MS 101 Alg & Trig test three midterm • 20 June 2014 • Name:

1. Use a spreadsheet to make an xy scatter graph of the following speed versus coefficient of drag data for a Brazuca soccer ball. Note that the actual function for the coefficient of drag is not logarithmic. A logarithmic curve is being used for the purposes of this test only.

   Speed (km/hour)	Coefficient of drag
   23	0.49
   40	0.40
   47	0.20
   62	0.18
   123	0.20

   1. Add a LOGARITHMIC trend line and equation to the graph. Write the logarithmic equation below:
   2. __________ Based on the logarithmic equation in part a, what will be the coefficent of drag at 100 kilometers per hour?
   3. __________ Based on the logarithmic equation in part a, at what speed will the coefficient of drag be 0.30?
2. Either make the calculation or solve for x as appropriate. Round answers to two decimal places.
   1. ____________ log₇1
   2. ____________ ln x = 1.0986123
   3. ____________ log 2 + log 3 = log x
   4. ____________ log x = 1
   5. ____________ $3e^{\left(\frac{x}{3}\right)}=445.2395$
   6. ____________ log_x21=1
   7. ____________ ln(x − 7) = 3.04452244
   8. ____________ $\frac{1}{2}\log x=6$
3. _________ Using a 45 foot long rope, Tommy in the center, Jamal walking in a circle with the rope taut, Maybelline would measure a length of 283 feet. Calculate the value of pi based on this data.
4. _________ The curve on a 400 meter track is roughly 100 meters long. What is the radius of this curve in meters?
5. _________ Convert $\frac{\mathrm{\pi }}{3}$ radians to degrees.
6. _________ Convert 45° to radians expressed as π over a number.
7. _________ Calculate: 100 sin(60°)
8. _________ Calculate: 100 cos(30°)
9. _________ Calculate: 200 sin(45°)
10. _________ Calculate: 200 cos(45°)
11. Suppose I want to inscribe a square inside a circle with a radius of 200. What will be the SVG coordinates of the four corners a, b, c, d? The center of the circle is at (0,0). Try to remember that the y-axis is "upside-down."
    
    1. ( ________ , _________ )
    2. ( ________ , _________ )
    3. ( ________ , _________ )
    4. ( ________ , _________ )