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:
- <em><u> It begins to move toward the right</u></em>
Explanation:
The given information can be summarized in this way:
- First force vector: Fg = - 8N (vertical down)
- Second force vector: Ft = 6N (horizonal right)
- Third force vector: FN = 8N (vertical up)
- Fourth vector: Ff = - 4N (horizontal left)
Following Newton's second law, net force equal mass times acceleration:
- Net force = mass × acceleration
To predict the motion, you apply Newton's second law in each direction (vertical and horizontal)
- <u>Vertical force balance:</u>
Net vertical force = 8N - 8N = 0. This means there is not motion in the vertical direction.
- <u>Horizontal force balance:</u>
Net horizontal force = 6N - 4N = 2N. This means there is a net force of 2N to the right, which lets you predict that the bone starts to accelerate to the right; this is, the bone begins to move toward the right.
The cube has 6 sides, each a square with dimensions 3 by 3,
the area of any of these squares is 3*3=9 square units.
The total area of the cube is 6*9 square units=54 square units
The volume of a cube with side length a is given by :
, thus the volume of the cube-shaped cell is 3*3*3=27 cube units.
(surface area):(volume)=54:27 = 2:1 =2
Answer:
the ratio of the numerical values is 2
(their ratio including units is 2/unit
The formula for getting the accumulated amount(compounded) is;
A =P(1+r%)∧n
Where A = Acumulated amount
P = principle (deposit)
r = interest rate and
n = period
Since the interst is compounded quartly,
period = (5×4)-3 = 17
A = 7100(1+2.8/100)∧17
= 7100×1.028∧17
= 11,353.80
The money she will end up earning in interest on the cd = $11,353.80
Take $190 and multiply it by 0.15 (28.5) and subtract that from $190= $161.50
