We want to simplify √(-48).
Note that
i² = -1 by definition.
Therefore
Answer: c.
Answer:
5
Step-by-step explanation:
Y= 1/8 x + 10
You do 8-11/-16-8= -3/-24= 1/8 that’s your slope
Then to get y intercept you plug in ur slope and coordinates of (8,11) into point slope form. And you get that the y intercept is 10.
Answers:
Horizontal Line: y = 5
Vertical Line: x = 8
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Explanation:
All horizontal lines are of the form y = k, for some constant k. We want the horizontal line to pass through (8,5), meaning every point on this horizontal line must have y coordinate 5. Therefore, y = 5 is the equation of the horizontal line. Two such points on this line are (1, 5) and (8, 5). All that matters is the y coordinate is 5. The x coordinate can be anything you want. The slope of any horizontal line is 0.
Flipping things around, all vertical lines will have the x coordinate of each point be the same value. Draw a vertical line through (8,5) and note how each point has x coordinate of 8. Two such points are (8,1) and (8,5). Therefore, the equation of the vertical line is x = 8. The y coordinate can be any value you want. The slope of any vertical line is undefined. Unlike the horizontal line, we cannot write this equation in slope intercept form (namely because the slope isn't defined).
You do the implcit differentation, then solve for y' and check where this is defined.
In your case: Differentiate implicitly: 2xy + x²y' - y² - x*2yy' = 0
Solve for y': y'(x²-2xy) +2xy - y² = 0
y' = (2xy-y²) / (x²-2xy)
Check where defined: y' is not defined if the denominator becomes zero, i.e.
x² - 2xy = 0 x(x - 2y) = 0
This has formal solutions x=0 and y=x/2. Now we check whether these values are possible for the initially given definition of y:
0^2*y - 0*y^2 =? 4 0 =? 4
This is impossible, hence the function is not defined for 0, and we can disregard this.
x^2*(x/2) - x(x/2)^2 =? 4 x^3/2 - x^3/4 = 4 x^3/4 = 4 x^3=16 x^3 = 16 x = cubicroot(16)
This is a possible value for y, so we have a point where y is defined, but not y'.
The solution to all of it is hence D - { cubicroot(16) }, where D is the domain of y (which nobody has asked for in this example :-).
(Actually, the check whether 0 is in D is superfluous: If you write as solution D - { 0, cubicroot(16) }, this is also correct - only it so happens that 0 is not in D, so the set difference cannot take it out of there ...).
If someone asks for that D, you have to solve the definition for y and find that domain - I don't know of any [general] way to find the domain without solving for the explicit function).
