Answer:
283.495
Step-by-step explanation:
Answer:
y = 2/3x + 5/3
Step-by-step explanation:
The slope of the line is ...
slope = (change in y)/(change in x) = (3-1)/(2-(-1)) = 2/3
Then the point-slope form of the desired line can be written ...
y = m(x -h) +k . . . . . slope m through point (h, k)
y = 2/3(x +1) +1 . . . . slope 2/3 through point (-1, 1)
y = 2/3x + 5/3 . . . . . . simplify to slope-intercept form
Answer:
<h3>#1</h3>
The normal overlaps with the diameter, so it passes through the center.
<u>Let's find the center of the circle:</u>
- x² + y² + 2gx + 2fy + c = 0
- (x + g)² + (y + f)² = c + g² + f²
<u>The center is:</u>
<u>Since the line passes through (-g, -f) the equation of the line becomes:</u>
- p(-g) + p(-f) + r = 0
- r = p(g + f)
This is the required condition
<h3>#2</h3>
Rewrite equations and find centers and radius of both circles.
<u>Circle 1</u>
- x² + y² + 2ax + c² = 0
- (x + a)² + y² = a² - c²
- The center is (-a, 0) and radius is √(a² - c²)
<u>Circle 2</u>
- x² + y² + 2by + c² = 0
- x² + (y + b)² = b² - c²
- The center is (0, -b) and radius is √(b² - c²)
<u>The distance between two centers is same as sum of the radius of them:</u>
<u>Sum of radiuses:</u>
<u>Since they are same we have:</u>
- √(a² + b²) = √(a² - c²) + √(b² - c²)
<u>Square both sides:</u>
- a² + b² = a² - c² + b² - c² + 2√(a² - c²)(b² - c²)
- 2c² = 2√(a² - c²)(b² - c²)
<u>Square both sides:</u>
- c⁴ = (a² - c²)(b² - c²)
- c⁴ = a²b² - a²c² - b²c² + c⁴
- a²c² + b²c² = a²b²
<u>Divide both sides by a²b²c²:</u>
Proved
Answer: the value of k is 3
Step-by-step explanation:
You have to find out what times 14 equals 42.
You divide 42 by 14 and then you get 3.
Hope this helps :)
