Engineering Mathematics Assignment

Added on - 21 Apr 2020

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Engineering MathematicsStudent Name:University21stJanuary 2018
Task 1:1)Simplify6x2+7x5x1by dividing.Solution6x2+7x5x1=6x2+10x3x5x1=2x(3x+5)1(3x+5)x1=(3x+5)(2x1)x1=2(3x+5)2)Resolve the following into partial fractions.a)x11x2x2Solutionx2x2=x22x+x2=x(x2)+1(x2)=(x+1)(x2)x11x2x2=x11(x+1)(x2)=Ax+1+Bx2x11(x+1)(x2)=A(x2)+B(x+1)(x+1)(x2)x11=A(x2)+B(x+1)x11=Ax2A+Bx+Bx=Ax+BxA+B=12A+B=113A=12A=44+B=1B=3Thus the answer is;Ax+1+Bx2=4x+13x24x+13x2b)
3x(x¿¿2+3)(x+3)¿Solution3x(x¿¿2+3)(x+3)=A(x¿¿2+3)+B(x+3)+Cx=A+B+Cx3+3x2+3x+9=A+B+Cx2(x+3)+3(x+3)=A+B+Cx2(x+3)+3(x+3)¿¿3x(x¿¿2+3)(x+3)=A(x+3)+B(x¿¿2+3)+Cx(x¿¿2+3)(x+3)¿¿¿3x=A(x+3)+B(x¿¿2+3)+Cx¿3x=Ax+3A+Bx2+3B+CxAx+2Bx=xAB=13A+3B=34A=2A=1212B=1B=32C=1Thus the answer is;A(x¿¿2+3)+B(x+3)=1/2(x¿¿2+3)+3/2(x+3)¿¿Task 2:3)We have;Temp, t(mins)246810Temp185161140122106
CurveThe body cools according to the Newton’s law following the following equation;θ(t)=θ0ektThe initial temperature of the body is 201.9Usingexcel,weareabletocomputetheequationθ(t)=θ0ektand the answer is given below;Thus the equation is;θ(t)=212.63e0.07tTime it takes the body to reach 500C is;θ(t)=212.63e0.07t=50e0.07t=50212.63=0.23515ln(e0.07t)=ln(0.23515)0.07tln(e)=ln(0.23515)Thenatural logarithmofeis1.
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