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Ana and Taylor are on the lacrosse team and practicing their passes. The vertical height, [tex]\(a(x)\)[/tex], of Ana's pass [tex]\(x\)[/tex] feet from where it was thrown is modeled in this table.

[tex]\[
\begin{array}{|c|c|c|c|c|c|c|c|}
\hline
x & 0 & 10 & 20 & 30 & 40 & 50 & 60 \\
\hline
a(x) & 0 & 20 & 32 & 36 & 32 & 20 & 0 \\
\hline
\end{array}
\][/tex]

The vertical height, [tex]\(t(x)\)[/tex], of Taylor's pass [tex]\(x\)[/tex] feet from where it was thrown is modeled by this equation.
[tex]\[
t(x) = -0.05(x^2 - 50x)
\][/tex]

Complete the statements comparing their passes.

The difference of the maximum heights is [tex]\(\square\)[/tex] feet.

The difference of the total distances traveled is [tex]\(\square\)[/tex] feet.

Sagot :

GinnyAnsweridn
To compare the maximum heights and the total distances traveled of Ana's and Taylor's passes, let's analyze the provided data:

For Ana:
- From the table, the vertical heights at various distances [tex]\(x\)[/tex] are given.
- The maximum height achieved by Ana's pass, [tex]\(a(x)\)[/tex], is 36 feet.
- The total distance traveled by Ana's pass is 60 feet.

For Taylor:
- The vertical height for Taylor's pass, [tex]\(t(x)\)[/tex], is given by the equation [tex]\( t(x) = -0.05(x^2 - 50x) \)[/tex].
- The maximum height Taylor's pass achieves is 31.25 feet.
- The total distance traveled by Taylor's pass, determined by solving the roots of the equation, is 50 feet.

From this data, we can compute the differences:
1. The difference in the maximum heights:
[tex]\[ 36 - 31.25 = 4.75 \text{ feet} \][/tex]

2. The difference in the total distances traveled:
[tex]\[ 60 - 50 = 10.0 \text{ feet} \][/tex]

Therefore:
- The difference of the maximum heights is [tex]\( 4.75 \)[/tex] feet.
- The difference of the total distances traveled is [tex]\( 10.0 \)[/tex] feet.
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