Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
x^2/3 + y^2/3 = 4
(-3√3, 1)
(astroid) ​

Answers

Answer 1

Differentiate both sides of

[tex]x^{2/3} + y^{2/3} = 4[/tex]

implicite with respect to x :

[tex]\dfrac23 x^{-1/3} + \dfrac23 y^{-1/3} \dfrac{\mathrm dy}{\mathrm dx} = 0[/tex]

Solve for the derivative dy/dx :

[tex]x^{-1/3} + y^{-1/3} \dfrac{\mathrm dy}{\mathrm dx} = 0 \\\\ y^{-1/3} \dfrac{\mathrm dy}{\mathrm dx} = - x^{-1/3} \\\\ \dfrac{\mathrm dy}{\mathrm dx} = -\dfrac{x^{-1/3}}{y^{-1/3}} \\\\ \dfrac{\mathrm dy}{\mathrm dx} = -\left(\dfrac yx\right)^{1/3}[/tex]

Get the slope at the given point (-3√3, 1) :

[tex]\dfrac{\mathrm dy}{\mathrm dx}(-3\sqrt3,1) = -\left(\dfrac{1}{-3\sqrt3}\right)^{1/3} = \dfrac1{(3\sqrt3)^{1/3}} = \dfrac1{\sqrt3}[/tex]

Then the equation of the tangent line to the curve through (-3√3, 1) is

[tex]y - 1 = \dfrac1{\sqrt3}(x+3\sqrt3) \\\\ \boxed{y = \dfrac1{\sqrt3}x + 4}[/tex]


Related Questions

Can someone help me solve x?

Answers

9514 1404 393

Answer:

  x = 1

Step-by-step explanation:

The diagram is intended to show you that the whole is the sum of the part:

  11 = (10x -1) +(2x)

  11 = 12x -1 . . . . . . . collect terms

  12 = 12x . . . . . . . . add 1 to both sides

  1 = x . . . . . . . . . . . divide both sides by 12

The value of x is 1. The lengths of the segments are 9 and 2.

select all zeros of the function (x)=(x+10)(x-5) (x+1)

Answers

answer: -10, -1, 5



have a great day :)

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Someone help, please solve this and explain

Answers

Answer:

A

Step-by-step explanation:

Perimeter = 2W + 2L

134 = 2(29) + 2x

134 - 58 = 2x

x = 76/2

x = 38 (length)

A = 2L + 2(29) >= 134 (more or equal = >=)

write 3.01 as a mixed number

Answers

3 1/100 ‏‏‎ ‎ ‏‏‎ ‎ ‏‏‎ ‎ ‏‏‎ ‎ ‎ ‏‏‎ ‎ ‏‏‎ ‎ ‏‏‎ ‎ ‏‏‎ ‎ ‏‏‎ ‎ ‏‏‎ ‎ ‏‏‎ ‎ ‏‏‎ ‎ ‏‏‎ ‎ ‏‏‎ ‎ ‏‏‎ ‎ ‏‏‎

Add the mixed numbers.


Answers

9514 1404 393

Answer:

  1 5/24 + 7 22/24 = 8 27/24

Step-by-step explanation:

No change is required to the fraction on the first line:

  1 5/24 = 1 5/24

The fraction on the second line can be multiplied by 2/2 to make its denominator 24.

  7 11/12 = 7 22/24

The fraction on the third line is the sum of the fractions on the other two lines. It is an improper fraction. We know this because the integer portion of the sum is shown as 8, not 9, as it would be if the fraction were reduced.

  5/24 +22/24 = 27/24

Then the sum is ...

  1 5/24 +7 22/24 = 8 27/24

_____

If the fraction on the final line were reduced, the sum would be 9 3/24 = 9 1/8.

A plumber has a 36-in. pipe. He must cut into two pieces so that one piece is 14 inches longer than the other. How long is each piece?

Answers

25 inches and 11 inches

5 years ago, the average age of ishan and his father was 27 years old. If ishan is now 1/3 of his father’s age, how old os ishan now?

