36
Step-by-step explanation:
4 5/8*3 is 13.875
500 decided by 13.875 is a little over 36, so you can make 36 full ribbons
Each pack of batteries cost $21 each.
And then you have $63.
The operation to be used: Division.
63 ÷ 21 ==
Answer: 3
= You can buy 3 packs of batteries with your $63.
No, these equations are not equivalent.
1/5, or one fifth, is part of a whole. Imagine you have a pie, cut into five pieces, and your friend comes over and eats four pieces, so now you have one of the five original pieces. That's what you have here.
5/5, or five fifths, is a whole. any number divided by itself is automatically one, so it is like making another pie and cutting it into five pieces, only this time no one eats any of it because it's burned or something. At the end, you have five pieces of pie
5/1 is actually just another way of writing plain old 5. To keep the pie example rolling, you have five pies, and no one eats any of these either, so they are all yours. You have 5 pies divided between one person, so at the end of the day you have 5 whole pies.
Hope that helped!
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).
