} \\ $$$$\:{of}\:{Covid}\:−\mathrm{19}\:{patient}\:.\:{It}\:{is}\:{claim} \\ $$$$\:{that}\:{the}\:{sensivity}\:{of}\:{the}\:{test}\:{is}\:\mathrm{0},\mathrm{90} \\ $$$$\:{that}\:{is},\:{if}\:{a}\:{person}\:{has}\:{the}\:{disease},\: \\ $$$$\:{then}\:{the}\:{probability}\:{that}\:{the}\:{diagnostic} \\ $$$$\:{blood}\:{test}\:{comes}\:{back}\:{positive} \\ $$$$\:{is}\:\mathrm{0},\mathrm{90}.\:{In}\:{addition}\:,\:{the}\:{specificity} \\ $$$$\:{of}\:{the}\:{test}\:{is}\:\mathrm{0},\mathrm{95},\:{i}.{e}\:{if}\:{a}\:{person}\: \\ $$$$\:{is}\:{free}\:{the}\:{disease},\:{then}\:{the}\:{probability} \\ $$$$\:{that}\:{the}\:{diagnostic}\:{test}\:{comes}\:{back} \\ $$$$\:{negative}\:{is}\:\mathrm{0},\mathrm{95}.\: \\ $$$$\:{Let}\:{D}\:{and}\:{H}\:{is}\:{the}\:{event}\:{that}\:{a}\: \\ $$$$\:{randomly}\:{selected}\:{individual}\:{has} \\ $$$$\:{the}\:{disease}\:{and}\:{disease}−{free}\: \\ $$$$\:\left({healty}\right),\:{respectively}. \\ $$$$\:{a}.\:{What}\:{is}\:{the}\:{positive}\:{predictive}\: \\ $$$$\:\:{value}\:{of}\:{the}\:{GeNose}\:{C}\mathrm{19}−{S}\:{test}? \\ $$$$\:\:{That}\:{is},\:{given}\:{that}\:{the}\:{blood}\:{test}\: \\ $$$$\:{is}\:{positive}\:{for}\:{disease},\:{what}\:{is}\:{the} \\ $$$$\:{probability}\:{that}\:{person}\:{actually}\:{has} \\ $$$$\:\:{the}\:{disease}?\: \\ $$$$\: \\ $$$$\:{b}.\:{If}\:{the}\:{doctor}\:{perfoms}\:{the}\:{test}\:{for} \\ $$$$\:{the}\:{second}\:{time}\:,\:{taking}\:{P}\left({D}\right)\:{equals} \\ $$$$\:{to}\:{the}\:{value}\:{of}\:{probability}\:{you} \\ $$$$\left.\:{obtained}\:{from}\:{part}\:{a}\right),\:{determine}\: \\ $$$$\:{the}\:{update}\:{positive}\:{predictive}\: \\ $$$$\:\:{value}\:{of}\:{the}\:{test}.\: \\ $$

Question Number 206511    Answers: 1   Comments: 3

Question Number 206501    Answers: 0   Comments: 9

If x^(log_3 x − 1) = log_3 x + 3 Find: log_3 x_1 + log_3 x_2 = ?

$$\mathrm{If} \\ $$$$\mathrm{x}^{\boldsymbol{\mathrm{log}}_{\mathrm{3}} \:\boldsymbol{\mathrm{x}}\:−\:\mathrm{1}} \:\:=\:\:\mathrm{log}_{\mathrm{3}} \:\mathrm{x}\:+\:\mathrm{3} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{log}_{\mathrm{3}} \:\mathrm{x}_{\mathrm{1}} \:+\:\mathrm{log}_{\mathrm{3}} \:\mathrm{x}_{\mathrm{2}} \:=\:? \\ $$

Question Number 206500    Answers: 2   Comments: 0

If asin^2 θ + bcos^2 θ = c, bsin^2 φ + acos^2 φ = d and atanθ = btanφ then prove that (1/a) + (1/b) = (1/c) + (1/d) .

$$\mathrm{If}\:{a}\mathrm{sin}^{\mathrm{2}} \theta\:+\:{b}\mathrm{cos}^{\mathrm{2}} \theta\:=\:{c},\:{b}\mathrm{sin}^{\mathrm{2}} \phi\:+\:{a}\mathrm{cos}^{\mathrm{2}} \phi\:=\:{d} \\ $$$$\mathrm{and}\:{a}\mathrm{tan}\theta\:=\:{b}\mathrm{tan}\phi\:\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{{a}}\:+\:\frac{\mathrm{1}}{{b}}\:=\:\frac{\mathrm{1}}{{c}}\:+\:\frac{\mathrm{1}}{{d}}\:. \\ $$

