Maths-
General
Easy

Question


The function f models Jack's pulse, in beats per minute (bpm), as a function of his speed, in kilometers per hour (km/h), on a stationary bicycle. Based on the model, what was Jack's pulse, in bpm, when his sped was 0 km/h?

  1. 4
  2. 15
  3. 63
  4. 123

The correct answer is: 63


    HINT: Observe the graph at speed at speed = 0 km/hr we find the graph cuts in between 60-65 .so ,pulse is 63 as per option checking only option lies between 60-65 is option C.
    Explanation:IF the mathematical proof required instead of option checking
    Step 1: Finding any two points to find the equation of line
    The line passes through (3,75) and (8,95)
    Step 2 : Finding equation for line passing through {(3.75),(8,95)}
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell y minus y 1 equals fraction numerator y to the power of 2 minus y 1 end exponent over denominator x 2 minus x 1 end fraction left parenthesis x minus x 1 right parenthesis end cell row cell y minus 75 equals fraction numerator 95 minus 75 over denominator 8 minus 3 end fraction left parenthesis x minus 3 right parenthesis end cell row cell y minus 75 equals 20 over 5 left parenthesis x minus 3 right parenthesis end cell row cell y minus 75 equals 4 left parenthesis x minus 3 right parenthesis end cell end table
    at x = 0 ,
    table attributes columnspacing 1em end attributes row cell y minus 75 equals 4 left parenthesis 0 minus 3 right parenthesis end cell row cell y minus 75 equals negative 12 end cell row cell y equals 75 minus 12 equals 63 right parenthesis end cell row cell therefore text  at  end text x equals 0 km divided by text  hr then  end text y equals 63 bpm end cell end table
    therefore Jack's pulse in bpm, when he is at a speed of 0 km/hr is 63 bpm.
     

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