The parametric equations for a hit baseball are X(t) = 90t y(t) = -16t2 + 72t + 3 Where x and y are in feet and t is in seconds. 1) Make a table for t, x(t) and y (t) for t = 0 to 4.5, in intervals of 0.5 second 2) Sketch a graph of the travel distance (X) and the height (y) of the ball by plotting the points found above and labeling each with the t-value 3) The wall is 396 feet from home plate. how many seconds will it take the ball to reach that point? how high off the ground will the ball be? 4) what is the maximum height attained by the ball? how many seconds after contact with the bat is this height attained? how far downfield from home plate is this height attained? 5) if the outfielder puts one foot on the wall and jumps, he can attain a height of 11 feet. can he make the catch? 6) if the ball were to continue until it reached the ground, how long would that take? How many feet from home plate would that happen
Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
The parametric equations for a hit baseball are
X(t) = 90t
y(t) = -16t2 + 72t + 3
Where x and y are in feet and t is in seconds.
1) Make a table for t, x(t) and y (t) for t = 0 to 4.5, in intervals of 0.5 second
2) Sketch a graph of the travel distance (X) and the height (y) of the ball by plotting the points found above and labeling each with the t-value
3) The wall is 396 feet from home plate. how many seconds will it take the ball to reach that point? how high off the ground will the ball be?
4) what is the maximum height attained by the ball? how many seconds after contact with the bat is this height attained? how far downfield from home plate is this height attained?
5) if the outfielder puts one foot on the wall and jumps, he can attain a height of 11 feet. can he make the catch?
6) if the ball were to continue until it reached the ground, how long would that take? How many feet from home plate would that happen
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