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Sauron [17]
3 years ago
5

4. Prove the identity 8 sin^2x cos^2x = 1 - cos 4x.​

Mathematics
1 answer:
shusha [124]3 years ago
5 0
  • Here you go
  • hope it helps

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Write the equation of the circle with the center (3,2) and (-6,-4)
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Answer: y=2/3x

Step-by-step explanation:

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Find y<br> y= |x−5| + |x+5| (if x&gt;5)
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Answer:

y=2x if x>5.

Step-by-step explanation:

|x-5|=x-5 \text{ if } x-5 \ge 0. This means when x \ge 5.

|x-5|=-(x-5) \text{ if } x-5 \le 0. This means when x \le 5.

It doesn't matter where the 5 is included since either x-5 or -(x-5) would product 0 at x=5.

|x+5|=x+5 \text{ if } x+5 \ge 0. This means when x \ge -5.

|x+5|=-(x+5) \text{ if } x+5 \le 0. This means when x \le -5.

The same statement here about x=-5 as I about x=5 with the earlier expression.

So anyways we have x>5.

This means y=|x-5|+|x+5| can be rewritten as

y=(x-5)+(x+5)=(x+x)+(-5+5)=2x+0=2x.

y=2x

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3 years ago
What is the equation of a line perpendicular to why=2x-6 that passes through (5,4)
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Answer:

y = ½(13- x)

Step-by-step explanation:

Step 1. Find the<em> slope (m₁) of the original line </em>

The equation for the original line is

      y = 2x - 6

slope = m₁ = 2

Step 2. Find the <em>slope (m₂) of the perpendicular line </em>

m₂ = -1/m₁     Substitute the value of m₁

m₂ = -1/2

Step 3. Find the <em>equation for the perpendicular line</em>

y = mx + b     Substitute the value of m₂

y = -½x + b

The line passes through (5, 4).  

4 = -½(5) + b     Add 5/2 to each side

4 = -5/2 + b     Add 2 to each side

b = 13/2  

y = -½x + 13/2

y = ½(13 – x)  

In the image, below, the red line is the graph of your original equation.

The blue line passing through (5, 4) is the perpendicular line.

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