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Ronch [10]
2 years ago
14

Identify the explicit formula for the sequence given by the following recursive formula:

Mathematics
1 answer:
Alex787 [66]2 years ago
7 0

If f(n) = f(n - 1) + 4, then

f(n - 1) = f(n - 2) + 4

and substituting this into the first equation gives

f(n) = f(n - 2) + 2•4

Similarly,

f(n - 2) = f(n - 3) + 4

so that

f(n) = f(n - 3) + 3•4

and so on.

Note the pattern:

f(n) = f(n - k) + k•4

so that when k = n - 1, we have

f(n) = f(n - (n - 1)) + (n - 1)•4

or

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

so that

[D] f(n) = -2 + 4 (n - 1)

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If Diana walks forward and her angle looking to the top of the building changes to 40°, how much closer is she to the building?
elena55 [62]

The closer Diana gets to the building, the smaller the angle becomes

Diana is 17.6 feet closer to the building

<h3>How to calculate the distance from the building</h3>

To calculate the distance between her and the building, we make use of the following tangent ratio

\tan(\theta) = \frac{h}{d}

Where:

  • \theta = 40^o
  • h represents the height of the building; h = 130
  • d represents the distance from the building

So, we have:

\tan(40) = \frac{130}{d}

Make d the subject

d = \frac{130}{\tan(40)}

Evaluate tan(40)

d = \frac{130}{0.8391}

d = 154.93

Initially, Diana is at a distance of 172.53.

The difference in both distance is:

\Delta d = 172.53 - 154.93

\Delta d = 17.6

Hence, Diana is 17.6 feet closer to the building

Read more about trigonometry ratios at:

brainly.com/question/4326804

7 0
2 years ago
Please give the the answer and dont send a file
Dahasolnce [82]

Answer:

-117

Step-by-step explanation:

x = 106 x 4 - (99+120+103+111+108)

x = 424 - 541

x = -117

Hope that helps!

7 0
3 years ago
Answer this geometry question
Basile [38]
The measure of the angle formed by 2 chords  that intersect inside the circle is 1/2 the sum of the chords' intercepted arcs. 
m∠RST = (143+33)/2 = 176/2 = 88°
6 0
3 years ago
The radius of a circle is 6 millimeters. What is the circle's circumference?
Gala2k [10]

Answer:

C =37.68 mm

Step-by-step explanation:

The circumference of a circle is given by

C = 2*pi*r

C = 2(3.14)*6

C =37.68 mm

4 0
3 years ago
Read 2 more answers
SOMEONE PLEASE HELP ME UNDERSTAND THIS. THANK YOU
telo118 [61]
Its really unclear i don't know what the paper says
can you please rescan it and send back in
5 0
3 years ago
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