For the vectors u 4 2 and v 5 4 calculate proj u and scal u

3 85 8 190 9 230

Determine whether the following statements are true and give an explanation or counterexample Assume x 0 and y 0 a In xy Inx Iny b In 0 1 c In x y Inx Iny d 2 2Inx 1 e The area under the curve y and above the x axis on the interval 1 e is 1 a Choose the correct answer below OA The statement is false because In 35 In 5 In 7 OB The statement is true For x 0 and y 0 In xy Inx In y by the Product Rule of Logarithms OC The statement is false because In 5 In 7 In 5 7 OD The statement is true For x 0 and y 0 In xy Inx In y by the Quotient Rule of Logarithms

Problem 1 Use the method of cylindrical shells to find the volume when the region bounded by y 1 x x 0 x 1 and the x axis and rotated around the y axis

Water has a density of 1 0 g mL Which of these objects will float in water Object I mass 50 0 g volume 53 1 mL Object II mass 71 7 g volume 51 4 mL Object III mass 100 0 g volume 50 0 mL OI only O I III II only O II III

Evaluate the indicated function for f x x2 1 and g x x 3 algebraically If possible use a graphing utility to verify yo answer f g t 5

Use a graphing utility to graph the three functions in the same viewing window f x x 3x 2 g x f x h x f 3x Describe the graph of g relative to the graph of f O g x is a reflection in the y axis O g x is a horizontal shrink O g x is a reflection in the x axis O g x is a horizontal stretch Describe the graph of h relative to the graph of f Oh x is a reflection in the x axis Oh x is a reflection in the y axis O h x is a horizontal stretch O h x is a horizontal shrink

For each problem below the magnitude of the horizontal and vertical components of vector V are given In each case find the magnitude of V 27 Vx 30 V 40 29 Vx 35 0 V 26 0 31 Vx 4 5 V 3 8 28 V8 Vyl 6 30 Vx 45 0 V 15 0 32 Vx 2 2 V 5 8 33 Velocity A bullet is fired into the air with an initial velocity of 1 200 feet per second at an angle of 45 from the horizontal Find the magnitude of the horizontal and vertical components of the velocity vector 34 Velocity A bullet is fired into the air with an initial velocity of 1 800 feet per second at an angle of 60 from the horizontal Find the horizontal and vertical components of the velocity 35 Velocity Use the results of Problem 33 to find the horizontal distance traveled by the bullet in 3 seconds Neglect the resistance of air on the bullet 36 Velocity Use the results of Problem 34 to find the horizontal distance traveled by the bullet in 2 seconds 37 Velocity An arrow is shot into the air so that its horizontal velocity is 35 0 feet per second and its vertical velocity is 15 0 feet per second Find the velocity of the arrow

For each problem below the magnitude of the horizontal and vertical components of vector V are given In each case find the magnitude of V 27 Vx 30 V 40 29 Vx 35 0 V 26 0 28 Vx 8 V 6 30 Vx 45 0 V 15 0

Each problem below refers to a vector V with magnitude V that forms an angle with the positive x axis In each case give the magnitude of the horizontal and vertical components of V 19 V 40 0 30 21 V 13 8 0 24 2 23 V 420 0 36 10 20 V 40 0 60 22 V 17 6 0 67 2 24 V 380 0 16 40

Draw vectors representing the following velocities 1 30 miles per hour due north 2 30 miles per hour due south 3 30 miles per hour due east 4 30 miles per hour due west 5 50 centimeters per second N 30 W 6 50 centimeters per second N 30 E