WA6 - b if dr/dt is constant r 2 and dv/dt will be in...

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Robert E Goode MAT-231-GS004 Mentor: Dr. Paoletti 10/09/2011 Writing Assignment #6 Section 3.5 (6,16,20,26,34,52) and Section 3.4 (2,6,18a,20,22,24,30,32,34,44) Section 3.5 6. X 2 y+y 2 x = -3 X 2 y’_2xy+y 2 +2xyy’=0 =-y 2 -2xy=(x 2 +2xy)y’ Y’= y 2 -2xy/(x 2 +2xy) 16. coty= x-y (-csc 2 y)y’= 1-y’ Y’ = 1/(1-csc 2 y) = 1/-cot 2 y - -tan 2 y 20. In(xy)+5x=30 =lnx +lny +5x 1/x +1/yy’ +5 = 0 1/yy’ = -(1/x -5) Y’=-y/x-5y = (y+5xy)/x 26. X 3 -y 2 =0 3x 2 -2yy’=0 Y’=3x 2 /2y therefore at (1,1) y’=3/2 34. Y 2 =lnx2
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2yy’=1/x Y’=1/2xy @(e,1) y’=1/2e 52. X 2 y 2 -2x=3 2xy 2 +x 2 2yy’-2=0 Y’=(1-xy 2 )/(x 2 y) 2xyy’+x 2 (y’) 2 +2xyy’+y 2 =0 4xyy’+x 2 (y’) 2 +x 2 yy’’+y 2 =0 (4-4xy 2 )/x + (1-xy 2 ) 2 /x 2 y 2 + x 2 yy’’ + y 2 =0 X 4 y 3 y’’=2x 2 y 4 -2xy 2 -1 Y’’=2x2y 4 -2xy 2 -1/(x 4 y 3 ) Section 3.4 2. y= 2(x 2 -3x) Y’ = (4x-6)dx/dt X’=1/(4x-6) * y’ a. when x=3 and x’=2 y’ = 12 b. -5/2 6. y= 1/(1+x 2 ) X’ = 2 Y’=-2x/((1+x 2 ) 2 ) a. When x = -2, y’=8/25 cm/s b. When x=0, y’=0 c. when x=2 y’=-8/25 18.
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V=4/3πr 3 R’=2 V’=4πr 2 dr/dt a. when r = 6, dv/dt = 288π when r=24 dv/dt= 4608π
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Unformatted text preview: b. if dr/dt is constant r 2 and dv/dt will be in proportion 20. V=X 3 Dx/dt=3 Dv/dt=3x 2 dx/dt A. when x=1, dv/dt=9 b. when x=10 dv/dt = 900 22. V=πr 3 R’=2 Dv/dt=3πr 2 dr/dt a. when r =6 dv/dt = 216 b. when x=24 dv/dt = 3456π 24. V=1/3πr 2 h=1/3π25/144h 3 =25π/3*144 *h 3 Dv/dt=25π/144(h 2 ) dh/dt=144/(25πh 2 )dv/dt When h=8 dh/dt=9/10π 30. L 2 =144+x 2 2l dl/dt = 2x dx/dt Dx/dt=L/x*dl/dt = -4L/x dl/dt =-4ft/s When L=13 X= √(l 2-144) = 5 Dx/dt = -10.4ft/s b. if dx/dt = 4 dl/dt = -20/13 32. X 2 +y 2 =s 2 2x dx/dt +0 =2s ds/dt Dx/dt = s/x , x = 5√3 when s=10 Dx/dt = -277.13mph 34. S 2 =90 2 +x 2 Ds/dt = x/s dx/dt When x = 60 S = 30√13 Ds/dt=56/√13 44. Sin θ = 10/x Dx/dt= -1 ft/sec Cosθ(dθ/dt)=-10/x 2 * dx/dt Dθ/dt=-10dx/(x 2 dt)secθ = -10/25 2 (-1)25/(√25 2-10 2 ) = .017 rad/s...
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This note was uploaded on 11/15/2011 for the course MATH 231 taught by Professor Calculusi during the Fall '11 term at Thomas Edison State.

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WA6 - b if dr/dt is constant r 2 and dv/dt will be in...

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