developing expert voice

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developing expert voice

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

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