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MrRissso [65]
3 years ago
12

Is the relation a function? Explain your reasoning. Plz help will give brainliest

Mathematics
1 answer:
Goshia [24]3 years ago
6 0

Yes. Everything is a function.

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Consider the sequence {an}={3n+13n−3n3n+1}. Graph this sequence and use your graph to help you answer the following questions.
Fantom [35]

Part 1: You can simplify a_n to

\dfrac{3n+1}{3n}-\dfrac{3n}{3n+1} = \dfrac1{3n}+\dfrac1{3n+1}

Presumably, the sequence starts at <em>n</em> = 1. It's easy to see that the sequence is strictly decreasing, since larger values of <em>n</em> make either fraction smaller.

(a) So, the sequence is bounded above by its first value,

|a_n| \le a_1 = \dfrac13+\dfrac14 = \boxed{\dfrac7{12}}

(b) And because both fractions in a_n converge to 0, while remaining positive for any natural number <em>n</em>, the sequence is bounded below by 0,

|a_n| \ge \boxed{0}

(c) Finally, a_n is bounded above and below, so it is a bounded sequence.

Part 2: Yes, a_n is monotonic and strictly decreasing.

Part 3:

(a) I assume the choices are between convergent and divergent. Any monotonic and bounded sequence is convergent.

(b) Since a_n is decreasing and bounded below by 0, its limit as <em>n</em> goes to infinity is 0.

Part 4:

(a) We have

\displaystyle \lim_{n\to\infty} \frac{10n^2+1}{n^2+n} = \lim_{n\to\infty}10+\frac1{n^2}}{1+\frac1n} = 10

and the (-1)ⁿ makes this limit alternate between -10 and 10. So the sequence is bounded but clearly not monotonic, and hence divergent.

(b) Taking the limit gives

\displaystyle\lim_{n\to\infty}\frac{10n^3+1}{n^2+n} = \lim_{n\to\infty}\frac{10+\frac1{n^3}}{\frac1n+\frac1{n^2}} = \infty

so the sequence is unbounded and divergent. It should also be easy to see or establish that the sequence is strictly increasing and thus monotonic.

For the next three, I'm guessing the options here are something to the effect of "does", "may", or "does not".

(c) may : the sequence in (a) demonstrates that a bounded sequence need not converge

(d) does not : a monotonic sequence has to be bounded in order to converge, otherwise it grows to ± infinity.

(e) does : this is true and is known as the monotone convergence theorem.

5 0
3 years ago
Is 3x+4y=7 linear or nonlinear
Sloan [31]
Linear. It's in the form C= ax + by, so you back solve to get into the form you know is linear (y= mx + b). So using SADMEP (opposite of Pemdas) we can decide which order to solve for "Y=" in. 4y =7-3x. Y=((7-3X)/4). Y= 7/4 -3/4x. Y=-3/4x +7/4. Which is linear
3 0
3 years ago
Based on a smartphone​ survey, assume that ​58% of adults with smartphones use them in theaters. In a separate survey of 225 adu
tensa zangetsu [6.8K]

Answer:

b

Step-by-step explanation:

8 0
3 years ago
These marbles are placed in a bag and two of them are randomly drawn. What is the probability of drawing two pink marbles if the
Shalnov [3]

Answer:

2/10 * 2/10 = 1/25

Step-by-step explanation:

Suppose you have 10 marbles in a bag.

5 black , 2 pink and 3 blue

As if two pink marbles are selected then

for one pink marble

probability = event occurred / total outcomes

                 = 2/10

Similar probability for an other pink marbles

Probability for the drawing two pink marbles is

P = 2/10 * 2/10

 = 1/25

4 0
3 years ago
What is 6 tens x 10=
Effectus [21]
6 tens is the same as 60 so....
60 x 10 = 600
5 0
3 years ago
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