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
Arturiano [62]
2 years ago
6

Can someone please explain how to get the answer I've watched multiple videos on implicit derivatives and I still cant figure it

out.​

Mathematics
1 answer:
Arisa [49]2 years ago
7 0

We're given the implicit equation

x² + 2x + y² - 4y = 12

where "implicit" means that one of the variables is considered a function of the other. In this case, the variable y = y(x) depends on the value of the variable x - in other words, the possible values of y are implied by the value of x. We then say that this equation defines y as an implicit function of x.

We're also given the implicit derivative,

dy/dx = (-2x - 2)/(2y - 4)

which tells us the rate of change y as a function of both x and y. The value of dy/dx corresponds to the slope of the tangent line to the curve defined by the implicit equation above at some point (x, y).

The tangent line is horizontal when its slope is zero. This happens when

(-2x - 2)/(2y - 4) = 0

If y ≠ 2, then we can eliminate the denominator and we're left with

-2x - 2 = 0

Solve for x :

-2x = 2

x = -1

This tells us that the points on the curve with x-coordinate -1 have a tangent line to the curve that is horizontal.

The tangent line is vertical when its slope is undefined/infinite, or equivalently when the denominator of dy/dx is zero:

2y - 4 = 0

Solve for y :

2y = 4

y = 2

So any point on the curve with y-coordinate 2 will have a tangent line there that is vertical.

By completing the square in the implicit equation, we can easily identify where these points are located.

x² + 2x + y² - 4y = 12

x² + 2x + 1 + y² - 4y + 4 = 17

(x + 1)² + (y - 2)² = 17

This equation defines a circle centered at (-1, 2) with radius √17. When x = -1, we have

(y - 2)² = 17   ⇒   y = 2 ± √17

and when y = 2, we have

(x + 1)² = 17   ⇒   x = -1 ± √17

See the attached plot to see the circle and the tangents at these points.

You might be interested in
Write -0.89 as a fractions.
artcher [175]

Answer:

It would be -89/100

That is the lowest form and can not be reduced

5 0
3 years ago
Read 2 more answers
How to do double sided equations
Veronika [31]

Answer:

multiply each side

Step-by-step explanation: this is becasue when numbers are beside eachother they mean multiply


7 0
3 years ago
Change to a decimal. Round to hundredths if necessary.<br> 4 5/8
stepan [7]

Answer: The answer is 4.63✨

Step-by-step explanation: You have to round to 4.625 to the nearest hundredth consider the thousandths’ value of 4.625, which is 5 and equal or more than 5. Therefore, the hundredths value of 4.625 increases by 1 to 3.

4.625 rounded to the nearest hundredth = 4.63

5 0
2 years ago
Eve measured a county park and made a scale drawing. The picnic area, which is 68 yards wide in real life, is 34 inches wide in
mote1985 [20]

Answer:

Eve used scale as 2 yards is equal to 1 inch.

Step-by-step explanation:

Given:

Actual Picnic area = 68 yards.

Drawing Picnic area = 34 inches.

We need to find the scale used by Eve.

Solution:

Now we can say that;

scale used by Eve can be calculated by dividing Actual Picnic area from drawing picnic area.

framing in equation form we get;

scale used by Eve = \frac{68}{34} = 2\ yd/in

Hence Eve used scale as 2 yards is equal to 1 inch.

8 0
3 years ago
Juanita will work for 4 7/8 hours at her job on Saturday. if she also volunteers for 2 1/3 hours at the hospital, how many hours
zheka24 [161]

Answer:

I think it's D...maybe

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • Ahaahhhahhahhahahaha help
    7·1 answer
  • A parallelogram has a base of length x + 7 and a height of x + 2 and has an area of 50 square units. find the base and height of
    11·1 answer
  • There are 40 coins in a roll of nickles. Find the value of 25 rolls of nickels.
    10·2 answers
  • What is the justification for -3x+7=7x-3
    7·1 answer
  • Y+1.8=3.14 to a whole number
    5·1 answer
  • The class wants to raise a total of $1750. If they receive a profit of $1.75 from each candy bar sold, how many bars must they s
    10·2 answers
  • You have $2,000 on a credit card that charges a 16% interest rate. If you want to pay off the credit card in 5 years, how much w
    10·1 answer
  • Find the measure of the angle.<br> Can someone help?<br> I need to show the work.
    6·1 answer
  • I need answer ASAP <br> No links please
    13·1 answer
  • Solve for n.<br> n/5 +0.6=2
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!