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Brums [2.3K]
3 years ago
8

PLEASE HELP! I WILL GIVE BRAIN! NEED ANSWERED IN 10 MINUTE TOPS! PLEASE!!

Mathematics
1 answer:
uranmaximum [27]3 years ago
5 0

Answer:

6 is 81, 5 is the third one, 6 is 20, and 7 is 6

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Describe the rule for the sequence 2, 1, 2/3, 1/2, 2/5, 1/3, 1/7,...
Triss [41]

Multiply 2 by 1/2 to get 1.

Multiply 1 by 2/3 to get 2/3.

Multiply 2/3 by 3/4 to get 6/12 = 1/2.

Multiply 1/2 by 4/5 to get 4/10 = 2/5.

Multiply 2/5 by 5/6 to get 10/30 = 1/3.

Multiply 1/3 by 6/7 to get 6/21 = 2/7. (I suspect there's a typo in the question.)

And so on, so that the <em>n</em>th term in the sequence is multiplied by <em>n</em>/(<em>n</em> + 1) to get the (<em>n</em> + 1)th term.

Recursively, the sequence is given by

\begin{cases}a_1=2\\a_n=\dfrac{n-1}na_{n-1}&\text{for }n>1\end{cases}

We can solve this exactly by iterating:

a_n=\dfrac{n-1}na_{n-1}=\dfrac{n-1}n\dfrac{n-2}na_{n-1}=\dfrac{n-1}n\dfrac{n-2}{n-1}\dfrac{n-3}{n-2}a_{n-3}=\cdots

and so on down to

a_n=\dfrac{(n-1)\cdot(n-2)\cdot(n-3)\cdot\cdots\cdot3\cdot2\cdot1}{n\cdot(n-1)\cdot(n-2)\cdot\cdots\cdot4\cdot3\cdot2}a_1

or

a_n=\dfrac{(n-1)!}{n!}a_1

and with lots of cancellation, we end up with

a_n=\dfrac{a_1}n=\boxed{\dfrac2n}

6 0
2 years ago
what are the values of m∠abc, m∠cbf, and m∠dbe in the given figure? Explain or show your work. A good 55 points will go to the o
vesna_86 [32]

Step-by-step explanation:

m∠abc = m∠ebf = 58°

reason: vertical angles

m∠cbf = 180-m∠ebf = 180-58 = 122°

reason: Supplementary angles

m∠dbe = 90-m∠ebf = 90-58 = 32°

reason: complementary angles

5 0
3 years ago
16) Your salary goes from $8.75 an hour at your present job to $16.50 an hour in your new job. What is
Agata [3.3K]

Answer:

The percent change in salary from one job to the next is 88.57%.

Step-by-step explanation:

The previous salary of per hour =  $8.75 per hour

The current salary of per hour  = $16.50 per hour

Change in the salary rate per hour  =  Current salary  -  Previous Salary

                                                             = $16.50 per hour -  $8.75 per hour

                                                             =$7.75 per hour

⇒The change in the salary per hour rate is $7.75

Now, \textrm{Percentage Change in salary}  = \frac{\textrm{Change in the rate of salary}}{\textrm{Previous Salary}}  \times 100

= \frac{7.75}{8.75}  \times 100 = 88.57

or, the change in salary percentage is 88.57%

Hence, the percent change in salary from one job to the next is 88.57%.

4 0
3 years ago
Find the area of each circle. Round to the nearest tenth if necessary. Use 3.14 for pi
vlada-n [284]
153.94 I believe :) :)
7 0
3 years ago
What type of proof is used extensively in Geometry?
Nikolay [14]

Answer: two-column

Step-by-step explanation:

7 0
3 years ago
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