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Andrew [12]
3 years ago
7

Suppose the first term of a geometric sequence is multiplied by a nonzero constant, c. What happens to the following terms in th

e sequence? What happens to the sum of this geometric sequence? (This question has one right answer.) Give an example of a geometric sequence to illustrate your reasoning. (Many answers are possible.)
Mathematics
1 answer:
ratelena [41]3 years ago
6 0
The next  terms in the sequence will be multiplied by c, but the common ratio is still the same

example :

S = [1(3)^4 - 1]/ [3-1]  = 80/2 - 40

Hope this helps
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Step-by-step explanation:

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A hot air balloon is flying at an altitude of 800 feet. A passenger takes a picture of the top of a tree and estimates that the
nalin [4]

The height of the tree given the depression angle to the top and the base

is given by the tangent relationship of the two given angles.

Correct response:

  • The height of the tree is approximately <u>79.58 feet</u>
<h3 /><h3>Methods used for the calculation of the height of the tree</h3>

Given:

Altitude of the hot air balloon = 800 feet

Angle of depression to top of tree = 43°

Angle of depression to base of tree = 46°

Required:

Height of tree

Solution:

The horizontal distance of the balloon from the tree is given as follows;

  • \displaystyle tan(46^{\circ}) = \frac{Altitude \ of \ balloon}{Horizontal \ distance \ from \ tree} = \mathbf{\frac{800 \, feet}{Horizontal \ distance \ from \ tree}}

Therefore;

\displaystyle Horizontal \ distance \ of \ balloon \  from \ tree = \frac{800 \ feet}{tan(46^{\circ})}

  • \displaystyle tan(43^{\circ})  = \mathbf{\frac{Height \ of \ balloon \ above \ tree}{\dfrac{800 \, feet}{tan(46^{\circ})} }}

Therefore;

\displaystyle Height \ of \ balloon \ above \ tree = tan(43^{\circ}) \times \frac{800 \, feet}{tan(46^{\circ})}

  • Height of tree = Altitude of balloon - Height of balloon above tree

Therefore;

  • \displaystyle Height \ of \ tree = 800 \, feet - tan(43^{\circ}) \times \frac{800 \, feet}{tan(46^{\circ})} \approx \underline{  79.58 \, feet}

Learn more about angle of elevation and depression here:

brainly.com/question/1978238

4 0
2 years ago
There are two numbers, that sum up to 53. Three times the smaller number is equal to 19 more than the larger number. What are th
Taya2010 [7]

Answer:

x = 18  (Smaller number)

y = 35 (Larger number)

Step-by-step explanation:

To solve, begin by setting up a system of equations.

'x' being the smaller number, while

'y' is the larger number.

We can construct the equations:

x + y = 53

3x = y + 19

Rearrange the second equation to equal 'y':

3x - 19 = y

Plug this value of 'y' into the first equation:

x + 3x - 19 = 53

Combine like terms and simplify:

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4x = 72

x = 18

Plug in this value for 'x' into an equation to solve for 'y':

18 + y = 53

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7 0
3 years ago
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