1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Valentin [98]
3 years ago
8

Find where the slope of the curve is defined: x^2y-xy^2=4

Mathematics
1 answer:
Natali [406]3 years ago
3 0
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). 
You might be interested in
Alex lost $200 for the second round Alex lost $380 what has Alex loss after two rounds
KIM [24]

Answer:

$580

Step-by-step explanation:

Step 1:

$200 + $380

Answer:

$580

Hope This Helps :)

5 0
3 years ago
X^3 times x^? equals to x^17 <br><br> what’s the missing exponent?
ElenaW [278]

Answer:

  14

Step-by-step explanation:

The applicable rule of exponents is ...

  (a^b)(a^c) = a^(b+c)

__

You have ...

  (x^3)(x^a) = x^17

  x^(3+a) = x^17

Equating exponents, we get ...

  3 +a = 17

  a = 14

The missing exponent is 14.

5 0
3 years ago
Use your TVM Solver to determine the future balance in a mutual fund account (a type of investment account) if you make weekly p
Paladinen [302]

Answer:

  $46,141.71

Step-by-step explanation:

This looks about right, based on weekly deposits for the duration. However, I cannot vouch for it entirely, as the number of weekly deposits in 15 years will actually be 782.

_____

Computing this by hand doing the initial balance separately from the weekly deposits, I get a total of $46,252.10 using 782 weekly deposits. For that purpose, I tried to figure an equivalent weekly interest rate given monthly compounding and the fact there are 52 5/28 weeks in a year on average.

I suspect the only way to get this to the cent would be to build a spreadsheet with payment dates and interest computation/payment dates. Some months, there would be 5 deposits between interest computations; some years there would be 53 deposits.

5 0
3 years ago
Solve both equations for y and graph <br>-4x+y=-2<br>-6x+3y=2
JulijaS [17]
I put the solution on the paper

8 0
3 years ago
Read 2 more answers
What is 5+3*4-8+2*7 equal to
neonofarm [45]

Answer: 23 is your answer


Step-by-step explanation:


6 0
3 years ago
Read 2 more answers
Other questions:
  • 2x+5 is greater than 50
    6·2 answers
  • Please answer question 7 and 8 above
    9·1 answer
  • Solve the System by Substitution<br> by<br> X = 2y - 3<br> 4x - 5y = -3<br> X=<br> Y=
    9·1 answer
  • How many fewer people attended the pacers games than attended the clippers games
    8·1 answer
  • What is the equation of the graph below?
    7·1 answer
  • Mary wants to make a box she starts with a piece of cardboard whose length is 15cm and width is 10cm then she cuts them in congr
    6·1 answer
  • Am I getting this correct?
    11·1 answer
  • Find the measure of the angle indicated.
    5·1 answer
  • <img src="https://tex.z-dn.net/?f=%287x%5E%7B2%7D%29%282x%5E%7B4%7D%29%28-5x%29" id="TexFormula1" title="(7x^{2})(2x^{4})(-5x)"
    15·1 answer
  • 1/2 is the same number as
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!