Download Practice Test 3 - Basics of Mathematical Modeling - Fall 2008 | MMAT 3320 and more Exams Mathematics in PDF only on Docsity!
MMAT 3320
Test 3 4/29/08 Name
This test has 9 problems for a total of 100 points. Credit in problems marked Supporting work required is based on the completeness, clarity, and correctness of the supporting work, not just on the final “answer.” Not following the instructions in a problem may result in no credit for that problem.
Page 1 Page 2 Page 3 Page 4 Page 5 Page 6 Total
- (10 pts) Find the exact value of each of the following. To receive full credit, your work must include a carefully labelled diagram including appropriate reference triangles.
(a) csc(45◦)
(b) cot(2π/3)
- (8 pts) If sin(θ) = 2/5 and θ does not lie in Quadrant I, find the exact value of sec(θ). To receive full credit, your work must include a carefully labelled diagram with an appropriate reference triangle.
- (8 pts) Shown below is the graph of one period of y = sin(x). Sketch one period of the graph of y = sin(x − π 2 ) − 1.
- (8 pts) Shown below is the graph of one period of a sine curve. Find an equation for this sine curve.
- (12 pts) Water is poured into a bucket; the volume of water (in gallons) in the bucket t minutes after the water begins filling the bucket is given by V =
t.
(a) Complete the following table.
Beginning Ending Change Beginning Ending Change Average time time in time volume volume in volume fill rate (min) (min) (min) (gal) (gal) (gal) (gal/min)
(b) Based on your table, estimate the instantaneous rate that the bucket is being filled (gallons per minute) at time 9 minutes.
- (12 pts) A baseball is hit straight up into the air. Its height h (in feet) above the ground t seconds after being hit is given by h = 16t^2 + 40t + 5.
(a) What is the velocity of the ball 1.2 seconds after being hit?
(b) Find the maximum height above the ground that the ball achieves.
- (12 pts) Let f (x) = 3(2x + 5)^2.
(a) Use derivative rules to find and simplify the derivative f ′(x).
(b) Find the equation of the line tangent to the graph of f (x) at the point (− 1 , f (−1)).
- (16 pts) A farmer wishes to build a goat pen using 200 feet of fencing. The pen will be next to a large barn, using one side of the barn as one edge of the pen (and so no fencing is needed there). Looking down from above,
(a) If the farmer were to build a pen with the sides extending from the barn 20 feet, how long would the side parallel to the barn be if all of the fencing material was used? What would the area of this pen be?