Answers

Answer:

9

Step-by-step explanation:

3x9=27

Let the age of son be x.
Thus, age of father is 4x.
After 5 years, their ages will be x+5 and 4x+5 years respectively.
As per the question, we have
4x+5=3(x+5)
⇒4x+5=3x+15
⇒x=10
Age of father will be 4x=4×10=40 years.
Thus when son is 10 years old, father is 40 years

WHAT IS 300% ON 100 ?

Answers

Answer:

300.

Step-by-step explanation:

that's the answer.

Answer:

The answer would be 300

Step-by-step explanation:

300 x 100 = 30000

30000 ÷ 100 = 300

Hope this helps!!

fill in the blank (no word bank)

Answers

Answer:

Angle, Lengths

Step-by-step explanation:

Angle measurements and segment lengths are preserved as the transformations neither change the scale factor nor change the angle measurements

How would you describe the plants growth? Please help!!!!

Answers

Answer:

increasing

Step-by-step explanation:

it's increasing because throughout the days you can see that the plants growth is slowly progressing in this case going up on the grpah.

The Earth rotates at a unit rate of
.25 degrees per minute. How much
does the earth rotate in half of an
hour?

Answers

Answer:

it will rotate 7.5 degrees

Step-by-step explanation:

There are 450 kids in 6th grade. out of these kids 40% chose French as their connection. how many kid chose French?

Answers

Answer:

180 kids chose French

Step-by-step explanation:

40/100 = x/450

4/10 = x/450

10•45= 450

4•45= 180

chloe and her dog bingo walk 2/3 of a mile in 1/6 of an hour at this rate how far can they walk per hour

Answers

Answer:

2 miles

Step-by-step explanation:

In one hour, close and her dog can walk a total of 2 miles

Answer:

4

Step-by-step explanation:

2/3 x 6

2x2=4

Find the area and perimeter.
5.6 cm

Answers

Answer:

31.36cm;22.4cm

Step-by-step explanation:

hope this helps

Answer:

Answer: 31.36 cm² ; 22.4 cm

Area:

[tex]{ \rm{area = (side \times side)}} \\ { \rm{area = (5.6 \times 5.6)}} \\{ \underline{ \underline { \rm{ \: \: area = 31.36 \: {cm}^{2} \: \: }}}}[/tex]

Perimeter:

[tex]{ \rm{perimeter = (4 \times side)}} \\ { \rm{perimeter = (4 \times 5.6)}} \\ { \underline{ \underline{ \rm{ \: \: perimeter = 22.4 \: cm \: \: }}}}[/tex]

Find the difference of 2/3 and 3/5.

Answers

Answer:

1/15

Step-by-step explanation:

2/3*5/5 - 3/5*3/3( we are multiplying and dividing by the same number in order to get the same denominator. as 5/5 = 1 and 3/3= 1)

2/3*5/5 - 3/5*3/3

= 10/15-9/15

= 1/15

HELP LAST ATTEMPT MARKING AS BRAINLIEST

Answers

The answer would be x=24. First set equal to 180°, then combine like terms and solve.

The Students on each team who drew the greatest number will be the captain of that team. Place the players of the Tigers team in order from Least to Greatest.

Who was the captain of the Tiger Team?

Answers

Chan,Caleb ,Lydia, Ryan , Anya , Macy

A fast-food restaurant sells hamburgers and chicken sandwiches. On a typical weekday the demand for hamburgers is normally distributed with mean 313 and standard deviation of 57; the demand for chicken sandwiches is normally distributed with mean 93 and standard deviation 22.

Answers

Answer:

Cool can i come?

Step-by-step explanation:

A) Damien washes cars on his summer vacation to earn money. It took him 16 hours to wash 10 cars. Use scaling to complete the table to determine the number of cars Damien could wash in 40 hours. Number of Hours 16 40 032 부 I 20 20 6 Number of Cars 10 How many cars did Damien wash every hour? lo cars​

Answers

is it a big number or short number

The required number of cars that can be washed by Damien in 40 hours is 25.

