Math 151 WIR Spring 2010 c Benjamin Aurispa Math 151 Week in Review 12 Sections 5 5 5 7 6 1 1 A farmer wants to fence in a rectangular area along a river and divide it into 3 equal sized pens with fencing perpendicular to the water He is not going to build a fence along the river If he has 120 ft of 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 1 Math 151 WIR Spring 2010 c Benjamin Aurispa 3 A 20 m wire is cut into two pieces One piece is bent into an equilateral triangle and the other is bent into a circle How should the wire be cut if at all so that the total area enclosed is a maximum minimum 2 Math 151 WIR Spring 2010 c Benjamin Aurispa 4 A company is designing a cylinder which will have a volume of 2000 cm3 Find the dimensions of the cylinder that would minimize the cost of production 3 Math 151 WIR Spring 2010 c Benjamin Aurispa 5 Find the dimensions of the largest rectangle that can be inscribed in the area bounded by the top half of the ellipse 4x2 y 2 64 and the x axis 4 Math 151 WIR Spring 2010 c Benjamin Aurispa 6 Find f x for the following a f 0 x x4 b f 0 x 5 c f 00 x 3 1 x4 x 1 cos x ex f 0 7 x2 1 x x5 4 f 0 1 5 f 0 4 x d f 00 x x 4 ex f 0 3 f 1 2 5 Math 151 WIR Spring 2010 c Benjamin Aurispa 7 A particle in motion has acceleration given by the function a t sin t t3 1 Find the position function 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 function given that v 0 3 5 and r 0 0 0 6 Math 151 WIR Spring 2010 c Benjamin Aurispa 9 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 will the car travel before reaching a speed of 60 mph 88 m s 7 Math 151 WIR Spring 2010 c Benjamin Aurispa 11 A projectile is fired with a speed of 400 m s at an angle of elevation of 30 How far away will the projectile land 12 Calculate the following sums a 5 X 2i2 3 i 1 8 Math 151 WIR Spring 2010 c Benjamin Aurispa b 35 X 3i 3i 1 i 5 c 20 X i3 i 3 d n X 3i 2 2 i 1 9 Math 151 WIR Spring 2010 c Benjamin Aurispa 13 Represent the following sum using sigma notation 14 Calculate lim n n X 4 i 1 4i 3 n n 2 4i n 10 4 9 16 25 400 7 8 9 10 25
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