Does the following infinite series converge or diverge?

1 answer:

3 0

Look like that first one is supposed to have a denominator of 2.

This is a geometric series with a common ratio 4, so it diverges (absolute value 1 or more), meaning it has no sum. Choice C.

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A walking path across a park is represented by the equation Y equals negative 2X -7. A new path will be built perpendicular to t

Ulleksa [173]

So we are given an initial equation of: $y=2x-7$ .

We are told that a new path is going to be perpendicular to this line. So to find a slope that is perpendicular to a line, we take the slope of the known line (in this case 2) and we flip it and change the sign. So since this slope is essentially $\frac{2}{1}$ , we are going to flip it to make it $\frac{1}{2}$ and change the sign to make it $-\frac{1}{2}$ .

So now we know that the slope of the perpendicular line is $-\frac{1}{2}$ , we can start a new equation for this line:

$y=-\frac{1}{2}x+b$

We are also told that the path will intersect at (-2,-3) - this is a solution to the two lines. So to find b in this new equation, let's plug in the x and y values found in the point:

$-3=-\frac{1}{2}(-2)+b$