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3 years ago

HELP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Mathematics

1 answer:

Westkost [7]3 years ago

8 0

Answer:

f(0) =4

f(6) =8

Step-by-step explanation:

f(0) = ?

We know 0 is less than 5 so we use the first part of the step function

f(0) = 0+4

= 4

f(6) = ?

6 is between 5 and 7 so we use the second part of the step function

f(6) =8

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Find the number to which the sequence {(3n+1)/(2n-1)} converges and prove that your answer is correct using the epsilon-N defini

Nat2105 [25]

By inspection, it's clear that the sequence must converge to $\dfrac32$ because

$\dfrac{3n+1}{2n-1}=\dfrac{3+\frac1n}{2-\frac1n}\approx\dfrac32$

when $n$ is arbitrarily large.

Now, for the limit as $n\to\infty$ to be equal to $\dfrac32$ is to say that for any $\varepsilon>0$ , there exists some $N$ such that whenever $n>N$ , it follows that

$\left|\dfrac{3n+1}{2n-1}-\dfrac32\right|$

From this inequality, we get

$\left|\dfrac{3n+1}{2n-1}-\dfrac32\right|=\left|\dfrac{(6n+2)-(6n-3)}{2(2n-1)}\right|=\dfrac52\dfrac1{|2n-1|}$
$\implies|2n-1|>\dfrac5{2\varepsilon}$
$\implies2n-1\dfrac5{2\varepsilon}$
$\implies n\dfrac12+\dfrac5{4\varepsilon}$

As we're considering $n\to\infty$ , we can omit the first inequality.

We can then see that choosing $N=\left\lceil\dfrac12+\dfrac5{4\varepsilon}\right\rceil$ will guarantee the condition for the limit to exist. We take the ceiling (least integer larger than the given bound) just so that $N\in\mathbb N$ .

6 0

3 years ago

I NEED HELP ASAP I WILL MARK YOU BRAINLIEST

Sladkaya [172]

Answer:

63 degrees and 27 degrees

Step-by-step explanation:

Complementary angles are when two angles add to 90 degrees.

So, we can check if these pairs add up to 90 degrees.

45 + 95 = 140

38 + 42 = 80

30 + 51 = 81

63 + 27 = 90

The only pair of angles that are complementary is 63 degrees and 27 degrees.

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3 years ago

Pls answer quickly :)

baherus [9]

Answer:

median=mode

Step-by-step explanation:

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2 years ago

Is negative 17/24th bigger or smaller than negative 11/12

Triss [41]

It would be smaller because 11/12 = 22/24

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3 years ago

Mr. Leonard took a job through an employment agency. The job pays $88K per year. He must pay a fee to the employment agency. The

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This question shows you how to determine the amount of money Mr. Leonard makes in 4 weeks. It takes his total salary, divides it by 52 (there are 52 weeks in a year), then multiplies it by 4 (you need 4 weeks worth of pay).

This amount is shown as $6769.24.

He must pay the agency 22% of this, so change 22% to 0.22 and multiply it by the amount he makes in 4 weeks.

0.22 x 6769.24 = $1489.23

Mr. Leonard must pay the agency $1489.23 after the first 4 weeks.

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3 years ago