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During a match of badminton, Josh swings his racquet and hits the birdie high up into the air. The birdie's height above the ground in meters can be modeled by the expression 1.4+6t4.9t21.4 + 6t - 4.9t^2, where tt is the time in seconds after Josh hits the birdie.\newlineWhat does the number 1.41.4 represent in the expression?\newline(A)the height in meters of the birdie when Josh hits it\newline(B)the time in seconds from when Josh hits the birdie until it hits the ground\newline(C)the time in seconds from when Josh hits the birdie until it reaches its highest point\newline(D)the height in meters of the birdie when it reaches its highest point

Full solution

Q. During a match of badminton, Josh swings his racquet and hits the birdie high up into the air. The birdie's height above the ground in meters can be modeled by the expression 1.4+6t4.9t21.4 + 6t - 4.9t^2, where tt is the time in seconds after Josh hits the birdie.\newlineWhat does the number 1.41.4 represent in the expression?\newline(A)the height in meters of the birdie when Josh hits it\newline(B)the time in seconds from when Josh hits the birdie until it hits the ground\newline(C)the time in seconds from when Josh hits the birdie until it reaches its highest point\newline(D)the height in meters of the birdie when it reaches its highest point
  1. Expression Analysis: The expression for the birdie's height is 1.4+6t4.9t21.4 + 6t - 4.9t^2. To understand what 1.41.4 represents, we need to consider the terms of the expression when t=0t=0.
  2. Substitute t=0t=0: Substitute t=0t=0 into the expression to find the initial height of the birdie: 1.4+6(0)4.9(0)21.4 + 6(0) - 4.9(0)^2.
  3. Simplify Expression: Simplifying the expression with t=0t=0 gives us 1.4+001.4 + 0 - 0, which equals 1.41.4 meters.
  4. Initial Height Calculation: The number 1.41.4 represents the initial height of the birdie when Josh hits it, which corresponds to choice (A)(A).

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