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Question Number 74266 Answers: 0 Comments: 0

please kindly help me with the solutions to these question?very urgent please (1) if dy=x^3 dx. find the equation of y in terms of x if the curve passes through (1,1) 2) Given that the volume v(t) of cell at a time t changes according to ((dV(t))/dt)= sin t, with v(t)=4. find v(t) 3) Given (dP/dt) + 3P = 0. determine P (t) if p(0)= 4 4) Radium decomposes at a rate proportion to the amount present. if the half−life of the radium is 1000 years. what is the percentage lost in 100 years? 5) Calculate the pressure of a gas after phase transition at 171°K from 101.3kPa pressure at 472°K taking R = 0.1886kJ\kgK and L = 35.73kg

$${please}\:{kindly}\:{help}\:{me}\:{with}\:{the}\:{solutions}\:{to}\:{these}\:{question}?{very}\:{urgent}\:{please}\:\left(\mathrm{1}\right)\:{if}\:{dy}={x}^{\mathrm{3}} {dx}.\:{find}\:{the}\:{equation}\:{of}\:{y}\:{in}\:{terms}\:{of}\:{x} \\ $$$$\:{if}\:{the}\:{curve}\:{passes}\:{through}\:\left(\mathrm{1},\mathrm{1}\right) \\ $$$$\left.\mathrm{2}\right)\:{Given}\:{that}\:{the}\:{volume}\:{v}\left({t}\right)\:{of}\:{cell}\:{at}\:{a}\:{time}\:{t}\:{changes}\:{according}\:{to} \\ $$$$\frac{{dV}\left({t}\right)}{{dt}}=\:{sin}\:{t},\:{with}\:{v}\left({t}\right)=\mathrm{4}.\:{find}\:{v}\left({t}\right) \\ $$$$\left.\mathrm{3}\right)\:{Given}\:\frac{{dP}}{{dt}}\:+\:\mathrm{3}{P}\:=\:\mathrm{0}.\:{determine}\:{P}\:\left({t}\right)\: \\ $$$${if}\:{p}\left(\mathrm{0}\right)=\:\mathrm{4} \\ $$$$\left.\mathrm{4}\right)\:{Radium}\:{decomposes}\:{at}\:{a}\:{rate}\:{proportion}\:{to}\:{the}\:{amount}\: \\ $$$${present}.\:{if}\:{the}\:{half}−{life}\:{of}\:{the}\:{radium}\:{is} \\ $$$$\mathrm{1000}\:{years}.\:{what}\:{is}\:{the}\:{percentage}\:{lost}\:{in}\:\mathrm{100}\:{years}? \\ $$$$\left.\mathrm{5}\right)\:{Calculate}\:{the}\:{pressure}\:{of}\:{a}\:{gas}\:{after}\:{phase} \\ $$$${transition}\:{at}\:\mathrm{171}°{K}\:{from}\:\mathrm{101}.\mathrm{3}{kPa} \\ $$$${pressure}\:{at}\:\mathrm{472}°{K}\:{taking}\:{R}\:=\:\mathrm{0}.\mathrm{1886}{kJ}\backslash{kgK}\:{and}\:{L}\:=\:\mathrm{35}.\mathrm{73}{kg} \\ $$

Question Number 74265 Answers: 1 Comments: 0

Determine the values of m∈R for which the function f(x)=(1/(√(2x^2 −mx+m))) is the set of real numbers.

$${Determine}\:{the}\:{values}\:{of}\:{m}\in\mathbb{R}\:{for}\: \\ $$$${which}\:{the}\:{function}\:{f}\left({x}\right)=\frac{\mathrm{1}}{\sqrt{\mathrm{2}{x}^{\mathrm{2}} −{mx}+{m}}} \\ $$$${is}\:{the}\:{set}\:{of}\:{real}\:{numbers}. \\ $$

Question Number 74264 Answers: 0 Comments: 1

∫_0 ^x xe^x sin e^x e^x dx

$$\int_{\mathrm{0}} ^{{x}} {xe}^{{x}} \mathrm{sin}\:{e}^{{x}} {e}^{{x}} {dx} \\ $$

