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To get over a fence, a cat jumps with an initial upward velocity of 2020 feet per second and then lands back on the ground. Therefore, the cat's height above the ground in feet, tt seconds after it jumps, can be modeled by the expression 16t2+20t-16t^2 + 20t. This expression can be written in factored form as 16t(t1.25)-16t(t - 1.25). \newlineWhat does the number 1.251.25 represent in the expression?\newline(A)the height in feet of the cat at the start of its jump\newline(B)the height in feet of the cat when it reaches its highest point\newline(C)the time in seconds from when the cat jumps until it lands on the ground\newline(D)the time in seconds from when the cat jumps until it reaches its highest point

Full solution

Q. To get over a fence, a cat jumps with an initial upward velocity of 2020 feet per second and then lands back on the ground. Therefore, the cat's height above the ground in feet, tt seconds after it jumps, can be modeled by the expression 16t2+20t-16t^2 + 20t. This expression can be written in factored form as 16t(t1.25)-16t(t - 1.25). \newlineWhat does the number 1.251.25 represent in the expression?\newline(A)the height in feet of the cat at the start of its jump\newline(B)the height in feet of the cat when it reaches its highest point\newline(C)the time in seconds from when the cat jumps until it lands on the ground\newline(D)the time in seconds from when the cat jumps until it reaches its highest point
  1. Expression for Cat's Height: The expression for the cat's height is 16t2+20t-16t^2 + 20t, which can be factored as 16t(t1.25)-16t(t - 1.25).
  2. Finding Meaning of 1.251.25: To find the meaning of 1.251.25 in the expression, we set the factored form equal to zero: 16t(t1.25)=0-16t(t - 1.25) = 0.
  3. Solving for t: Solving for t, we get two solutions: t=0t = 0 and t=1.25t = 1.25.
  4. Significance of t=1.25t = 1.25: t=0t = 0 represents the time when the cat starts its jump, and t=1.25t = 1.25 represents another significant point in the cat's jump trajectory.
  5. Interpreting t=1.25t = 1.25: Since the expression models the height of the cat, the value t=1.25t = 1.25 seconds is when the cat's height is zero again, meaning it has landed.

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