MS 101 Alg & Trig test seven • Name:

  1. DayDensity
    (kg/m³)
    1156
    2160
    3161
    4162.5
    5163
    6163.5
    7164
    8165.5
    9166
    10166.5
    11166.7
    12167
    13167.5
    14169
    15169.5
    16170
    17171
    For the athletes in the MicroGames this summer top performance will depend in part on having the best equipment and gear. Running shoes lose their elastic rebound and cushion with age. The ethylene-vinyl acetate foams used in the midsole break down, crush, and increase in density with use. The data is based on placing running shoes with EVA forumula 147 into an impact machine for 120 minutes a day to simulate two hours of working out. The increase in density each day was recorded. (p140, Verdejo, 2003). Fit a logarithmic trend line to this data.
    1. Graph the data, add a LOGARITHMIC trend line and equation to the graph, and then write the logarithmic equation:
    2. ____________ Based on the logarithmic equation in part a, calculate the density for day 36.
    3. ____________ Based on the logarithmic equation in part a, calculate the day when the density would be predicted to be 175 kg/m³
    4. Solve the equation in part a for x, writing out the resulting inverse equation below:
  2. Calculate or solve for x the following expressions and equations.
    1. ____________ 140
    2. ____________ log1414
    3. ____________ log 10000
    4. ____________ ex = 8103.09
    5. ____________ ln x = 2.7726
    6. ____________ log5x = 2
    7. ____________ 6 ln(6x) = 32.2517
    8. ____________ e ( x 7 ) = 1096.6332
    9. ____________ ln(2) + ln (32) = ln(x)
    10. ____________ 2 log(3) − log(x + 144)= −2 log(5)
    11. ____________ x logxx = 100
  3. _________ The Pohnpei State track has been redone with a Conica Conipur track surface. Lane six of the newly refurbished and resurfaced track is 109 meters long. What is the radius of lane six in meters?
  4. Convert the following angles in radians to degrees
    2π 5 = _________° π 5 = _________° π 10 = _________°
  5. Convert 40° to radians expressed as π over a number:
  6. Convert 285° to radians expressed as π over a number:
  7. The following chart displays three functions. Each function is shown using a marker of a different shape: circles, squares, and triangles.
    Graph with shapes fed by different functions background rectangle major grid lines axes x-axis and y-axis a path a path data points as rectangles leftmost data set a path data points as circles data points as triangles text layers Functions y-axis labels -12.0 -9.6 -7.2 -4.7 -2.3 0.1 2.5 4.9 7.3 9.8 12.2 x-axis labels -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5
    1. __________ What marker shape is f(x) = ex?
    2. __________ What marker shape is f(x) = e−x?
    3. __________ What marker shape is function f(x) = 24 (1+ e -3x ) -12 ?
    4. ________________ What is the name of the type of function seen in letter c?
    5. ________________ On the 12th of June I introduced the function seen in letter c as being characteristic of the time versus velocity for what sport?
  8. Calculate the following values:
    1. __________________ Calculate: 100 sin(72°)
    2. __________________ Calculate: 100 cos(72°)
    3. __________________ Calculate: 100 tan(72°)
    4. __________________ Calculate: 100 sin(36°)
    5. __________________ Calculate: 100 cos(36°)
    6. __________________ Calculate: 100 cos(36°)
    7. __________________ Calculate: 100 sin(18°)
    8. __________________ Calculate: 100 cos(18°)
    9. __________________ Calculate: 100 tan(18°)
    10. __________________ Calculate: 100 sin(0°)
    11. __________________ Calculate: 100 cos(0°)
    12. __________________ Calculate: 100 tan(0°)
    13. __________________ Calculate: 100 tan(90°)
  9. Determine the SVG coordinates of the five vertices (corners) of a pentagon inscribed in a circle. The center of the circle is (0, 0). The radius of the circle is 100. Remember that in SVG coordinates +y is down, -y is up.
    Pentagon +x → +y (0,0) θ = 18° a b c φ 36° d e r = 100 r = 100
    1. ( ________ , _________ )
    2. ( ________ , _________ )
    3. ( ________ , _________ )
    4. ( ________ , _________ )
    5. ( ________ , _________ )
    Wave equation in terms of wavelength λ and distance x: y=asin ( 2πx λ )
    Wave equation in terms of period τ and time t: y=asin ( 2πt τ )
    Period τ and frequency f relationship: τ= 1f
  10. A RipStik lays down a wave according to the equation: y=16sin ( 2πx 32 )
    1. a = _______________ Write the amplitude a of the equation.
    2. λ = _______________ Write the wavelength λ of the equation.
  11. A spring oscillates vertically according to the equation: y=40sin ( 2πt 2.7 )
    1. a = _______________ Write the amplitude a of the equation.
    2. τ = _______________ Write the period τ of the equation.
    3. f = _______________ Calculate the frequency f of the equation.
  12. Sketch a graph of the following function: y=50cos ( 2πx 12 )
    Grid 12 x 10 on the thirties background rectangle major grid lines axes x y y-axis labels -50 -40 -30 -20 -10 0 10 20 30 40 50 x-axis labels 0 1 2 3 4 5 6 7 8 9 10 11 12
  13. A RipStik was swizzled across a large sheet of paper. The swizzle wave can be seen in the diagram.
    RipStik swizzle sine wave 5 cm distance = 150 cm time = 1.50 seconds RipStik riders Shanalin and Tristan
    1. ________ How many waves are shown in the diagram?
    2. λ = _______________ Write the wavelength λ
    3. a = _______________ Write the amplitude a.
    4. τ = _______________ Write the period τ.
    5. f = _______________ Calculate the frequency f.
    6. y = ______ sin( _________ x). Write out the equation of the wave in terms of the wavelength λ and distance x.
  14. Destroyer submarine Depth charges are explosives that detonate at a specific depth d under the surface of the water. A destroyer armed with depth charges is using a sonar to determine the angle θ and the distance r to a submarine.
    1. Write an equation for the angle θ in terms of r and d:
    2. d = _________ If the angle θ = 40° and the range r is 156 meters, what is the value of the depth d?
  15. Solve 5 sin x = 3 for x in degrees
  16. Solve 4(tan x)2 − 3 = 0 for x in degrees
  17. Given the equation for velocity, the launch angle θ, and the distance:
    distance d = 2 v 2 sin(θ) cos(θ) 9.8
    For a MicroGames javelin thrown at a velocity v = 8 m/s at θ = 40°
    1. vx = ______________ Calculate the horizontal velocity vx
    2. vy = ______________ Calculate the vertical velocity vy
    3. d = _____________Calculate the distance d the javelin will travel.
  18. For the vector u = 21 i + 20 j
    1. magnitude = __________ Calculate the magnitude.
    2. θ = __________ Calculate the direction angle in degrees.
  19. A shotput is thrown with a force of 55 Newtons at a direction angle of 33° to the horizontal. Write the force vector in i, j component form.
    SVG trigonometry problems θ = 33° 55
    F = ________ i + ________ j
  20. A force F of 6000 Newtons is being exerted at an angle of 20° to the horizontal on an object.
    1. F ⋅ d ___________ Calculate the energy (work) done to move the object 10 meters using the dot product.
    2. F ⨯ d ___________ Calculate the torque on the object if the lever arm distance is 0.3 meters using the cross product.
  21. Given a matrix A= [ 721 2002 ] and a matrix B= [ 720 2014 ]

    Write the matrix A + B | Write the matrix AB | Write the matrix 2A