A function assigns values. The maximum height of the particle is 484 ft.
A function assigns the value of each element of one set to the other specific element of another set.
Given that the function of the height of the particle is h(t) = −16t²+144t+160.
Now, to find the maximum of the function we need to differentiate the function, and then equate it with zero to find the value of t at which the height will be maximum.
[tex]h(t)=-16t^2+144t+160\\\\\dfrac{dh}{dt}=-16(2t)+144\\\\\dfrac{dh}{dt}=-32t+144[/tex]
Now, equate the function with 0, we will get,
[tex]0=-32t+144\\t = 4.5[/tex]
Further, plug in the value of t as 4.5 to get the maximum height.
[tex]h(t)=-16t^2+144t+160\\\\h(4.5)=-16(4.5^2)+144(4.5)+160\\\\h(4.5)= 484\rm\ ft[/tex]
Thus, the maximum height of the particle is 484 ft.
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