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2 years ago

1. Which formula defines the sequence f(1)=2, f(2)= 6, f(3)= 10, f(4)= 14, f(5)= 18?

Mathematics

1 answer:

Natasha_Volkova [10]2 years ago

7 0

Answer:

$f(n) =4 + f(n-1) \\for\ n>2$

Step-by-step explanation:

Given

$f(1)=2\\ f(2)= 6\\ f(3)= 10\\ f(4)= 14\\ f(5)= 18$

Required

Determine the formula

First, we need to solve common difference (d)

$d = f(n) - f(n-1)$

Take n as 2

$d = f(2) - f(2-1)$

$d = 6 - 2$

$d = 4$

Represent each function as a sum of the previous

$f(1) = 2$

$f(2) = 2 + 4 = f(1) + 4$

$f(3) = 6 + 4 = f(2) + 4$

$f(4) = 10 + 4 = f(3) + 4$

$f(5) = 14 + 4 = f(4) + 4$

Represent the function as $f(n)$

$f(n) =f(n-1) + 4$

Reorder

$f(n) =4 + f(n-1) \\for\ n>2$

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Answer:

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Therefore the value of tangent of ∠ $M$ is $42$ °.

Step-by-step explanation:

Given that,

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Diagram of the given triangle is shown below:

Now,

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Paul and jose are trying to measure the height of a tree. paul is standing 19m from the foot of the tree and measures the angle

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The firts thig we are going to do is create tow triangles using the angles of elevation of Paul and Jose. Since the problem is not giving us their height we'll assume that the horizontal line of sight of both of them coincide with the base of the tree.
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Now we can build a right triangle between Paul and the tree and another one between Jose and the tree as shown in the figure. Lets use cosine to find h in Paul's trianlge:
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Now we can use the law of sines to find the distance $x$ between Paul and Jose:
$\frac{sin(43)}{36.9} = \frac{sin(16)}{x}$
$x= \frac{36.9sin(16)}{sin(43)}$
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Now that we know the distance between Paul and Jose, the only thing left is add that distance to the distance from Paul and the base of the tree:
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