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developing expert voice

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  • 1.
    • 1. Jack made a bicycle ride from his home to Safeway. His bicycle wheels measure 66 cm of diameter, Safeway is located approximately 200m away from his home.
    • How many times will his bicycle’s wheels turn when he reaches Safeway.
    • If his bicycle’s air tube is located at 45 o angle from the frame center when he begin the ride. In which quadrant will it be when he reaches Safeway
  • 2.
    • So as we already know the
    • How many times will his bicycle’s will turn when he reaches Safeway
    • S (surface) and r (the radius) we
    • can easily find
    • Number of wheels turns is defined by
    • The revolution =
  • 3.
    • If Jack’s bicycle’s air tube is located at 45 o angle from the frame center when he begin the ride. In which quadrant will it be when he reaches Safeway.
    • Let is first thing convert The revolution = 96.4567
    • degree into radians in order to find the position of
    • the air tube when Jack reaches
    • Safeway. Whe have to multiply
    • the revolution by the angle
    • Jack Bicycles air tube will be in quandrant I when he reaches Safeway
  • 4.
    • 2. The historical daily data of Winnipeg, Manitoba weather follows a sinusoidal model with the maximum temperature of 32.5 o C on August 17, 2008 and a minimum temperature of -32.6 o C on January 13, 2009.
    • Sketch the weather graph and describe the variation of Sin and Cosine equation.
    • Predict the temperature on Christmas 2008.
  • 5.
    • Sketch the weather graph and describe the variation of Sin and Cosine equation
    • The equation of sin is of form f(x) = AsinB(x-C)+D
    • The equation of Cosine is of form g(x)= AcosB(x-C)+D
    • A which is the amplitude or the C determine the horizon shift
    • distance between max and min values in order to find the shift we
    • from the sinusoidal axis so must count number of days
    • Max temp = 32.5 on Aug 17, 2008 January 1 and August 17
    • Min temp = -32.6 on Jan 13, 2009 C= (31 + 28 + 31+ 30 + 31 +
    • 30 + 31+ 17) days
    • C = 229 days
    • amplitude D determine the vertical shift. In
    • order to find it we must first find
    • B which determine the period will be the sinusoidal axe which we will
    • Will be found by adding number of days get by subtracting the amplitude
    • Between Aug 17 and Jan 13, 2009 then from the maximum temperature
    • Multiply by 2 for a full period D = 32.5 – 32.55
    • ((31-17)+30+31+30+31+13)*2 = 298 days D = 0.05
  • 6.
    • with all the information we can now write the equation of Sinus and Cosines then sketch the graph
    • Sinus Cosines Equation
    • A = 32.55 A = - 32.55 Now we will only substitute the
    • information in these equation
    • f(x) = AsinB(x-C)+D g(x) = AcosB(x-C)+D
    • C = 229 – (298*(1/4)) C = + 229
    • C = 184 f(x) = 32.55 sin( (x-184))+ 0.05
    • D = 0.05 D = 0.05
    • g(x) = - 32.55 Cos( (x-229))+0.05
  • 7.
    • , Winnipeg temperature change for 2008-2009
    • 32.5 0
    • Jan 1, 2008 17 Aug, 2008 13 Jan, 2009
    • 1day 184 days 229 days 527 days
    • -32.6 0
    Days Temperature Cosines Sinus
  • 8.
    • Predict the temperature on Christmas 2008.
    • Christmas is always on December 25 th The temperature will be of by adding all the days from Jan 1 st to December 25 th we will have then substitute the number in the equation
    • (31+28+31+30+31+30+31+31+30+31+30+31)= 359days
    • f(204) = 32.55 sin( (359-226))+ 0.05
    • f(204) = 10.82 o
  • 9.
    • 3.
    • After using the addition and multiplication logarithmic rules we get
    • by getting rid of logarithm
    • we have
    • After simplification we get a
    • quadratic equation
    • by using the quadratic formula
    • x = -0.4276
    • x = - 4.625
    • there is no solution
  • 10.
    • Algebraically determine how many days will have a temperature lower than 0 o and lower.
    • 0 = 32.55 sin( (x-226)) + 0.05
    • sin( (x-226))= -0.05/32.55
    • -0.001536 = (x-226))
    • Sin = - 0.001536
    • (x-226) = - 0.001536/( )
    • = - 0.001536
    • (x-226) = - 072849
    • x = -07728+226
    • x = 225.92 approximately 226 days will be under 0 o