Question Number 74263 Answers: 0 Comments: 1

∫_0 ^x e^x cos e^x e^x dx

$$\int_{\mathrm{0}} ^{{x}} {e}^{{x}} \mathrm{cos}\:{e}^{{x}} {e}^{{x}} {dx} \\ $$

Question Number 74246 Answers: 2 Comments: 0

Question Number 74244 Answers: 2 Comments: 0

Find x x^(log_(4 ) (√x)) =x^(log_4 x) −2

$${Find}\:{x} \\ $$$${x}^{{log}_{\mathrm{4}\:} \sqrt{{x}}} ={x}^{{log}_{\mathrm{4}} {x}} −\mathrm{2} \\ $$

Question Number 74240 Answers: 1 Comments: 3

Question Number 74235 Answers: 3 Comments: 0

Question Number 74234 Answers: 0 Comments: 0

f(x)=(1/((4x^3 ))^(1/5) ) find f^ ′(x) with using lim_(h→0) ((f(x+h)−f(x))/h)

$${f}\left({x}\right)=\frac{\mathrm{1}}{\sqrt[{\mathrm{5}}]{\mathrm{4}{x}^{\mathrm{3}} }} \\ $$$$ \\ $$$${find}\:{f}^{\:} '\left({x}\right) \\ $$$$ \\ $$$${with}\:{using}\:\underset{{h}\rightarrow\mathrm{0}} {{lim}}\frac{{f}\left({x}+{h}\right)−{f}\left({x}\right)}{{h}} \\ $$

Question Number 74231 Answers: 1 Comments: 2

Question Number 74226 Answers: 0 Comments: 0

Question Number 74225 Answers: 1 Comments: 0

let p(x)=(1+jx)^n −(1−jx)^n with j=e^((i2π)/3) 1) determine the roots of p(x) and factorize P(x) inside C[x] 2) decompose the fraction F(x)=(1/(p(x)))

$${let}\:{p}\left({x}\right)=\left(\mathrm{1}+{jx}\right)^{{n}} −\left(\mathrm{1}−{jx}\right)^{{n}} \:\:{with}\:{j}={e}^{\frac{{i}\mathrm{2}\pi}{\mathrm{3}}} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{the}\:{roots}\:{of}\:{p}\left({x}\right)\:{and}\:{factorize}\:{P}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{2}\right)\:{decompose}\:{the}\:{fraction}\:{F}\left({x}\right)=\frac{\mathrm{1}}{{p}\left({x}\right)} \\ $$

Question Number 74224 Answers: 1 Comments: 2

find ∫ (x^2 +1)^(1/4) cos((1/2)arctan((1/x)))dx and ∫ (x^2 +1)^(1/4) sin((1/2)arctan((1/x)))dx

$${find}\:\int\:\:\:\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{4}}} \:{cos}\left(\frac{\mathrm{1}}{\mathrm{2}}{arctan}\left(\frac{\mathrm{1}}{{x}}\right)\right){dx}\:\:{and} \\ $$$$\int\:\:\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{4}}} {sin}\left(\frac{\mathrm{1}}{\mathrm{2}}{arctan}\left(\frac{\mathrm{1}}{{x}}\right)\right){dx} \\ $$

Question Number 74223 Answers: 1 Comments: 0

calculate f(a)=∫_0 ^1 (√(x^2 +ax+1))dx and g(a)=∫_0 ^1 ((xdx)/(√(x^2 +ax+1))) with ∣a∣<2 2)find the value of ∫_0 ^1 (√(x^2 +(√2)x+1))dx and ∫_0 ^1 ((xdx)/(√(x^2 +(√2)x+1)))

$${calculate}\:\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{{x}^{\mathrm{2}} +{ax}+\mathrm{1}}{dx}\:\:\:{and}\:{g}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{xdx}}{\sqrt{{x}^{\mathrm{2}} +{ax}+\mathrm{1}}} \\ $$$${with}\:\:\mid{a}\mid<\mathrm{2} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{{x}^{\mathrm{2}} +\sqrt{\mathrm{2}}{x}+\mathrm{1}}{dx}\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{xdx}}{\sqrt{{x}^{\mathrm{2}} +\sqrt{\mathrm{2}}{x}+\mathrm{1}}} \\ $$

Question Number 74219 Answers: 0 Comments: 0