Why is using a compass and straightedge and compass better than technology
1 answer:
Technology comes from the Greek root , meaning art or craft.
For the Greeks, a straightedge and compass was technology.
The nice thing about a straightedge and compass construction of any length is that there's always a corresponding algebraic form consisting of natural numbers combined via addition, subtraction, multiplication, division and square rooting (of positive numbers). So we get an "exact" answer, at least using radicals.
Compare that to the typical calculating technology we use today where the square roots turn into approximations. The calculator is worse, turning an exact answer into an approximation.
Straightedge and compass constructions play a large role in the development of mathematics but they're not really better, it's just how things went. By restricting ourselves to straightedges (linear equations) and compasses (circles, quadratic equations) we restricted the possible lengths we could construct. Understanding exactly how propelled mathematics forward for a couple of thousand years.
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Answer:
The maximum height of the baseball is 9 feet
Step-by-step explanation:
we have
where
p(t) ----> baseball position above the ground in feet
t ----> the time in seconds
v_0 ----> is the initial velocity in ft/sec
p_0 ---> initial position above the ground
we have
substitute the given values
This is the equation of a vertical parabola open downward
The vertex represent a maximum
Convert the quadratic equation in vertex form
Factor -16 leading coefficient
Complete the square
Rewrite as perfect squares
The vertex is the point (0.5,9)
The maximum height of the baseball above the ground is the y-coordinate of the vertex
therefore
The maximum height of the baseball is 9 feet