ttps/www falsecd ld-4820274&c; Math2412 PreCalculus Winter -Mini mich Homework:

Question

ttps/www falsecd ld-4820274&c; Math2412 PreCalculus Winter -Mini mich Homework: Section 11.3 Homework Score: 0 of 1 pt 26 of 31 (28 complete) 11.3.87 Initially, a pendulum swings through an arc of 10 feet On each successive swing, the length of the arc is 0.9 of the previous length (a) What is the length of the arc of the eighth swing? (b) On which swing is the length of the arc first less than 5 feet? (c) After 15 swings, what total length will the pendulum have swung? (d) When it stops, what total length will the pendulum have swung? (a) The length of the arc of the eighth swing in foet is (Round your answer to three decimal places.) Enter your answer in the answer box and then click Check Answer. Clear All 3 remaining DOLL 8 Tab Caps LockA

Explanation / Answer

Ans(a):
Given that first arc length=10 feet
Then 2nd arc length=10(0.9)^1 feet
Then 3rd arc length=10(0.9)^2 feet

similarly nth arc length=10(0.9)^(n-1) feet

So to find length of 8th swing plug n=8
we get =10(0.9)^(8-1) feet =10(0.9)^7 feet = 4.782969 feet

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Ans(b):
Arc length of nth swing =10(0.9)^(n-1) feet
10(0.9)^(n-1) <5
(0.9)^(n-1) <5/10
(0.9)^(n-1) <0.5
(n-1)*ln(0.9) >ln(0.5)
n-1 >ln(0.5)/ln(0.9)
n-1 > 6.5788
n > 7.5788
So answer will be 8th swing.

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Ans(c):
Sum of first n terms of geometric sequence is given by
Sn=a[r^n-1]/=[r-1]
Obtained equation is geometric where a=10, r=0.9, n=15
Sn=10[0.9^15-1]/[0.9-1]
Sn=10[0.20589-1]/[-0.1]
Sn=10[-0.79411]/[-0.1]
Sn=10[7.9411]
Sn=79.411
Hence answer is 79.411

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Ans(d):
stops means we are considering infinite terms of geometric sum
Soo=a/(1-r)
where a=10, r=0.9
=10/[1-0.9]
=10/0.1
=100
Hence answer is 100

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