4.1.10Using similar triangles10 x + y=6y3x= y2Differentiating,dx 3 dy=dt 2 dtwhendy=3dtdx 3= 3 = 4.5dt 2rate =dy dx+= 3 + 4.5 = 7dt dtRate of shadow moving is 7.5ft/s4.1.16V = x3dv 3x 2 dx=dtdtGivendx= 0.5 and x = 4dtdv1= 3 42 = 24dt2Volume increasing at rate of 24 m3 /s4.1.26r5=h 16r=5h16Find the surface area S of the cone asS = rl + r 2= rr 2 + h2 + r 2= (55 25 2h) ( h) + h2 + ( h)161616getting the derivativeS=528125h+h2256256ds5281 dh 25dh=+2hdt256 dt 256dtds5281 dh 25dh=+hdt256 dt 128dtdh= 10 and h = 10dtds528125=(10) +(10)(10)dt256128= 71.64Surface area of the water is deceasing at rate of 71.64 ft 2/min4.1.30b 3=h 43b= h4Volume of the gas1V = bh 102315 2= 5 h h =h44Getting derivativedv 15dh= 2h dt4dt=15h dh2 dtdv=5dth=15=15 dh2 dt2 dh=3 dtheight of the water is increasing at rate of4.1.38tan =x40Getting the derivative,sec 2 d1 dx=dt 40 dt(1 + tan2 )d1 dx=dt40 dtx 2d1 dx(1 + ( ) ) ==40dt 40 dtd40dx= 2dt x + 1600 dtGiven,dx= 20 and x = 30dtd40= 2 20dt 30 + 1600d8=rad/sdt 254.1.44z 2 = 902 + 602z = 3013Getting derivative of z 2 = x 2 + 9022m/min32Zdzdx= 2xdtdtdz x dx=dt z dtGiven,dx= 22, x = 60 and z = 3013dtdz60=(22)dt ...

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