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