Find the slope of a line perpendicular to y=-2/5x+4/5.

Mathematics

1 answer:

Inga [223]3 years ago

7 0

For two lines to be perpendicular their slopes must be negative reciprocals of one another, mathematically:

m1*m2=-1

In this case, our reference line has a slope of -2/5 so our perpendicular slope must satisfy:

-2m/5=-1

-2m=-5

m=-5/-2

m=5/2

....

The negative reciprocal property can be more easily understood by realizing that the angle of a line is:

tanα=m

α=arctanm

So if one line, A, has a slope of m and the other, B, has a slope of -1/m

A=arctan m, B=arctan -1/m

B-A=90° (feel free to use any value for m that you choose to see that this is true, so if the two lines differ by 90°, they are indeed perpendicular)

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Geometric Series assistance

Levart [38]

we have been asked to find the sum of the series

$\sum _{n=1}^5\left(\frac{1}{3}\right)^{n-1}$

As we know that a geometric series has a constant ratio "r" and it is defined as

$r=\frac{a_{n+1}}{a_n}=\frac{\left(\frac{1}{3}\right)^{\left(n+1\right)-1}}{\left(\frac{1}{3}\right)^{n-1}}=\frac{1}{3}$

The first term of the series is $a_1=\left(\frac{1}{3}\right)^{1-1}=1$

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On simplification we get

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2 years ago

Point A is at (-1,-9) and Point M is at (0.5,-2.5).

leva [86]

Midpoint Formula: $(\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})$

So firstly, let's start with the x-coordinates. Since we know the midpoint's x-coordinate and point A's x-coordinate, we can solve for point B's x-coordinate as such:

$\frac{-1+x}{2}=0.5\\\\-1+x=1\\\\x=2$