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vagabundo
1 month ago
11

A projectile is thrown upward so that its distance above the ground after t seconds is given by the function h(t) = -16t² + 704t

. After how many seconds does the projectile take to reach its maximum height? Show your work for full credit.
Mathematics
1 answer:
Inessa [12.5K]1 month ago
5 0
H(t) = -16t² + 704t = -16(t² - 44t)
Transforming to vertex form: -16(t² - 44t + 484) + 704
h(t) = -16(t - 22)² + 704
The projectile reaches its peak height after 22 seconds, corresponding to the vertex of the parabola at (22, 704).
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Answer: C) HF measures 4 units and GH is 2 units.

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To demonstrate the similarity of ΔDFE and ΔGFH according to the SSS similarity theorem, we require:

\frac{DF}{GF}=\frac{FE}{FH}=\frac{DE}{GH}\\\\\Rightarrow\frac{DG+GF}{GF}=\frac{FH+EH}{FH}=\frac{DE}{GH}\\\\\Rightarrow\frac{5+15}{5}=\frac{12+HF}{FH}=\frac{8}{GH}\\\\\Rightarrow\frac{20}{5}=\frac{12+HF}{FH}\ and\ \frac{20}{5}=\frac{8}{GH}\\\\\Rightarrrow4HF=12+HF\ and\ GH=\frac{8}{4}\\\\\Rightarrow3HF=12\ and\ GH=2\\\\\Rightarrow HF=4\ and\ GH=2

Thus, to confirm that △DFE is similar to △GFH utilizing the SSS similarity theorem and the data from the diagram, it is essential to establish that HF measures 4 units and GH measures 2 units.

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Refer to the attached document.

Step-by-step explanation:

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A rational expression is provided, and we need to compute the quotient.

We will utilize long division to obtain the quotient.

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