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3 years ago

How is a function different from a relationship that is not a function?

Mathematics

1 answer:

Degger [83]3 years ago

4 0

A function is a special relationship between two sets in which each input value corresponds to exactly one output value

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Find the area of the shaded segment. Round your answer to the nearest square centimeter. Will make brainliest answer if correct

allochka39001 [22]

First find the area of the circle using A=pi*r^2
pi*36
Then divide this by 4 because the shaded region is 1/4 of the circle
(36*pi)/4=9*pi
Final answer: B

6 0

2 years ago

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

<img src="https://tex.z-dn.net/?f=%5Csqrt%7B4x%2B1%7D-5%3D0%5C%5C%5C%5C%5C%5C%5C%5C%5Csqrt%7B5x-1%7D%2B3%3Dx%5C%5C" id="TexFormu

adoni [48]

Answer:

what topic is this please

8 0

2 years ago

You are given a loaded six-sided die. Such a die can produce any integer from 1 to 6. The die rolls a 4 three times as often as

beks73 [17]

I would say 6 bc it’s a die of 6 and u get it 6 times

6 0

2 years ago

The options are 1. is, is not

djverab [1.8K]

Answer:

1. is not

2. increase

3. remain the same

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers