Answer:
Let x = cost of your friend's lunch.
x + x + 3 = 19
x= 8
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).
The answer is that Ryu saved $17.50
Explanation: Two ways to look at it, 35% is the same as saying 35 hundredths or 0.35. We know that anytime there’s an of in a math problem it means multiply, so you multiply .35x50 and you get 17.5 or $17.50.
Explanation 2: you can look at the 50 as the 100%, so if you divide 100% by 100 you get 1% so that’s what we’re going to start with dividing the 50 by 100 and you get .5, and now that you have 1% you can multiply that by 35 to get the 35%. Which is 17.5
The answer should be B, but I might be wrong.
The answer to number one is C
and the answer to number two is A
