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
ZanzabumX [31]
3 years ago
12

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. 7x2 + xy + 7y2 = 15, (1, 1

) (ellipse)
Mathematics
1 answer:
riadik2000 [5.3K]3 years ago
7 0
Assume y=y(x).

7x^2+xy+7y^2=15
\dfrac{\mathrm d}{\mathrm dx}[7x^2+xy+7y^2]=\dfrac{\mathrm d}{\mathrm dx}[15]
14x+y+x\dfrac{\mathrm dy}{\mathrm dx}+14y\dfrac{\mathrm dy}{\mathrm dx}=0
\dfrac{\mathrm dy}{\mathrm dx}(x+14y)=-(14x+y)
\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{14x+y}{x+14y}

The slope of the tangent line to the curve at (a,b) is then -\dfrac{14a+b}{a+14b}, so the tangent to (1,1) has slope

\dfrac{\mathrm dy}{\mathrm dx}\bigg|_{x=1,y=1}=-\dfrac{15}{15}=-1

The point-slope form of the tangent line is then

y-1=-(x-1)\iff y=-x+2
You might be interested in
Trigonometry
ludmilkaskok [199]

Answer:

⅘ or 0.8

Step-by-step explanation:

Hypotenuse² = 3² + 4²

Hypotenuse = 5

Sin(θ) = 4/5

5 0
3 years ago
What is the slope of a line that is parallel to the line y = 3/4x + 2?
alexandr402 [8]
3/4
when it’s parallel it has the same slope!
5 0
3 years ago
Can someone please tell me if this angle is supplementary or complementary
DaniilM [7]

Answer:

Step-by-step explanation:

Since the angles both come off of the straight line, they are supplementary, and they add up to equal 180 degrees.

2x + 4x + 24 = 180 and

6x + 24 = 180 and

6x = 156 so

x = 26

8 0
3 years ago
Work out the surface area of the solid cuboid.<br><br> The diagram is not drawn to scale.
yKpoI14uk [10]

Answer

surface \ area = 2( lb + bh+hl) = 2(6 + 12 + 8) =2*26 = 52cm^2

7 0
3 years ago
Read 2 more answers
Please help!!!!! Geometry! (Will give Brainliest)
dezoksy [38]

Answer:

Side N: 20

Equation: 5 × 4 = 20

Step-by-step explanation:

Look at the other sides, and try to find a "pattern". Just by looking at the bottoms of the triangles, I saw 4 on BC and 16 on FG. I know that 4 times 4 equals 16, so that could be and option.

Now look at the left side. AB has a length of 3, and EF has a length of 12. I know that 3 times 4 is 12. Both times, there was an increase of 4 between the sides of the triangles.

Now, let's apply this to the last side. 5 times 4 is 20. So, the last side would be 20 on triangle EFG, and the equation would be 5 × 4 = 20.

7 0
3 years ago
Other questions:
  • What fraction of the Hexagon is shaded?
    5·2 answers
  • Hell plzzzzzzzzzzzzzzzzzzzzzzzz​
    14·2 answers
  • Angle P measures 112 degrees, what are the measures of angle N and O?
    15·1 answer
  • How would you explain to someone the rules of a horizontal translation where we are subtracting from the inputs(within the paren
    10·1 answer
  • Find the product. Simplify your answer.<br> (2u–4)(u2+2u–1)
    10·1 answer
  • Please help! <br><br> Which angle is a vertical angle with ZEFD?<br> - - - -
    6·1 answer
  • What is the slope on this graph
    7·1 answer
  • -3x is less than or equal to 3, the solution of the inequality is?
    7·1 answer
  • Find the value of 7xº - (6x)".
    15·2 answers
  • Agri-small business limited expenses on petrol for their fleet is r 4 850.00 at the end of september and they have a balance of
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!