Find the slope m of a line perpendicular to a line with known slope −6.

Mathematics

2 answers:

Nataly_w [17]3 years ago

8 0

Answer:

Step-by-step explanation:

The slope of perpendicular line to the a given line with a known slope is the opposite inverse of that slope. An opposite inverse is the number written as fraction flipped around and its sign changed. (negatives become positives and positives become negatives)

-6 can be written as -6/1

The opposite inverse is 1/6

<em>PLEASE MARK BRAINLIEST</em>

Ipatiy [6.2K]3 years ago

7 0

Answer:

1/6

Step-by-step explanation:

Perpendicular lines have slopes whose product is -1. That is ...

-6m = -1

m = 1/6 . . . . . divide by -6

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2 years ago

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Answer:

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Step-by-step explanation:

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2 years ago

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larisa86 [58]

Answer:

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Step-by-step explanation:

$\frac{ {tan}^{2}x }{2} - 2 {cos}^{2}x = 1 \\ \\ \frac{ {tan}^{2}x - 4{cos}^{2}x }{2} = 1 \\ \\ {tan}^{2}x - 4{cos}^{2}x = 2 \\ \\ \frac{{sin}^{2}x}{{cos}^{2}x} - 4{cos}^{2}x = 2 \\ \\ \frac{{sin}^{2}x - 4{cos}^{4}x}{{cos}^{2}x} = 2 \\ \\ {sin}^{2}x - 4{cos}^{4}x = 2{cos}^{2}x \\ \\ 4{cos}^{4}x + 2{cos}^{2}x - {sin}^{2}x = 0 \\ \\ 4{cos}^{4}x + 2{cos}^{2}x + {cos}^{2}x - 1= 0 \\ \\ 4{cos}^{4}x + 3{cos}^{2}x - 1= 0 \\ \\ 4{cos}^{4}x + 4{cos}^{2}x - {cos}^{2}x - 1= 0 \\ \\4{cos}^{2}x({cos}^{2}x + 1) - 1({cos}^{2}x + 1) = 0 \\ \\ ({cos}^{2}x + 1)(4{cos}^{2}x - 1) = 0 \\ \\ ({cos}^{2}x + 1) = 0 \: or \: (4{cos}^{2}x - 1) = 0 \\ \\ {cos}^{2}x = - 1 \: or \: 4{cos}^{2}x = 1 \\ \\ {cos}x = \sqrt{ - 1} \: which \: is \: not \: possible \\ \therefore \: {cos}^{2}x = \frac{1}{4} \\ \\ \therefore \: {cos}x = \pm\frac{1}{2} \\ \\ \therefore \: {cos}x = \frac{1}{2} \: or \: {cos}x = - \frac{1}{2} \\ \\ \therefore \: {cos}x = {cos}60 \degree \: or \: {cos}x = {cos}120 \degree \\ \\ \therefore \:x = 60 \degree \: \: or \: \: x = 120 \degree$