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natka813 [3]
3 years ago
5

What is the length of segment AD.

Mathematics
1 answer:
slamgirl [31]3 years ago
7 0

Answer:

AD= 5.82 units (3 s.f.)

Step-by-step explanation:

Please see attached picture for full solution.

*skipped these steps in the beginning:

∠ABC +∠ABD= 180° (adj. ∠s on a str. line)

90° +∠ABD= 180°

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What is the first term of the geometric sequence whose fifth term is 1/24 and tenth term is 1/768
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An=a1r^(n-1)

given
a5=1/24
a10=1/768

we know that
a5=1/24=a1r^(5-1) and
a10=1/768=a1r^(10-1)

so
1/24=a1r^4
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(a1r^9)/(a1r^4)=r^5=(1/768)/(1/24)=1/32

r^5=1/32
take 5th root of both sides
r=1/2

we have
a5=a1r^4=1/24
evaluate r^4 or (1/2)^4
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a1(1/16)=1/24
times both sides by 16/1
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a1=2/3

the first term is 2/3



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