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PilotLPTM [1.2K]
3 years ago
8

What is the 3rd term of the sequence? a1 = 40 and an = 0.5(an – 1) a3 =

Mathematics
1 answer:
777dan777 [17]3 years ago
8 0
\bf \begin{array}{llll}
term&value\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
a_1&40\\\\
a_2&0.5(a_{n-1})\\
&0.5(a_{2-1})\\
&0.5(a_1)\\
&0.5(40)\\
&20\\\\
a_3&0.5(a_{3-1})\\
&0.5(a_2)\\
&0.5(20)
\end{array}
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A certain bridge arch is in the shape of half an ellipse 106 feet wide and 33.9 feet high. At what horizontal distance from the
nata0808 [166]

Answer:

The horizontal distance from the center is 49.3883 feet

Step-by-step explanation:

The equation of an ellipse is equal to:

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Where a is the half of the wide, b is the high of the ellipse, x is the horizontal distance from the center and y is the height of the ellipse at that distance.

Then, replacing a by 106/2 and b by 33.9, we get:

\frac{x^2}{53^{2} } +\frac{y^2}{33.9^{2} } =1\\\frac{x^2}{2809} +\frac{y^2}{1149.21} =1

Therefore, the horizontal distances from the center of the arch where the height is equal to 12.3 feet is calculated replacing y by 12.3 and solving for x as:

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