Question:

Mathematics

1 answer:

-Dominant- [34]3 years ago

6 0

C I took the tests on eg today

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A geometric sequence is shown below 2,-6,18,-54,162,... part A: what a recursive relationship for this sequence. Explain how you

fgiga [73]

<h3>Answer:</h3>

a_n = -3a_(n-1); a_1 = 2
a_n = 2·(-3)^(n-1)

<h3>Step-by-step explanation:</h3>

A) The problem statement tells you it is a geometric sequence, so you know each term is some multiple of the one before. The first terms of the sequence are given, so you know the first term. The common ratio (the multiplier of interest) is the ratio of the second term to the first (or any term to the one before), -6/2 = -3.

So, the recursive definition is ...

... a_1 = 2

... a_n = -3·a_(n-1)

B) The explicit formula is, in general, ...

... a_n = a_1 · r^(n -1)

where r is the common ratio and a_1 is the first term. Filling in the known values, this is ...

... a_n = 2·(-3)^(n-1)

6 0

3 years ago

A man finds that the angle of elevationof a building is 22º. After walking 20 m towards the building, he finds that the angle of

tensa zangetsu [6.8K]

Answer:

<em>The height of the building is 21.38 m</em>

Step-by-step explanation:

<u>Trigonometric Ratios</u>

The ratios of the sides of a right triangle are called trigonometric ratios.

The image attached shows the measures and angles provided in the problem. The first angle of elevation is y=22°, the man walks B=20 m and finds the new angle of elevation is x=33°.

It's required to find the height of the building H.

The tangent ratio relates the opposite side with the adjacent side of a given angle. Applying it to the larger triangle:

$\displaystyle \tan y=\frac{\text{opposite leg}}{\text{adjacent leg}}$