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Yuliya22 [10]
3 years ago
14

To which subsets of the real numbers does the number 82 belong?

Mathematics
1 answer:
larisa86 [58]3 years ago
3 0
We know that
<span>82 is an integer, a whole number, a natural number, and a rational number (since 82 = 82/1)

</span><span>So
82 belongs to the set of integers, set of whole numbers, set of natural numbers, and the set of rational numbers</span>
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I need to know the next term in the sequence AND the nth term of all the sequences
ANEK [815]

I see you already did the ones where you figured out the formula.  There's a fun way that doesn't require figuring out the formula, called a forward difference table.

Let's work out the first one to learn the technique.  We write the sequence and under it the forward differences,

2 5 10 17 26

3 5  7  9

2 2 2  

We got 3=5-2, 5=10-5, 7=17-10, etc and the same for subsequent lines.  Eventually we get to an all constant line and we stop.

To extend the table we just add some constants to the constant line and work our way back up:

2 5 10 17 26 37 50

3 5  7  9  11  13

2 2 2   2  2

So we get 11 as 9+2 and 37 as 26+11 for our answer which matches the answer you already got.

Let's do the ones you haven't.

2 8  18 32 50 72

6 10 14 18  22

4  4  4   4  

Answer: 72

3 9  19  33 51   73

6 10 14  18  22

4 4  4    4

Answer: 73

2 11 26 47 74  107

9 15 21 27  33

6 6  6    6

Answer: 107

Three's our limit so I'll leave the last one to you.

---

A comment says we need the functions.  They're all quadratics.  I'll tell you how they want you to do it and how to do it in general.

They just want you to recognize these are all pretty close to just u_n=n^2.   The one that goes 3 12 27 etc. we recognize as just u_n=3n^2.   The one that goes 2 8 18 is just u_n =2n^2.  The one that goes 3 9 19 is one more than that so u_n=2n^2+1. The one that goes 2 11 26... is one less than 3 12 27 so is u_n=3n^2-1.  Again I'll leave the last one.

----

We can do these quadratics in general.  Let's work from our difference table.  If we have

f(n) = an^2 + bn + c

and we form the difference table for f(1), f(2), f(3) we get

a+b+c   4a+2b+c   9a+3b+c

3a+b     5a+b

2a

so we can use the first columns of our difference tables to get our polynomial.  

2 8  18 32 50 72

6 10 14 18  22

4  4  4   4  

Answer: 72

So we have 2a=4, so a=2

3a+b=6, so b=6-3(2)=0

a+b+c=2 so c=2-0-2=0

That gives us the obvious answer

u_n = 2n^2

3 9  19  33 51   73

6 10 14  18  22

4 4  4    4

Answer: 73

We have 2a=4 again so a=2, 3a+b=2 so b=0, and a+b+c=3 so c=1 giving

u_n = 2n^2+1

2 11 26 47 74  107

9 15 21 27  33

6 6  6    6

Answer: 107

2a=6 gives a=3

3a+b=9 gives b=0

a+b+c=2 gives c= -1

u_n = 3n^2-1

3 0
2 years ago
A ball is thrown from an initial height of 2 meters with an initial upward velocity of 15/ms . The ball's height h (in meters) a
Irina-Kira [14]
The height that a ball reaches at a certain time t is given by the equation,
           h = 2 - 15t + 5t²
We are asked to compute for the values of t that would allow the ball to reach a height of 7 meters. 

Substitute the 7 to the equation,
         7 = 2 - 15t + 5t²
Transposing,
               5t² - 15t - 7 + 2 = 0
Simplifying,
               5t² - 15t - 5 = 0
Divide the equation by 5,
               t² - 3t - 1 = 0

The values of t can be calculated through the quadratic formula,
             t = (-b +/- sqrt(b² - 4ac))/2a

Substituting, 
             t = (3 +/-sqrt (9 - 4(-1)) / 2(1)
              t = 3.3 or t = -0.30

Since, we cannot have t as a negative number hence, our final answer is:
      <em> t = 3.3 s</em>
4 0
2 years ago
Solve for indicated side. Round to the nearest hundredth.<br> Z=
Diano4ka-milaya [45]

Answer:

z ≈ 145.62

Step-by-step explanation:

using the sine ratio in the right triangle

sin18° = \frac{opposite}{hypotenuse} = \frac{45}{z} ( multiply both sides by z )

z × sin18° = 45 ( divide both sides by sin18° )

z = \frac{45}{sin18} ≈ 145.62 ( to the nearest hundredth )

6 0
1 year ago
Pls answer show work, At a store, notebooks are on sale for 78% off the regular price. The cost of a notebook is represented by
Assoli18 [71]

Answer:

<h2>C</h2>

Step-by-step explanation:

<h3> dont subtract the cost of the notebook by 0.78 while multiping it with the cost.</h3>
5 0
3 years ago
What is the volume of the cylinder shown below?
Anastasy [175]

<em>here's</em><em> your</em><em> solution</em>

<em> </em><em> </em><em> </em><em>=</em><em>></em><em> </em><em>it </em><em>is </em><em>given </em><em>that</em><em>. </em>

<em> </em><em> </em><em> </em><em> </em><em> </em><em>=</em><em>></em><em> </em><em>height</em><em> </em><em>of </em><em>cylinder</em><em> </em><em>=</em><em> </em><em>1</em><em>5</em><em>u</em><em>n</em><em>i</em><em>t</em>

<em> </em><em> </em><em> </em><em> </em><em> </em><em>=</em><em>></em><em> </em><em>radius</em><em> </em><em>of</em><em> </em><em>base </em><em>=</em><em> </em><em>9</em><em>u</em><em>n</em><em>i</em><em>t</em>

<em> </em><em> </em><em> </em><em> </em><em> </em><em>=</em><em>></em><em> </em><em>volume</em><em> of</em><em> </em><em>cylinder</em><em> </em><em>=</em><em> </em><em>π </em><em>r^</em><em>2</em><em>h</em><em> </em><em>cubic </em><em>unit</em>

<em> </em><em> </em><em> </em><em> </em><em>=</em><em>></em><em> </em><em>now,</em><em> </em><em>putting</em><em> the</em><em> value</em><em> of</em><em> </em><em>height</em><em> and</em><em> </em><em>radius </em>

<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>in </em><em>above </em><em>formula </em>

<em> </em><em> </em><em> </em><em> </em><em>=</em><em>></em><em> </em><em> </em><em>volume</em><em> </em><em>=</em><em> </em><em>2</em><em>2</em><em>/</em><em>7</em><em> </em><em>*</em><em>9</em><em>*</em><em>9</em><em>*</em><em>1</em><em>5</em>

<em> </em><em> </em><em> </em><em> </em><em>=</em><em>></em><em> </em><em>volume</em><em> </em><em>=</em><em> </em><em>3</em><em>6</em><em>1</em><em>7</em><em>7</em><em>c</em><em>u</em><em>b</em><em>i</em><em>c</em><em> </em><em>unit</em>

4 0
3 years ago
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