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
Rainbow [258]
3 years ago
15

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2 + 6xy + 12y2 = 28, (2,

1) (ellipse)
Mathematics
1 answer:
navik [9.2K]3 years ago
5 0

Answer:

The equation of the tangent line is y = -\frac{5}{18}\cdot x +\frac{14}{9}.

Step-by-step explanation:

Firstly, we obtain the equation for the slope of the tangent line by implicit differentiation:

2\cdot x + 6\cdot y + 6\cdot x \cdot y' + 24\cdot y \cdot y' = 0

2\cdot (x + 3\cdot y) + 6\cdot (x + 4\cdot y) \cdot y' = 0

6\cdot (x + 4\cdot y) \cdot y' = -2\cdot (x+3\cdot y)

y' = -\frac{1}{3}\cdot \left(\frac{x + 3\cdot y}{x + 4\cdot y} \right) (1)

If we know that (x,y) = (2, 1), then the slope of the tangent line is:

y' = -\frac{1}{3}\cdot \left(\frac{2+3\cdot 1}{2 + 4\cdot 1} \right)

y' =-\frac{5}{18}

By definition of tangent line, we determine the intercept of the line (b):

y = m\cdot x + b

b = y - m\cdot x (2)

If we know that (x,y) = (2,1) and m = -\frac{5}{18}, then the intercept of the tangent line is:

b = 1 - \left(-\frac{5}{18} \right)\cdot (2)

b = \frac{14}{9}

The equation of the tangent line is y = -\frac{5}{18}\cdot x +\frac{14}{9}.

You might be interested in
What is the surface area of the cube below?
makvit [3.9K]

Answer:384

Step-by-step explanation:

5 0
3 years ago
Kyle bought a DVD that cost $19.23, including tax. She gave the sales clerk a $20 bill. How much change should Kyle receive?
maxonik [38]

Answer: Kyle received $0.77

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
What’s the difference between numbers that are to the power of with parentheses and no parentheses. For example (-2/5)^3 and -2/
Verdich [7]

Answer:

See below

Step-by-step explanation:

The first one 'cubes' the denominator AND the numerator:

(-2/5)^3  = -2/5  * -2/5  * -2/5 =  -8/125

The second one 'cubes' only the denominator:

-2/5^3  = -2 / (5 * 5 * 5) =  - 2 / 125

8 0
2 years ago
For triangle ABC with A=103, B=24, a=16, find angle C
Ilya [14]

Answer:

given A=103° , B=24°

In triangle ABC,

A+B+C=180° [angle sum property of triangle]

103°+24°+C=180°

127°+C=180°

C=180°-127°

C=53°

hope it help u dear...

5 0
3 years ago
If the absolute value of x is 4, what is the value of x?
natima [27]
The absolute value of x is 4
4 0
3 years ago
Other questions:
  • How fast was the plane traveling ?
    11·2 answers
  • Please help thank you.
    9·1 answer
  • serena is the manager at a coffee shop the amount of money she earns is represented by m=21h. how much more per hr does she earn
    10·1 answer
  • While traveling across flat land, you notice a mountain directly in front of you. The angle of elevation to the peak is 1.5°. Af
    12·1 answer
  • Assume that the samples are independent and that they have been randomly selected. A marketing survey involves product recogniti
    5·1 answer
  • A shoe salesman earns a commission of 20% of all shoe sales made. Yesterday he sold 2 pairs of shoes for $80 each and 3 pairs of
    12·1 answer
  • A bag of valentine candies has 24 red candies 14 white candies and 12 pink candies what is the probability that you will randoml
    10·1 answer
  • Solve the following equations for x (3x-6)=18
    13·2 answers
  • The drop that riders experience on Dr. Doom’s Free Fall can be modeled by the quadratic function, h(t) = −9.8t2−5t + 39
    10·1 answer
  • Help me with 11 please I’m crying Perform indicated operations
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!