Answer:Multiply by the reciprocal, also sometimes referred to as "Keep, Change, Flip." Here is how it works. You rewrite the division question as a multiplication question by flipping the second fraction over. Next, keep the first number, change the division to multiplication and then flip the second fraction over.
Step-by-step explanation:
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).
Answer:
Number of Cups = 19
Step-by-step explanation:
Given
Size of Soup = 6.5 litres
SIze of cup = 330 ml
Required
Number of Cups.
First, it'll be assumed that the size of cups are uniform (the same).
The number of cups needed is calculated by dividing the size of soup by the size of the cup;
Number of Cup = Size of Soup/Size of Cup
Number of Cup = 6.5 litres/ 330 ml
<em>Convert units;</em>
<em>1 litres = 1000 ml</em>
<em>So,</em>
<em>6.5 litres = 6.5 * 1,000 ml</em>
<em>6.5 litres = 6,500 ml</em>
<em></em>
So,
Number of Cups = 6500 ml/330 ml
Number of Cups = 19.696969697
From the solution above, Naveed will definitely be able to serve 19 cups. The remaining fractional part won't fill a cup;
Hence, Number of Cups = 19
Answer:
b) 36 inches
Step-by-step explanation:
Length of the wire = Outside circumference of the cylindrical tube * length of the cylinder
= 4 * 9
= 36 inches
Length of the wire will be same to the surface area of the cylinder
Surface area of cylinder = circumference * length
