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Vanyuwa [196]
3 years ago
11

8. Write the equation of a line that is perpendicular to the given line and that passes through the

Mathematics
1 answer:
avanturin [10]3 years ago
8 0
Y - 3 = 8/3(x + 2)...the slope here is 8/3. A perpendicular line will have a negative reciprocal slope. All that means is " flip " the slope and change the sign. So our perpendicular line will have a slope of -3/8

y - y1 = m(x - x1)
slope(m) = -3/8
(-2,3)....x1 = -2 and y1 = 3
now we sub
y - 3 = - 3/8(x - (-2)...not done yet
y - 3 = -3/8(x + 2) <===

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Answer:

\boxed{a_n \:  =  \: 64 \:  \times  \: ( -  \frac{3}{4} ) ^{n \:  -  \: 1} }

Step-by-step explanation:

  • We first compute the ratio of this geometric sequence.

r \:  =  \:  \frac{ - 48}{64}  \\  \\ r   \:  =  \:  \frac{36}{ - 48}  \\  \\  r \:  =  \:  \frac{ - 27}{36}

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r \:  =  \:   -  \frac{3 }{4}   \\  \\ r   \:  =  \:   -  \frac{3 }{4}  \\  \\  r \:  =  \:    -  \frac{3 }{4}

  • We deduce that it is the common ratio because it is the same between each pair.

r \:  =  \:  -  \frac{3 }{4}

  • We use the first term and the common ratio to describe the equation:

a_1 \:  =  \: 64; \: r \:  =  \:  -  \frac{3 }{4}

<h3>We apply the data in this formula:</h3>

\boxed{a_n \:  =  \: a_1 \:   \times  \:  {r}^{ n \:  -  \: 1} }

_______________________

<h3>We apply:</h3>

\boxed {\bold{a_n \:  =  \: 64 \:   \times  \:  {( -  \frac{3}{4} )}^{ n \:  -  \: 1} }}

<u>Data</u>: The unknown "n" is the term you want

<h3><em><u>MissSpanish</u></em></h3>
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