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
cricket20 [7]
3 years ago
14

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2/3 + y2/3 = 4 (−3 3 , 1)

(astroid)
Mathematics
1 answer:
vovikov84 [41]3 years ago
8 0

Answer with Step-by-step explanation:

We are given that an equation of curve

x^{\frac{2}{3}}+y^{\frac{2}{3}}=4

We have to find the equation of tangent line to the given curve at point (-3\sqrt3,1)

By using implicit differentiation, differentiate w.r.t x

\frac{2}{3}x^{-\frac{1}{3}}+\frac{2}{3}y^{-\frac{1}{3}}\frac{dy}{dx}=0

Using formula :\frac{dx^n}{dx}=nx^{n-1}

\frac{2}{3}y^{-\frac{1}{3}}\frac{dy}{dx}=-\frac{2}{3}x^{-\frac{1}{3}}

\frac{dy}{dx}=\frac{-\frac{2}{3}x^{-\frac{1}{3}}}{\frac{2}{3}y^{-\frac{1}{3}}}

\frac{dy}{dx}=-\frac{x^{-\frac{1}{3}}}{y^{-\frac{1}{3}}}

Substitute the value x=-3\sqrt3,y=1

Then, we get

\frac{dy}{dx}=-\frac{(-3\sqrt3)^{-\frac{1}{3}}}{1}

\frac{dy}{dx}=-(-3^{\frac{3}{2}})^{-\frac{1}{3}}=-\frac{1}{-(3)^{\frac{3}{2}\times \frac{1}{3}}}=\frac{1}{\sqrt3}

Slope of tangent=m=\frac{1}{\sqrt3}

Equation of tangent line with slope m and passing through the point (x_1,y_1) is given by

y-y_1=m(x-x_1)

Substitute the values then we get

The equation of tangent line is given by

y-1=\frac{1}{\sqrt3}(x+3\sqrt3)

y-1=\frac{x}{\sqrt3}+3

y=\frac{x}{\sqrt3}+3+1

y=\frac{x}{\sqrt3}+4

This is required equation of tangent line to the given curve at given point.

You might be interested in
Jamilla is buildiing a square sandbox with sides 7 feet long. She wants to put sand 2 ft deep in the box. How much sand should J
jonny [76]

volume = 7*7*2 = 49*2=98

 she needs to get 98 cubic feet of sand

3 0
3 years ago
Read 2 more answers
Esther wants to have $150,000 in 10 years. She plans to invest $18,000 to start and make yearly payments of $2,500 to the accoun
Bezzdna [24]

Answer:

No

Step-by-step explanation:

She will have made $69,717.37

Please mark brainlest

4 0
2 years ago
-5m + 2m<br> ANSWER ASAP PLEASE
abruzzese [7]

Answer:

the answer is -3m

4 0
3 years ago
Read 2 more answers
(10-3)(-2)<br><br> giving brainlist out
Kryger [21]

Answer:

i think the answers 5

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
The diameter of a circle is 8 centimeters. A central angle of the circle of the circle intercepts an arc of 12 centimeters. What
Studentka2010 [4]

Answer:

The measure of the angle is 3\ radians

Step-by-step explanation:

we know that

The formula to calculate the arc length of a circle is equal to

L=r\theta

where

r is the radius of the circle

\theta is the measure of the angle in radians

In this problem we have

L=12\ cm, r=8/2=4\ cm

substitute in the formula and solve for \theta

12=4\theta

\theta=12/4

\theta=3\ radians

5 0
3 years ago
Read 2 more answers
Other questions:
  • Which math problem is being modeled on the number line
    12·1 answer
  • i'm doing operations with complex numbers and i understand everything until there's a number in front of the parentheses so plea
    6·1 answer
  • Angie and Kim are sharing a large sub sandwich. Angie ate
    6·1 answer
  • How many quarts are equivalent to 14 liters? Round your answer to the nearest tenth.
    9·2 answers
  • Does 2 times 36 equal 3 times 24
    9·1 answer
  • Which of the following math statements contains variables? check all that apply
    6·2 answers
  • What is 130° in radians?
    14·1 answer
  • During a thunderstorm, 4
    8·2 answers
  • HELP ME WITH THIS ASAP
    6·2 answers
  • The railroad company wants to sell $3,854 in tickets. If each ticket costs $41, how many tickets will the railroad have to sell
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!