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MeowieMeowMeow6500
23.08.2020 •
Mathematics
A geometric sequence is shown on the graph below. What is the formula for the nth term of the sequence?
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Ответ:
aₙ = 40*(1/2)ⁿ⁻¹
Step-by-step explanation:
As per graph we have:
a₁ = 40, a₂ = 20, a₃ = 10, a₄ = 5, a₅ = 2.5So the first term is 40 and common ratio is
20/40= 10/20 = 5/10 = 2.5/5 = 1/2Formula for nth term is:
aₙ = a₁rⁿ⁻¹aₙ = 40*(1/2)ⁿ⁻¹Ответ:
The surveyor is 36.076 kilometers far from her camp and her bearing is 16.840° (standard form).
Step-by-step explanation:
The final position of the surveyor is represented by the following vectorial sum:
And this formula is expanded by definition of vectors in rectangular and polar form:
Where:
If we know that
,
,
and
, then the resulting coordinates of the final position of the surveyor is:
According to this, the resulting vector is locating in the first quadrant. The bearing of the vector is determined by the following definition:
And the distance from the camp is calculated by the Pythagorean Theorem:
The surveyor is 36.076 kilometers far from her camp and her bearing is 16.840° (standard form).