Given that,
Damien washes cars on his summer vacation to earn money. It took him 16 hours to wash 10 cars. Use scaling to complete the table to determine the number of cars Damien could wash in 40 hours, is to be determined.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
Let the number of cars that were washed in 40 hours be x,
Now, according to the question.
16 / 10 = 40 / x
x = 400 / 16
x = 25

Thus, the required number of cars that can be washed by Damien in 40 hours is 25.

Learn more about arithmetic here:

brainly.com/question/14753192

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interquartile range 245 297 323 369 388

Answers

The interquartile range of the data set is 107.5 :)

Factor 24m6−30m4−45m3.

Answers

Answer:

3m³(8m³-10m-15)

Step-by-step explanation:

Assuming the question isn't asking for factoring over the complexes,

24m⁶−30m⁴−45m³

3m³(8m³-10m-15)

robby raises holstein and jersey cows on his farm in the ratio of 7:5 if he has a total of 48 cows on his farm how many holstein cows does he own?

Answers

Answer:

28

Step-by-step explanation:

The total amount of cows is 48 and is split into 12 groups (7+5).

So 1 group is 48÷12=4

1 group=4

He owns 7 groups of Holstein cows.

So if 1 group is 4, 7 groups is 7x4=28.

28

The number of Holstein cows, if The ratio of Holstein and jersey cows is 7:5, and the Total number of cows is  48, is 28.

What is ratio?

It is the contrast of two different quantities. For instance, if your father weighs 90 kg, and you weigh 30 kg, the weight ratio is 1:3. If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio. A proportion is an equation that equalizes two ratios.

Given:

The ratio of Holstein and jersey cows is 7:5,

Total number of cows = 48

Calculate the values as shown below,

Assume the number of Holstein cows is 7x

7x + 5x = 48

12x = 48

x = 4

Thus, the number of Holstein cows is 7 × 4 = 28

To know more about Ratios:

https://brainly.com/question/13419413

#SPJ2

A movie package can be added to a customer's cable TV service for a cost of $8 per month. How much will the additional Movie package cost for 13 months?

Answers

Should be $104 because, $8 X 13 Months equals to $104

b) In 3x?, the 3 is called the____

please help​

Answers

Answer:

3 is the coefficient

Step-by-step explanation:

The number in front of the variable is called the coefficient

3x

3 is the coefficient

x is the variable

Find the measure of angle B

Answers

Answer: 283.9953 degrees

Explanation:
A whole circle is 360 degrees. If we know one angle portion of the circle, we can subtract it from 360 to find the remaining angle.

360 - 76.0047 = 283.9953

=
angle E and angle F are supplementary. If mangleF =
(9x - 38)° and mangleF = (2x + 42), find mangleF

=

Answers

Answer:

jhhffffffffffffffffffffhfbrsjjssssssssssss

Step-by-step explanation:

HELP LAST ATTEMPT !?!!!!!

Answers

Answer:

x=31

Step-by-step explanation:

2x+1=63 [Vertically opposite angles]

2x=63-1

x=62/2

x=31

A women buys 23 pounds of potatoes. She gives 10% of them to a neighbor and 15% of them to her mother. How many pounds dose she have left?

Answers

Answer:

= 17.25 pounds (Answer)

Step-by-step explanation:

Potatoes she bought = 23 pounds

Amount she gave outsiders= 10+15=25%

= 23×25/100= 23/4=5.75 pounds

Potatoes left with her= 23 — 5.75

= 17.25 pounds (Answer)

Answer:

17.25 pounds

Step-by-step explanation:

10% of 23 is 2.3

15% of 23 is 3.45

Add them together you get 5.75

Subtract 5.75 from 23

Answer is 17.25

What is the range of the function graphed below?

Answers

I’m not 100% sure but I think it’s the first one

What is reciprocal of 2 1/2

Answers

Answer:

0.4

Step-by-step explanation:

type in a calculator 1 divide by 2.5 to get the answer

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