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
Rina8888 [55]
3 years ago
13

Use implicit differentiation to find an equation of the tangent line to the curve at the given points. (x2 + y2)2 = 3x2y − y3;

Mathematics
1 answer:
Andrew [12]3 years ago
5 0

Answer:

a.y+1=0

b.2x+4y=1

Step-by-step explanation:

We are given that

(x^2+y^2)^2=3x^2y-y^3

a.(0,-1)

Differentiate w.r.t x

2(x^2+y^2)(2x+2yy')=6xy+3x^2y'-3y^2y'.....(1)

Substitute x=0 and y=-1 in equation (1)

2(0+1)(-2y')=-3y'

-4y'+3y'=0

-y'=0

y'=0

m=y'=0

Point-slope form:

y-y_0=m(x-x_0)

Using the formula

y+1=0

This is required equation of tangent line to the given curve at point (0,-1).

b.(-1/2,1/2)

Substitute the value in equation (1)

2(1/4+1/4)(-1+y')=6(-1/2)(1/2)+3(1/4)y'-3(1/4)y'

2(2/4)(-1+y')=-3/2+3/4y'-3/4y'

-1+y'=-3/2

y'=-3/2+1=\frac{-3+2}{2}=-\frac{1}{2}

m=y'=-1/2

Again using point-slope formula

y-1/2=-1/2(x+1/2)

\frac{2y-1}{2}=-\frac{1}{4}(2x+1)

2y-1=-\frac{1}{2}(2x+1)

4y-2=-2x-1

2x+4y=2-1

2x+4y=1

You might be interested in
Fraction (12 4/9 + 1 2/9) +3 5/9
sveticcg [70]
12 4/9 + 1 2/9=13 6/9+3 5/9=16 11/9 that answer is farther simpled 17 2/9
so the final answer is 17 2/9
6 0
3 years ago
A paper cup is tossed 50 times. It lands right side up 11 times, upside down 14 times, and on its side 25 times. What percent of
Lynna [10]

Answer

28 percent

Step-by-step explanation:

divide 14/50

3 0
3 years ago
What is the least significant place in 0.1030
olchik [2.2K]
<h3>Least Significant Digit Place (LSD)</h3>

The Least Significant Digit Place, or LSD, is the digit with the least value in a string of numbers.

In 0.1030, there are 4 different significant places. 0.<u>1030</u>

For 0.1030, the least valuable digit place is the 0.103<u>0</u>. This is because this numeral appears at the end of the string, and is the least valuable.

5 0
2 years ago
Read 2 more answers
Solve. *25 points*<br><br> 1/2 divided by 2/3 =?
Colt1911 [192]

Answer:

The answer is 3/4

Step-by-step explanation:

When you divide two fractions, such as 1/2 ÷ 2/3, you have to flip the second fraction and then you simply multiply the numerators with each other and the denominator with each other.

7 0
2 years ago
Caleb got $10 of allowance money and babysat his cousin for $8 per hour this week. He earned a total of $46 this week. Which equ
bearhunter [10]
The answer to this question is 126 hours
8 0
3 years ago
Other questions:
  • In ΔHIJ, the measure of ∠J=90°, the measure of ∠H=71°, and JH = 2 feet. Find the length of IJ to the nearest tenth of a foot.
    10·1 answer
  • Which of these is equal to cos 47°?
    13·2 answers
  • Show that if X is a geometric random variable with parameter p, then
    5·1 answer
  • Micah paid $45 for 14.5 gallons of gas. What is the estimated cost of one gallon of gas?
    11·2 answers
  • PLEASE HELP I WILL MARK YOU BRAINLIEST. Ms. Simmons is using sticky notes to write reminders to herself. Each sticky note is 5/6
    5·1 answer
  • Find the values of x and y in the figure below:
    9·2 answers
  • A group of friends were working on a student film. They spent $570 on equipment,
    8·2 answers
  • the total distance of a car moves varies directly with the time in hours.the car moves a total distance of 812 miles in 14 hours
    7·1 answer
  • Bananas sell for $0.49 for 1 pound. How much will 1.31 pounds cost?
    6·2 answers
  • The regular price of a tennis racquet is $79.99 and the sale price is $64.99. Find the percent of discount to the nearest whole
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!