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3 years ago

10) please help I don't understand this question at all

Mathematics

1 answer:

malfutka [58]3 years ago

3 0

We can determine this to be a Geometric Sequence with:

a = 2
r = 1/2
an = ?

We must first find an. We know that an = 1/256, therefore we can use this formula to discover an:

an = a * r^n-1
1/256 = 2 * 1/2^n-1
1/256 / 2 = 1/2^n-1
1/512 = 1/2^n-1
log(1/512) = log(1/2^n-1)
9 = n - 1
10 = n

Therefore, we know an = 10

Now we input it into this equation and solve:

Sn = a(1-r^n/1-r)
Sn = 2(1-1/2^10/1-1/2)
Sn = 2(1023/1024 / 1 / 2)
Sn = 2(1023/1024 * 2 / 1)
Sn = 2(2046/1024)
Sn = 2(1023/512)
Sn = 1023/256
Sn = 3.992

Geez, that took awhile... xD

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We are being told that:

Lamaj rides his bike over a piece of gum and continues riding his bike at a constant rate. This keeps the wheel of his bike in Simple Harmonic Motion and the Trigonometric equation that models the height of the gum in centimeters above the ground at any time, t, in seconds. can be written as:

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This indicates the position of y; so y = 12 cm

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$\mathbf{12 = 34 cos ( \pi(t-1.25))+34}$

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$\mathbf{12 = 34 sin ( \pi(t-1.25))+34}$

$\dfrac {12-34}{34} = sin (\pi(t-1.25))$

$\dfrac {-22}{34} = sin (\pi(t-1.25))$

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Hence, the gum will reach 12 cm first at 2.527 sec and second time at 2.72 sec.

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