Math 151 WIR, Spring 2010,cBenjamin AurispaMath 151 Week in Review 12Sections 5.5, 5.7, & 6.11. A farmer wants to fence in a rectangular area along a river and divide it into 3 equal-sized pens withfencing perpendicular to the water. He is not going to build a fence along the river. If he has 120 ftof fencing available to use, find the maximum area of the field.2. Find the closest point on the line y = −3x + 4 to the point (1, 5).1Math 151 WIR, Spring 2010,cBenjamin Aurispa3. A 20-m wire is cut into two pieces. One piece is bent into an equilateral triangle and the other is bentinto a circle. How should the wire be cut (if at all) so that the total area enclosed is a maximum?minimum?2Math 151 WIR, Spring 2010,cBenjamin Aurispa4. A company is designing a cylinder which will have a volume of 2000 cm3. Find the dimensions of thecylinder that would minimize the cost of production.3Math 151 WIR, Spring 2010,cBenjamin Aurispa5. Find the dimensions of the largest rectangle that can be inscribed in the area bounded by the top halfof the ellipse 4x2+ y2= 64 and the x-axis.4Math 151 WIR, Spring 2010,cBenjamin Aurispa6. Find f(x) for the following.(a) f0(x) = x4−3x4+1x(b) f0(x) = 5 +1x2+ 1+ cos x + ex, f(0) = 7(c) f00(x) =√x + x5/4x, f0(1) = 5, f(0) = 4(d) f00(x) = x − 4 − ex, f(0) = 3, f(1) = 25Math 151 WIR, Spring 2010,cBenjamin Aurispa7. A particle in motion has acceleration given by the function a(t) = sin t + t3+ 1. Find the positionfunction given that v(0) = 0 and s(0) = 3.8. An object in motion has acceleration given by a(t) =< 2, et+ 4 >. Find the position vector functiongiven that v(0) =< 3, 5 > and r(0) =< 0, 0 >.6Math 151 WIR, Spring 2010,cBenjamin Aurispa9. An object is thrown down from a 500 ft ledge with a speed of 15 ft/s.(a) Find the distance of the object above the ground at time t.(b) With what velocity does the object hit the ground?10. A car traveling at a speed of 30 mph (44 m/s) applies a constant acceleration of 8 m/s2. How far willthe car travel before reaching a speed of 60 mph (88 m/s)?7Math 151 WIR, Spring 2010,cBenjamin Aurispa11. A projectile is fired with a speed of 400 m/s at an angle of elevation of 30◦. How far away will theprojectile land?12. Calculate the following sums.(a)5Xi=1(2i2+ 3)8Math 151 WIR, Spring 2010,cBenjamin Aurispa(b)35Xi=53i− 3i+1(c)20Xi=3i3(d)nXi=1(3i + 2)29Math 151 WIR, Spring 2010,cBenjamin Aurispa13. Represent the following sum using sigma notation.47+98+169+2510+ · · · +4002514. Calculate
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