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h(t)=-4.9t^(2)+18 t+0.5 The equation models h, the height, in meters, of a soccer ball t seconds after the goalkeeper kicks it. Which of the following statements is the best interpretation of the ordered pair (3,10.4) ? Choose 1 answer: A At 3 seconds after the kick, the distance between the soccer ball and the goalkeeper is 10.4 meters. (B) At 3 seconds after the kick, the soccer ball is traveling at a speed of 10.4 meters per second. (C) At 3 seconds after the kick, the height of the soccer ball is 10.4 meters. (D) At 10.4 seconds after the kick, the height of the soccer ball is 3 meters.

h(t)=−4.9t2+18t+0.5 h(t)=-4.9 t^{2}+18 t+0.5 \newlineThe equation models h h , the height, in meters, of a soccer ball t t seconds after the goalkeeper kicks it. Which of the following statements is the best interpretation of the ordered pair (3,10.4) (3,10.4) ?\newlineChoose 11 answer:\newline(A) At 33 seconds after the kick, the distance between the soccer ball and the goalkeeper is 1010.44 meters.\newline(B) At 33 seconds after the kick, the soccer ball is traveling at a speed of 1010.44 meters per second.\newline(C) At 33 seconds after the kick, the height of the soccer ball is 1010.44 meters.\newline(D) At 1010.44 seconds after the kick, the height of the soccer ball is 33 meters.

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Q. h(t)=−4.9t2+18t+0.5 h(t)=-4.9 t^{2}+18 t+0.5 \newlineThe equation models h h , the height, in meters, of a soccer ball t t seconds after the goalkeeper kicks it. Which of the following statements is the best interpretation of the ordered pair (3,10.4) (3,10.4) ?\newlineChoose 11 answer:\newline(A) At 33 seconds after the kick, the distance between the soccer ball and the goalkeeper is 1010.44 meters.\newline(B) At 33 seconds after the kick, the soccer ball is traveling at a speed of 1010.44 meters per second.\newline(C) At 33 seconds after the kick, the height of the soccer ball is 1010.44 meters.\newline(D) At 1010.44 seconds after the kick, the height of the soccer ball is 33 meters.
  1. Given function: We are given the function h(t)=−4.9t2+18t+0.5h(t) = -4.9t^2 + 18t + 0.5, which models the height of a soccer ball at time tt seconds after being kicked. We need to interpret the ordered pair (3,10.4)(3,10.4).
  2. Interpret ordered pair: The ordered pair (3,10.4)(3,10.4) means that when t=3t = 3 seconds, the height h(t)h(t) of the soccer ball is 10.410.4 meters. We can check this by substituting t=3t = 3 into the function h(t)h(t).
  3. Substitute and calculate: Substitute t=3t = 3 into the function: h(3)=−4.9(3)2+18(3)+0.5h(3) = -4.9(3)^2 + 18(3) + 0.5.
  4. Calculate square: Calculate the square of 33: (3)2=9(3)^2 = 9.
  5. Multiply −4.9-4.9: Multiply −4.9-4.9 by 99: −4.9×9=−44.1-4.9 \times 9 = -44.1.
  6. Multiply 1818: Multiply 1818 by 33: 18×3=5418 \times 3 = 54.
  7. Add results with constant: Add the results of the previous steps and include the constant term: −44.1+54+0.5-44.1 + 54 + 0.5.
  8. Perform addition: Perform the addition: −44.1+54+0.5=10.4-44.1 + 54 + 0.5 = 10.4.
  9. Confirmation of calculation: The calculation confirms that h(3)=10.4h(3) = 10.4 meters. Therefore, the ordered pair (3,10.4)(3,10.4) means that at 33 seconds after the kick, the height of the soccer ball is 10.410.4 meters.

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