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goldfiish [28.3K]
3 years ago
13

Evaluate the geometric series . 254 255 508 510

Mathematics
2 answers:
Svetach [21]3 years ago
5 0
A1<span> is the first term in the </span>sequence<span>. To find the explicit </span>formula, you will need to be given the first term and use the value in the formula<span>. r is the common ratio for </span>the geometric sequence<span>. You will be given this value or be given information to compute it.</span>
mihalych1998 [28]3 years ago
3 0

Answer with explanation:

The given geometric series is : 254, 255, 508, 510,....

→If you will look at the first term and third term , it is

 254, 254 × 2,

So,First Half of the series will be as follows :

254×1, 254×2, 254×3,254×4,254×5........

→And if you will look at the second term and fourth term, it is as follows:

255, 255×2,

So,Second Half of the series will proceed as follows:

  255×1, 255×2, 255×3, 255×4,.........

⇒So, the whole series will be as follows:

254, 255, 254×2,255×2,254×3,255×3,254×4,255×4,....

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Answer:

cos(V)=\frac{39}{89}=.44

∠V=64.01°

Step-by-step explanation:

sin(angle)=\frac{opposite}{hypotenuse}

cos(angle)=\frac{adjacent}{hypotenuse}

tan(angle)=\frac{opposite}{adjacent}

  • The cosine of an angle is equal to the side adjacent to the angle over the hypotenuse, the longest side.
  • With this in mind:

cos(V)=\frac{39}{hypotenuse}

  • We need to find the hypotenuse of this triangle. This is relativly easy to do with a right triangle; we can just use the Pythagorean Theorem.
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a^2+b^2=c^2\\(39)^2+(80)^2=c^2\\1521+6400=c^2\\c=\sqrt{7921} \\c=89

  • Our hypotenuse is 89. Now we can finish solving for ∠V.

cos(V)=\frac{39}{89}\\V=cos^-^1(\frac{39}{89})\\

∠V=64.01°

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