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1. The height (in meters) of a shot cannonball follows a trajectory given by $h(t) = -4.9t^2 + 14t - 0.4$ at time $t$ (in seconds). For how many seconds is the height of the cannonball at least $6$ meters?

2. What is the smallest distance between the origin and a point on the graph of $y=\dfrac{1}{\sqrt{2}}\left(x^2-3\right)$?

3. What is the maximum value of $4(x + 7)(2 - x)$, over all real numbers $x$?

 

thank you

 Nov 2, 2020
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1     solve     6 = -4.9t^2+14t-0.4          using quadratic equation      a = -4.9    b = 14    c = - 6.4  

                                                        you will get two values of t   the time above 6 is between these times

 

3  Max will occur at the point between the two zeroes    -7  and 2      middle is - 2.5

      use this value for x in the equation to find the max value of the equation

 Nov 2, 2020

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