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just olya [345]
3 years ago
6

The x-coordinate of point P is positive, and the y-coordinate of point P is positive. In which quadrant is point P?

Mathematics
2 answers:
mestny [16]3 years ago
8 0

The answer is Quadrant 1  

torisob [31]3 years ago
6 0
Quadrant 1, or the “top right” in which everything is positive.
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Prove the following by induction. In each case, n is apositive integer.<br> 2^n ≤ 2^n+1 - 2^n-1 -1.
frutty [35]
<h2>Answer with explanation:</h2>

We are asked to prove by the method of mathematical induction that:

2^n\leq 2^{n+1}-2^{n-1}-1

where n is a positive integer.

  • Let us take n=1

then we have:

2^1\leq 2^{1+1}-2^{1-1}-1\\\\i.e.\\\\2\leq 2^2-2^{0}-1\\\\i.e.\\2\leq 4-1-1\\\\i.e.\\\\2\leq 4-2\\\\i.e.\\\\2\leq 2

Hence, the result is true for n=1.

  • Let us assume that the result is true for n=k

i.e.

2^k\leq 2^{k+1}-2^{k-1}-1

  • Now, we have to prove the result for n=k+1

i.e.

<u>To prove:</u>  2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1

Let us take n=k+1

Hence, we have:

2^{k+1}=2^k\cdot 2\\\\i.e.\\\\2^{k+1}\leq 2\cdot (2^{k+1}-2^{k-1}-1)

( Since, the result was true for n=k )

Hence, we have:

2^{k+1}\leq 2^{k+1}\cdot 2-2^{k-1}\cdot 2-2\cdot 1\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{k-1+1}-2\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-2

Also, we know that:

-2

(

Since, for n=k+1 being a positive integer we have:

2^{(k+1)+1}-2^{(k+1)-1}>0  )

Hence, we have finally,

2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1

Hence, the result holds true for n=k+1

Hence, we may infer that the result is true for all n belonging to positive integer.

i.e.

2^n\leq 2^{n+1}-2^{n-1}-1  where n is a positive integer.

6 0
3 years ago
?? anyone know thank you
lana66690 [7]

Answer:

19/20 is the correct answer

7 0
2 years ago
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how do you select a month of the year at random what is the probability that the month ends with the ER
wel

Answer:

4/12 or 1/3

Step-by-step explanation:

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3 years ago
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A study was done by an online retail store to determine the rate at which users used its website. A graph of the data that was c
mariarad [96]

Answer:

The correct answer is C.

Step-by-step explanation:

First, we can eliminate A and D since it is obviously only 36 months.

Note that the question asks what can be interpreted from the <em>range</em> of the graph.

The range is the number of users in thousands (per month) (as can be seen from the side title).

While B is technically correct, it wrongly interprets the range. C is the best choice.

The correct answer is C.

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Goodmorning hope you have a great day :)
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Answer:

hello good morning.have a nice day

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