Answer:
You need to give us the possible answers first.
Step-by-step explanation:
The driver can drive around the track 54 times for $12. Thus for one dollar, he can drive around the track 54/12 times, or 4.5 times. If for each dollar he drives around 4.5 times, for 8 dollars, he can drive around 8*4.5 or 36 times.
If there are 207 students in 9 classes, in 1 class, there are 207/9 students, or 23 students per class. Since there are 23 students per class and there are classes, there are a total of 23*6 or 138 students in total.
Liam practices 24 times in 4 days. Thus he practices 24/4 or 6 times per day. His brother practices 12 times in 3 days. Thus he practices 12/3 or 4 times a day. Thus their rates are not equivalent.
We asked to solve the volume of the cone and we know that the formula for solving the volume is shown below:
V = 1/3*pi*r²*h where "r" for the radius and "h" for the height
We have the given values such as:
r= diameter/2 = 12/2
r= 6 inches
h=6 inches
Solving for the volume:
V= 1/3 *pi*6²*6
V=72pi in³
The answer is the letter "A" 72pi inches³.
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).