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Leokris [45]
2 years ago
13

Identify the type of sequence shown in the table below and select the appropriate response. (5 points)

Mathematics
2 answers:
Anton [14]2 years ago
8 0

Its geometric as you are multiplying by -3 each time

Ipatiy [6.2K]2 years ago
7 0

Answer:

<h2>The given sequence is geometric, which reason is -3.</h2>

Step-by-step explanation:

If we pay attention to the sequence, we would observe that f(n) is increasing by a reason of -3, because

12(-3)=-36\\-36(-3)=108\\108(-3)=-324\\-324(-3)=972

So, basically, each term is being multiplied by -3, that's what makes the sequence, which is a geometric sequence, because it's being built by a factor, that is, a number which multiplies each term.

When you have to deduct if you have a arithmetic sequence or a geometric sequence, you need to observe if such sequence is increasing or decreasing faster. Like this case, you can see that the numbers are increasing rapidly, that means it's built based on a factor, not a difference, because when we use a difference to form a sequence, that will grow slower and it would be an arithmetic sequence.

Therefore, the given sequence is geometric, which reason is -3.

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Which of the following in an identity?
sammy [17]
By "which is an identity" they just mean "which trigonometric equation is true?"

What you have to do is take one of these and sort it out to an identity you know is true, or...

*FYI: You can always test identites like this:
Use the short angle of a 3-4-5 triangle, which would have these trig ratios:
sinx = 3/5    cscx = 5/3
cosx = 4/5   secx = 5/4
tanx = 4/3    cotx = 3/4
Then just plug them in and see if it works. If it doesn't, it can't be an identity!

Let's start with c, just because it seems obvious.
The Pythagorean identity states that sin²x + cos²x = 1, so this same statement with a minus is obviously not true.

Next would be d. csc²x + cot²x = 1 is not true because of a similar Pythagorean identity 1 + cot²x = csc²x. (if you need help remembering these identites, do yourslef a favor and search up the Magic Hexagon.)

Next is b. Here we have (cscx + cotx)² = 1. Let's take the square root of each side...cscx + cotx = 1. Now you should be able to see why this can't work as a Pythagorean Identity. There's always that test we can do for verification...5/3 + 3/4 ≠ 1, nor is (5/3 +  3/4)².

By process of elimination, a must be true. You can test w/ our example ratios:
sin²xsec²x+1 = tan²xcsc²x
(3/5)²(5/4)²+1 = (4/5)²(5/3)²
(9/25)(25/16)+1 = (16/25)(25/9)
(225/400)+1 = (400/225)
(9/16)+1 = (16/9)
(81/144)+1 = (256/144)
(81/144)+(144/144) = (256/144)
(256/144) = (256/144)
5 0
2 years ago
The radius of the cylinder is 3 inches and the height is 8 inches. Find the volume of the cylinder.
Dafna11 [192]

Answer:

1584/7 in² ≈ 226.3 in²

Step-by-step explanation:

Given,

  • Radius R = 3 in
  • Height H = 8 in
  • Volume V = ?

We know that,

Volume(Cylinder) = πr²h

Substitute values,

  • π(3²)8
  • 9(8)π
  • 72π

Taking π as 22/7

  • 72*22/7
  • 1584/7 ≈ 226.3 in²

5 0
1 year ago
A package of colored paper contains 20 pieces of yellow paper. This represents 25% of the total pieces of colored paper in the p
rewona [7]

<u />the answer may be 125 because 20 pieces of colored paper is only part and then the whole would be 125 because  divided by  is 5 so 25 times 5 is 125.

6 0
3 years ago
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Mumz [18]
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3 years ago
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zalisa [80]

Answer:

Any real number strictly larger than 9 and strictly less than 21.

Step-by-step explanation:

By triangle inequality, the sum of the lengths of any two sides are greater than the length of the third side.

We therefore could set up three inequalities.

x+6>15, x+15>6, 15+6>x

Solving these, we get x>9, x>-9, x<21 i.e. 9 < x < 21.

7 0
2 years ago
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