Topic 8: Line of Best Fit 28. The number of students enrolled at Beach Manor Preschool during various years is given in the Use the line of best fit to predict the number of students enrolled in 2010. table below. Year 1984 Entrants 39 1990 1987 45 52 1993 61 1996 72 1999 78 2002 85

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A: (a) ∫145x2x3-2dx Let x3-2=y dy=3x22x3-2dx⇒2x3-23x2dy=dx ∴∫145x2x3-2dx=∫i62103y2dy=109y3i62=109623+i

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A: (a) Given fx=a3x3+a2x2+a1x+a0 Given SIMPf,n-∫abfxdx≤b-a5180n4maxx∈a,bfivx…

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Q: perimeter P. 8. An equilateral triangle has the same perimeter as a regular pentagon. Find the side…

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Q: Show that You may take for granted that max z€0,2 VI -in

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Q: 3. Use cylindrical coordinates to compute the integral Z !!! √x² + ² dv D where D is the solid…

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Q: ou decide to make monthly payments into a retirement fund earning 4.75% compounded monthly.  Note:…

A: Given  monthly deposit =$130 rate =4.75% compounded monthly amount =$353000 Formula  A=P1+rnnt-1rn

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Q: 1. Consider the region R bounded by y = x² and y = 3x a. What is the area of R? b. What is perimeter…

A: According to the Bartleby guidelines,I solved only first 3 subparts.

Q: 1. Consider the region R bounded by y = x² and y = 3x a. What is the area of R? b. What is perimeter…

A: V=2π∫03x3x-x2dx   =2π∫033x2-x3dx   =2πx3-x4403   =2π27-814   =13.5π

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Q: 200a -24b -44c -39d 8e 14f -16g 4h 44i 3j 40a 250b -50c 2d 14e -22f 23g 18h -23i 45j 5a -40b 180c…

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Q: 3. Let f(z) = sin z where z € C. Determine where f is differentiable and show that f'(z) = = - cos x…

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Q: 5. Prove using Venn Diagram X u (YNZ) = (XUY) N (Xu Z) O a с B B O C B

A: We can solve as follows

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A: Look at domain ,range of the function. If f is one one, onto in that domain then f has inverse.

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Q: Prove that bx c+1 ax² + (x-a) (x −b) (x-c) (x-b) (x-c) x-c 11 x³ + + (x-a)(x-b)(x-c)

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Q: .

A: Given: A=1111 To solve parts (a) , (b) and (c)

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Q: For ony d If'(x)) (V) (x)) SIMP (fin) - f(x) dx | ≤ (b-a) 5 180n4 ETabyl max b where RIGHT(fin) is…

A: (a) Given fx=a3x3+a2x2+a1x+a0 Simpf,n-∫abfxdx≤b-a5180n4maxx∈a,bfivx…