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Monica [59]
3 years ago
12

What is the slope of the line that passes through the points (7, -4) and (7, 0)? Write your answer in the simplest form.

Mathematics
1 answer:
olga55 [171]3 years ago
5 0

Answer:

The slop is undefined

i.e. m=\infty

Step-by-step explanation:

Considering the slope formula

\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

As the points are (7, -4) and (7, 0)

Here:

  • (x₁, y₁) = (7, -4)
  • (x₂, y₂) = (7, 0)

\mathrm{When\:}y_1\ne \:y_2\mathrm{\:and\:}\:x_1=x_2\mathrm{\:the\:slope\:is\:}\infty

so

  \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

            =\frac{\left(0-\left(-4\right)\right)}{\left(7-7\right)}

             =\frac{0-\left(-4\right)}{0}

             =\infty    

Therefore, the slop is undefined i.e. m=\infty

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2. Find the general relation of the equation cos3A+cos5A=0
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<h2>Answer:</h2>

A=\frac{\pi}{8}+\frac{n\pi}{4}or\ A=\frac{\pi}{2}+n\pi

<h2>Step-by-step explanation:</h2>

<h3>Find angles</h3>

cos3A+cos5A=0

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<h3>Transform the expression using the sum-to-product formula</h3>

2cos(\frac{3A+5A}{2})cos(\frac{3A-5A}{2})=0

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<h3>Combine like terms</h3>

2cos(\frac{8A}{2})cos(\frac{3A-5A}{2})=0\\\\  2cos(\frac{8A}{2})cos(\frac{-2A}{2})=0

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<h3>Divide both sides of the equation by the coefficient of variable</h3>

cos(\frac{8A}{2})cos(\frac{-2A}{2})=0

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<h3>Apply zero product property that at least one factor is zero</h3>

cos(\frac{8A}{2})=0\ or\ cos(\frac{-2A}{2})=0

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<h2>Cos (8A/2) = 0:</h2>

<h3>Cross out the common factor</h3>

cos\ 4A=0

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<h3>Solve the trigonometric equation to find a particular solution</h3>

4A=\frac{\pi}{2}or\ 4A=\frac{3\pi}{2}

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<h3>Solve the trigonometric equation to find a general solution</h3>

4A=\frac{\pi}{2}+2n\pi \ or\\ \\ 4A=\frac{3 \pi}{2}+2n \pi\\ \\A=\frac{\pi}{8}+\frac{n \pi}{4\\}

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<h2>cos(-2A/2) = 0</h2>

<h3>Reduce the fraction</h3>

cos(-A)=0

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<h3>Simplify the expression using the symmetry of trigonometric function</h3>

cosA=0

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<h3>Solve the trigonometric equation to find a particular solution</h3>

A=\frac{\pi }{2}\ or\ A=\frac{3 \pi}{2}

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<h3>Solve the trigonometric equation to find a general solution</h3>

A=\frac{\pi}{2}+2n\pi\ or\ A=\frac{3\pi}{2}+2n\pi,n\in\ Z

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<h3>Find the union of solution sets</h3>

A=\frac{\pi}{2}+n\pi

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<h2>A = π/8 + nπ/4 or A = π/2 + nπ, n ∈ Z</h2>

<h3>Find the union of solution sets</h3>

A=\frac{\pi}{8}+\frac{n\pi}{4}\ or\ A=\frac{\pi}{2}+n\pi ,n\in Z

<em>I hope this helps you</em>

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