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Lapatulllka [165]
3 years ago
6

100 points Use the line tool to graph the equation on the coordinate plane. y=3/4x

Mathematics
1 answer:
Ad libitum [116K]3 years ago
5 0

Answer:

The equation of line passes through the origin with slope m is given by:

y=mx

Given the equation:

y = \frac{3}{4}x

Slope = 3/4

y-intercept = 0

To Graph the equation on the coordinate plane.

Let us consider some values of x and y to make table.

x           y = \frac{3}{4}x  

0                  0

2                  1.5

4                   3

6                   4.5

8                   6

10                  7.5

Now, you can plot these points on the coordinate plane using line tool as shown below.

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Determine if the following infinite series converges or diverges
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Using limits, it is found that the infinite sequence converges, as the limit does not go to infinity.

<h3>How do we verify if a sequence converges of diverges?</h3>

Suppose an infinity sequence defined by:

\sum_{k = 0}^{\infty} f(k)

Then we have to calculate the following limit:

\lim_{k \rightarrow \infty} f(k)

If the <u>limit goes to infinity</u>, the sequence diverges, otherwise it converges.

In this problem, the function that defines the sequence is:

f(k) = \frac{k^3}{k^4 + 10}

Hence the limit is:

\lim_{k \rightarrow \infty} f(k) = \lim_{k \rightarrow \infty} \frac{k^3}{k^4 + 10} = \lim_{k \rightarrow \infty} \frac{k^3}{k^4} = \lim_{k \rightarrow \infty} \frac{1}{k} = \frac{1}{\infty} = 0

Hence, the infinite sequence converges, as the limit does not go to infinity.

More can be learned about convergent sequences at brainly.com/question/6635869

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