12x²-9x = 0
3x(4x-3)=0
4x-3=0
4x=3
x=3/4
so either x = 0 or x = 3/4
Answer: 6.48
Step-by-step explanation:
Mean is 79.4, population size is 5
MAD formular is addition of variance point /population size
n∑∣xi−xˉ∣
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).
<h3>
Answer: 11 cans</h3>
======================================================
Explanation:
SA = surface area of the sphere
SA = 4*pi*r^2
SA = 4*pi*8^2
SA = 804.247719
The surface area is roughly 804.247719 sq ft.
I used the calculator's stored version of pi to get the most accuracy possible.
Since 1 paint can covers 75 sq ft, divide that surface area over 75 to find out how many cans you need.
804.247719/75 = 10.72330292
Round up to the nearest integer to get 11
You'll have leftover paint, but it's better to go over the goal than come up short.
Answer:
5/4
Step-by-step explanation:
Make a proportion:
16/4 = 5/x
Cross Multiply:
20 = 16x
x = 5/4
