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kakasveta [241]
2 years ago
11

Can someone please answer. There is a picture. There is only one question. Thank you so much

Mathematics
1 answer:
Sloan [31]2 years ago
3 0
So than you check this graph so you see that the radius has a length of 4 units 
from what result that thet x^2 +y^2 =4 

so the choice 3rd is right sure 
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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
Evaluate 1/2m - 2/3n when m = 3 and n = 8.
Anika [276]

Answer:

1/2(3)-2/3(8)

3/2-9/3

<u>3</u>-<u>9</u>

2.3

<u>9</u><u>-</u><u>3</u><u>2</u>

6

<u>-23</u>

6

7 0
3 years ago
Which of the following numbers is greatest, or furthest to the right on the number line? {56, 39, 74, 81, 62}
Dimas [21]
The greatest number is 81
4 0
3 years ago
Read 2 more answers
16. Carrie is packing her clothes in moving
joja [24]

Answer:

I don't get it but in my opinion I would say it's 4

5 0
3 years ago
Correct answers only!
alina1380 [7]

Answer:

$39

Step-by-step explanation:

Using the given formula :

I = P × R × T

I = 30 × 10/100 × 3

I = $9

She have = 30 + 9 = $39

3 0
2 years ago
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