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
Necesito que alguien resuelva este ejercicio paso a paso y me lo explique como lo desarrollo y como llego a ese resultado pero l
Kobotan [32]

Answer:

translate to English please thanks!

8 0
3 years ago
For each figure answer the following questions
Rudiy27

9514 1404 393

Answer:

  a) ∆ABC ~ ∆EDC by AA similarity

  b) ED/AB = 3/4

  c) 15 cm

Step-by-step explanation:

a) Two angles in each triangle are the same, so the AA similarity postulate can be used to declare the ∆ABC ~ ∆EDC. (Each triangle includes a right angle and angle C.)

__

b) Corresponding sides are ED/AB, DC/BC, EC/AC. The ratio of corresponding sides is ED/BC = (12 cm)/(16 cm) = 3/4.

__

c) Using the ratios identified above, we have ...

  DC/BC = 3/4 = x/(20 cm)

  x = 3/4(20 cm)

  x = 15 cm

8 0
3 years ago
BRAINLIEST TO CORRECT ANSWER!!
BartSMP [9]

120/1500=x/100, x=8

So, you make 8% commision, meaning you now have to do this:

x/1300=8/100, so x=$104

3 0
3 years ago
Read 2 more answers
A small tree was planted at a height of 6 feet. The tree has been planted for 16 months, and is now 49.2 feet tall. Which equati
Jet001 [13]

Answer:

YOU MUST HAVE ONC WONDERED WHAT IS CHICKEN PO0. WELL IM HERE TO TELL YOU. PLEASE STOP EATING IT. IT MUGHT BE BAD FOR YOU.

ALS OTHE ANSWEER IS A>6x+16=49>2

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
What is 78 in scientific notation
4vir4ik [10]
Well first you take 78 and turn it to 7.8 
then multiply by 10000 
therefore 7.8*10000= ?
3 0
3 years ago
Other questions:
  • How to solve? Sarah has a $100 she gave 3/4 of the money to her sister. She gave a 1/2 of the rest of the money to her friend. H
    13·1 answer
  • What is [(1/16) + (1/4)] * [(2/3) * (1/4)]? Simplify the answer and write as a proper fraction. *
    5·1 answer
  • How many fourths are in 5 1/2?
    12·1 answer
  • What is 4, 4.9, 4 3/4, 4.329 in order from greatest to least
    5·2 answers
  • Identify the domain and range
    15·1 answer
  • Is (9,9) a solution of the following linear
    6·1 answer
  • In a group of 700 people only 5% of them have red hair how many people hade red hair
    8·1 answer
  • PLS HELPPPPPP NOWEW!!!!
    5·1 answer
  • Select ALL the true statements about the scatter plot below.
    11·1 answer
  • A card is chosen at random from a standard deck.
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!