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Anni [7]
2 years ago
8

What would the integer 500 equal using powers of 10? How did you come up with that answer?

Mathematics
1 answer:
strojnjashka [21]2 years ago
8 0
Hello,

500=10^x
==> Log 500=xLog10
==>x=log 500
==>x=2,6989700043360188047862611052755...


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Dont really understand how to do this
bija089 [108]

Answers:

t_{10} = -22 \ \text{ and } S_{10} = -85

========================================================

Explanation:

t_1 = \text{first term} = 5\\t_2 = \text{first term}-3 = t_1 - 3 = 5-3 = 2

Note we subtract 3 off the previous term (t1) to get the next term (t2). Each new successive term is found this way

t_3 = t_2 - 3 = 2-3 = -1\\t_4 = t_3 - 3 = -1-3 = -4

and so on. This process may take a while to reach t_{10}

There's a shortcut. The nth term of any arithmetic sequence is

t_n = t_1+d(n-1)

We plug in t_1 = 5 \text{ and } d = -3 and simplify

t_n = t_1+d(n-1)\\t_n = 5+(-3)(n-1)\\t_n = 5-3n+3\\t_n = -3n+8

Then we can plug in various positive whole numbers for n to find the corresponding t_n value. For example, plug in n = 2

t_n = -3n+8\\t_2 = -3*2+8\\t_2 = -6+8\\t_2 = 2

which matches with the second term we found earlier. And,

tn = -3n+8\\t_{10} = -3*10+8\\t_{10} = -30+8\\t_{10} = \boldsymbol{-22} \ \textbf{ is the tenth term}

---------------------

The notation S_{10} refers to the sum of the first ten terms t_1, t_2, \ldots, t_9, t_{10}

We could use either the long way or the shortcut above to find all t_1 through t_{10}. Then add those values up. Or we can take this shortcut below.

Sn = \text{sum of the first n terms of an arithmetic sequence}\\S_n = (n/2)*(t_1+t_n)\\S_{10} = (10/2)*(t_1+t_{10})\\S_{10} = (10/2)*(5-22)\\S_{10} = 5*(-17)\\\boldsymbol{S_{10} = -85}

The sum of the first ten terms is -85

-----------------------

As a check for S_{10}, here are the first ten terms:

  • t1 = 5
  • t2 = 2
  • t3 = -1
  • t4 = -4
  • t5 = -7
  • t6 = -10
  • t7 = -13
  • t8 = -16
  • t9 = -19
  • t10 = -22

Then adding said terms gets us...

5 + 2 + (-1) + (-4) + (-7) + (-10) + (-13) + (-16) + (-19) + (-22) = -85

This confirms that S_{10} = -85 is correct.

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2 years ago
The perimeter of the entire garden.
Leno4ka [110]
Add up all the lengths of the garden and you will be able to get the perimeter.
8 0
1 year ago
6,600,000,000 exponential notation
jeyben [28]

Answer:

6.6 x 10^9

Step-by-step explanation:

8 0
2 years ago
You have a recipe that indicates to use 3 parts milk for every 2 parts sugar You use 12 cups of milk How much sugar do you need
Stells [14]
Proportion
3 parts milk. 12cups
2 parts sugar X

8 cups sugar

8 0
3 years ago
Suppose you roll a die. Find the probability of each event. Show your work. Simplify all answers.
Tema [17]

Answers:

a) 1/6

b) 0

Step-by-step explanation:

a) this is the way i remember

on a 6 sided dice there are <em>6</em> outcomes. 5 is 1 of those outcomes. so its 1/<em>6</em>

b) there no 7 on a six sided dice so its impossible. impossible outcomes are represented as 0

7 0
2 years ago
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