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
Step2247 [10]
3 years ago
12

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. y 2 ( y 2 − 4 ) = x 2 ( x

2 − 5 ) , ( 0 , − 2 ) (devil's curve) y2(y2-4)=x2(x2-5), (0,-2) (devil's curve)
Mathematics
1 answer:
yawa3891 [41]3 years ago
4 0

Answer:

y = -2

Step-by-step explanation:

To find the equation of the tangent we apply implicit differentiation, and then we take apart dy/dx

The equation is

y^2(y^2-4)=x^2(x^2-5)

implicit differentiation give us

\frac{d}{dx}[y^2(y^2-4)=x^2(x^2-5)]\\\\2y\frac{dy}{dx}(y^2-4)+y^2(2y\frac{dy}{dx})=2x(x^2-5)+x^2(2x)\\\\4y^3\frac{dy}{dx}-8y\frac{dy}{dx}=2x^3-10x+2x^3\\\\\frac{dy}{dx}=\frac{4x^3-10x}{4y^3-8y}

But we know that

m=\frac{dy}{dx}\\y=mx+b

Hence, for the point (0,-2) and by replacing for dy/dx

m=\frac{dy}{dx}_{(0,-2)}=\frac{4(0)+10(0)}{4(-2)^3-8(-2)}=0

Hence m=0, that is, the tangent line to the point is a horizontal line that cross the y axis for y=-2. The equation is:

y=(0)x+b = -2

HOPE  THIS HELPS!!

You might be interested in
Identify a and b for the hyperbola with equation
Nady [450]

Answer:

identify a and b for the hyperbola with equation

7 0
2 years ago
What is the graph of the inequality 3x+2y>-5
Doss [256]

Answer:

The graph with solution is shown below.

Step-by-step explanation:

We need to find the x-intercept and y-intercept for given equation.

For  x-intercept , substitute y=0

Considering inequality sign as equality and simplifying,

3x+2y=-5\\3x+0=-5\\x=-\frac{5}{3} , point is (-\frac{5}{3} ,0)

Similarly,

For y-intercept , substitute x=0

We get,

3x+2y=-5\\0+2y=-5\\y=-5/2 , point is (0,-\frac{5}{2})

We locate this two points on the graph now and join them.

The joining line will be dotted as the inequality has just 'greater than' symbol. The region above the dotted line is the solution to graph.

4 0
3 years ago
Elin has 1/3 hour to warm up for her gymnastics meet. She must complete each 6 different stretches. She spends an equal amount o
Novay_Z [31]

Answer:

1/18 hr per stretch

Step-by-step explanation:

total # of hrs / # of stretches

1/3 hr / 6 stretches = 1/18 hr per stretch

7 0
3 years ago
Read 2 more answers
Which of these best describes the asthenosphere inside of the earth's mantle?
nordsb [41]

Hello there

1) asthenosphere lies below lithosphere and part of uppermantle.

it's highly viscous and behaves plastic.

it lies approximately 70-150 km below surface depending which . (50km below oceanic crust and 150km below continental crust)

2) 1/2 '4 =1/16 (4 is to the power of 1/2)

hope this helps

thank you

Best Regards Queen Z

8 0
3 years ago
D. Add the interest payment to the government's $6 trillion expenditures for the next year, and assume that tax revenues remain
disa [49]

Answer:

Spike spanish ????????????

8 0
2 years ago
Other questions:
  • The length of a rectangular field is 24 meters. This is 3 meters was than twice the width. Find the width.
    12·1 answer
  • What are the solutions to the equation (2x – 5)(3x – 1) = 0? x= 5 or x + 1
    5·1 answer
  • The work of a student trying to solve the equation 4(2x − 1) = 11 + 3x + 5 is shown below: Step 1: 4(2x − 1) = 11 + 3x + 5 Step
    11·1 answer
  • Y=1/6x+5 in standard form using integers.
    6·2 answers
  • A recipe that makes 6 servings calls for 1 1/5 cups of juice.
    9·1 answer
  • Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. (Enter your answers as a comma-
    10·1 answer
  • A taxi charges $3.00 to pick you up and $1.00 for every mile driven. How could
    9·2 answers
  • R1 663 200 in words?​
    6·1 answer
  • Which proportion models the following problem:
    13·1 answer
  • A
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!