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Sergio039 [100]
3 years ago
13

Ann races her bicycle for 200 ft. A wheel of her bicycle turns 40 times as the bicycle travels this distance. What is the diamet

er of the wheel?
Use the value 3.14. Round your answer to the nearest tenth. Do not round any intermediate steps.
Mathematics
1 answer:
andre [41]3 years ago
7 0

Answer:

1.6 ft

Step-by-step explanation:

Each time the wheel does a complete turn, the bike moves forward a distance equal to the wheel's circumference.  Since the bike moves 200 ft after 40 rotations, the length of the wheel's circumference is:

C = 200 ft / 40

C = 5 ft

Circumference is π times the diameter.  So the diameter of the wheel is:

C = πd

5 ft = πd

d = 1.6 ft

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How to find the x intercept of 3y=2x-6: (when y is 0)

3(0) = 2x - 6

     0 = 2x - 6
   +6        + 6
-------------------------
     6 = 2x
  ------ -----
     2     2
      
     x = 3


How to find the y intercept of 3y=2x-6: (when x  is 0)

 3y = 2(0) - 6

 y = 0 - 6

  3y = -6
------  -----
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   y = -2















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Check the forward differences of the sequence.

If \{a_n\} = \{2,6,12,20,30,42,\ldots\}, then let \{b_n\} be the sequence of first-order differences of \{a_n\}. That is, for n ≥ 1,

b_n = a_{n+1} - a_n

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Let \{c_n\} be the sequence of differences of \{b_n\},

c_n = b_{n+1} - b_n

and we see that this is a constant sequence, \{c_n\} = \{2, 2, 2, 2, \ldots\}. In other words, \{b_n\} is an arithmetic sequence with common difference between terms of 2. That is,

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and we can solve for b_n in terms of b_1=4:

b_{n+1} = b_n + 2

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b_{n+1} = (b_{n-2}+2) + 2\times2 = b_{n-2} + 3\times2

and so on down to

b_{n+1} = b_1 + 2n \implies b_{n+1} = 2n + 4 \implies b_n = 2(n-1)+4 = 2(n + 1)

We solve for a_n in the same way.

2(n+1) = a_{n+1} - a_n \implies a_{n+1} = a_n + 2(n + 1)

Then

a_{n+1} = (a_{n-1} + 2n) + 2(n+1) \\ ~~~~~~~= a_{n-1} + 2 ((n+1) + n)

a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))

a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))

and so on down to

a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2

\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}

6 0
2 years ago
The 5th term in a geometric sequence is 120. The 7th term is 30. What are the possible values of the 6th term of the sequence.
klemol [59]

Answer:

± 60

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aₙ = a₁ * rⁿ⁻¹

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