<h2><u>Circle Equations</u></h2>
<h3>Write the standard form of the equation of the circle with the given characteristics.</h3><h3>Center: (0, 0); Radius: 2</h3>
To determine the equation of a circle, use the standard form of a circle (x - h)² + (y - k)² = r² where,
- <u>(h, k)</u> is the center; and
- <u>r</u> is the radius
Substitute the values of the center and radius to the standard form.
<u>Given:</u>
<u>(0, 0)</u> - <u>center</u>
<u>2</u> - <u>radius</u>
- (x - h)² + (y - k)² = 2²
- (x - 0)² + (y - 0)² = 4
- x² + y² = 4
<u>Answer:</u>
- The equation of the circle is <u>x² + y² = 4</u>.
Wxndy~~
<h3>Answer:</h3>
y = 2·sec((x -3π/2)/2) -4
<h3>Explanation:</h3>
The general shape of the curve suggests the parent function is a secant or cosecant function. Here, we choose to use the secant. It might help to familiarize yourself with the graph of a secant function (shown in the second attachment).
The centerline between the local maximum and local minimum is at -4, so that is the vertical offset.
The distance between that centerline and a local maximum or minimum is 2 units, so the vertical expansion factor is 2.
The horizontal distance between the local maximum and local minimum is 2π, so represents a horizontal expansion by a factor of 2.
The location of the local minimum is at x=3π/2, so that represents the horizontal offset.
The form of the function with these various transformations is ...
... g(x) = (vertical scale factor) × f((x - (horizontal offset))/(horizontal expansion factor)) - (vertical offset)
Filling in the function and the various values, we get ...
... y = 2·sec((x -3π/2)/2) -4
Answer:
x = - 3
Step-by-step explanation:
2x - 10 + 6 = 7x - 7 - 2x + 12
2x - 4 = 5x + 5
- 5 - 4 = 5x - 2x
-9 = 3x
x = - 9/3
x = - 3
To get from one even number to the next even number you have to add 2.
Ex. 4, 6, 8. If I start with 4, I have to add 2 to 4 to get to 6, and add 4 to 4 to get to 8. Since we don't know the starting point in this word problem we start with'x' and add 2 and add 4.
x = (x + 2) + (x + 4)
x = 2x + 6
The first equation
Not sure about the statement
movement down 5 units
move right 2 units