Please help me solve this problem

Mathematics

1 answer:

brilliants [131]3 years ago

7 0

Answer:

72 in²

Step-by-step explanation:

lateral area: the surface area of a 3D figure, but excluding the area of any bases

the lateral area of this prism is the sum of the three rectangular sides.

calculate the third side of the triangle first because it's also the side of one of the rectangle:

√(5² - 4²) = 3

4 × 6 + 5 × 6 + 3 × 6 = 72

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H=7 + 29t-16t^2 find all values of t for which the balls height is 19ft

NikAS [45]

$\bf \qquad \textit{initial velocity}\\\\
\begin{array}{llll}
\qquad \textit{in feet}\\\\
h(t) = -16t^2+v_ot+h_o
\end{array} 
\quad 
\begin{cases}
v_o=\textit{initial velocity of the object}\\
h_o=\textit{initial height of the object}\\
h=\textit{height of the object at "t" seconds}
\end{cases}\\\\
-------------------------------\\\\$

$\bf h(t)=7+29t-16t^2\qquad h(t)=19\implies 19=7+29t-16t^2
\\\\\\
16t^2-29t+12=0\impliedby \textit{now, let's use the quadratic formula}
\\\\\\
t=\cfrac{-(-29)\pm\sqrt{(-29)^2-4(16)(12)}}{2(16)}\implies t=\cfrac{29\pm\sqrt{841-768}}{32}
\\\\\\
t=\cfrac{29\pm\sqrt{73}}{32}\implies t\approx 
\begin{cases}
1.17\\
0.64
\end{cases}$

so hmm check the picture below, thus the ball hits 19 feet of height twice, once on the way up, and once on the way down, at about 0.64 seconds and at 1.17 seconds.