Question Number 206491    Answers: 2   Comments: 1

Question Number 206490    Answers: 1   Comments: 0

Resuelve la siguiente integral ∫ ((cos (t))/( ((sin^7 (t)∙cos^5 (t)))^(1/4) )) dt

$${Resuelve}\:{la}\:{siguiente}\:{integral} \\ $$$$\int\:\frac{\mathrm{cos}\:\left({t}\right)}{\:\sqrt[{\mathrm{4}}]{\mathrm{sin}^{\mathrm{7}} \left({t}\right)\centerdot\mathrm{cos}^{\mathrm{5}} \left({t}\right)}}\:{dt} \\ $$

Question Number 206489    Answers: 1   Comments: 0

Resuelve la siguiente integral ∫ ((sin (t))/( ((sin^7 (t)∙cos^5 (t)))^(1/4) )) dt

$${Resuelve}\:{la}\:{siguiente}\:{integral} \\ $$$$\int\:\frac{\mathrm{sin}\:\left({t}\right)}{\:\sqrt[{\mathrm{4}}]{\mathrm{sin}^{\mathrm{7}} \left({t}\right)\centerdot\mathrm{cos}^{\mathrm{5}} \left({t}\right)}}\:{dt} \\ $$

Question Number 206484    Answers: 1   Comments: 0

Question Number 206477    Answers: 3   Comments: 0

If a>b>0 and 4a^2 + b^2 = 4ab Find: ((a − b)/(a + b)) = ?

$$\mathrm{If}\:\:\:\mathrm{a}>\mathrm{b}>\mathrm{0}\:\:\:\mathrm{and}\:\:\:\mathrm{4a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:=\:\mathrm{4ab} \\ $$$$\mathrm{Find}:\:\:\:\frac{\mathrm{a}\:−\:\mathrm{b}}{\mathrm{a}\:+\:\mathrm{b}}\:=\:? \\ $$

Question Number 206475    Answers: 1   Comments: 0

If (a^2 /(12)) − 5b^3 = −30 Find: (2/(45)) a^2 − (8/3) b^3 = ?

$$\mathrm{If}\:\:\:\frac{\mathrm{a}^{\mathrm{2}} }{\mathrm{12}}\:−\:\mathrm{5b}^{\mathrm{3}} \:=\:−\mathrm{30} \\ $$$$\mathrm{Find}:\:\:\:\frac{\mathrm{2}}{\mathrm{45}}\:\mathrm{a}^{\mathrm{2}} \:−\:\frac{\mathrm{8}}{\mathrm{3}}\:\mathrm{b}^{\mathrm{3}} \:=\:? \\ $$

Question Number 206473    Answers: 4   Comments: 0

If 4^p = 5 Find: 2^(3p) = ?

$$\mathrm{If}\:\:\:\mathrm{4}^{\boldsymbol{\mathrm{p}}} \:=\:\mathrm{5} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{2}^{\mathrm{3}\boldsymbol{\mathrm{p}}} \:=\:? \\ $$

Question Number 206471    Answers: 1   Comments: 0

If asinθ = bcosθ = ((2ctanθ)/(1 − tan^2 θ)) then prove that (a^2 − b^2 )^2 = 4c^2 (a^2 + b^2 ).

$$\mathrm{If}\:{a}\mathrm{sin}\theta\:=\:{b}\mathrm{cos}\theta\:=\:\frac{\mathrm{2}{c}\mathrm{tan}\theta}{\mathrm{1}\:−\:\mathrm{tan}^{\mathrm{2}} \theta}\:\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{that}\:\left({a}^{\mathrm{2}} \:−\:{b}^{\mathrm{2}} \right)^{\mathrm{2}} \:=\:\mathrm{4}{c}^{\mathrm{2}} \left({a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \right). \\ $$

Question Number 206466    Answers: 1   Comments: 1

Question Number 206458    Answers: 3   Comments: 0

if f(x)=(√(x−x^2 )) then f^(−1) (x)=?

$${if}\:{f}\left({x}\right)=\sqrt{{x}−{x}^{\mathrm{2}} }\:\:\:\:\:{then}\:\:{f}^{−\mathrm{1}} \left({x}\right)=? \\ $$

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