find the equation for the line tangent to the parametric curve: xy==t3−9t9t2−t4 x=t3−9ty=9t2−t4 at the points where t=3t=3 and t=−3t=−3. for t=3t=3, the tangent line (in form y=mx by=mx b) is

Answers

Answer 1

To find the equation for the line tangent to the parametric curve at the point where t=3, we need to find the values of x and y at t=3 and the corresponding slopes.

Given the parametric equations: x=t^3−9t and y=9t^2−t^4.

At t=3, we have:

x = (3)^3 - 9(3) = 0

y = 9(3)^2 - (3)^4 = 54

To find the slope at t=3, we need to find dy/dx:

dy/dt = 18t - 4t^3

dx/dt = 3t^2 - 9

dy/dx = (dy/dt) / (dx/dt)

      = (18t - 4t^3) / (3t^2 - 9)

At t=3, we have:

dy/dx = (18(3) - 4(3)^3) / (3(3)^2 - 9)

     = -6

Therefore, the slope of the tangent line at t=3 is -6. To find the equation of the tangent line, we use the point-slope form- y - 54 = (-6)(x - 0)

Simplifying  y = -6x + 54

So the equation of the tangent line at t=3 is y = -6x + 54x

For t=-3, we can repeat the same process to find the equation of the tangent line. However, since the curve is symmetric about the y-axis, the tangent line at t=-3 will have the same equation as the tangent line at t=3, except reflected across the y-axis. Therefore, the equation of the tangent line at t=-3 is y = 6x + 54.

To know more about tangent lines refer here

https://brainly.com/question/31326507

SPJ11


Related Questions

what special name is given to the domain in a linear programming problem

Answers

Answer:

Mathematics

Step-by-step explanation:

Linear programming (LP, also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization).

Help meh ill mark you all 4 plz if you can

Answers

Answer:

Step-by-step explanation:

5+ 1 7/8 = 6 7/8

3 - 1 3/4 = 1 1/4

7 3/4 + 4 = 11 3/4

4- 2 3/7 = 1 4/7

n the diagram, the measure of angle 9 is 85°.

4 lines intersect to form 16 angles. The angles created, clockwise from top left are 1, 2, 3, 4; 5, 6, 7, 8; 9, 10, 11, 12; 13, 14, 15, 16.

Which angle must also measure 85°?
Angle2
Angle5
Angle11
Angle12

Answers

Answer:

The real answer is angle 5

Step-by-step explanation:

The angle 11 must measure the angle 85. The correct option is C.

What are lines and angles?

An infinitely long row of evenly spaced dots that extends in both directions makes up a line. Its length is the only dimension it has. An illustration of a line is a horizontal mark made on a piece of paper. A figure made by two rays that intersect at the same endpoint is referred to as an angle.

Given that in the diagram, the measure of angle 9 is 85°. 4 lines intersect to form 16 angles. The angles created, clockwise from the top left are 1, 2, 3, 4; 5, 6, 7, 8; 9, 10, 11, 12; 13, 14, 15, 16.

The measure of angle 9 is equal to the measure of angle 11. it means that angle 9 and angle 11 are equal to 85 degrees. The image is attached with the answer below. Shows the angle 9 and angle 11 are vertically opposite angles.

To know more about lines and angles follow

https://brainly.com/question/25770607

#SPJ6

Is this a right triangle?

Answers

Answer:

No, one of the angles has to be 90º for it to be a right triangle

Step-by-step explanation:

Answer:

no. it doesn't have a right angle.

Solve for x. 3 - √x = 0

Answers

Answer:

x = 9

Step-by-step explanation:

3 - √x = 0

Subtract 3 from both sides of the equation

3 - 3 - √x = 0 - 3

-√x = -3

Divide both sides by -1

-√x / -1 = -3 / -1

√x = 3

Take the square of both sides

(√x) ² = 3²

X = 9

sebuah kantong berisi 20 kelereng merah dan 15 kelereng putih.toni memiliki 3 kantong yang berisi kelereng dengan jumlah yang sama. jika Toni memberikan 45 kelereng kepada adiknya, sisa kelereng Toni adalah​

Answers

Answer:

60

Step-by-step explanation:

The computation of the rest of the marbles is given below:

Since there is 20 red and 15 white marbles

Also the 3 bags contains same marbles

So if he gives 45 marbles, so the remaining would be

= (20 + 15) × 3 - 45

= 35 × 3 - 45

= 105 - 45

= 60

d-1/2=5/12 what is d??

Answers

Answer:

d = [tex]\frac{11}{12}[/tex]

Step-by-step explanation:

1) To solve for d, isolate it in the equation. So, to get rid of the [tex]-\frac{1}{2}[/tex] with the d, add [tex]\frac{1}{2}[/tex] to both sides.

[tex]d-\frac{1}{2} = \frac{5}{12} \\d - \frac{1}{2} +\frac{1}{2} = \frac{5}{12} + \frac{6}{12} \\d = \frac{11}{12}[/tex]

Thus, d = [tex]\frac{11}{12}[/tex].

Is my answer correct???

Answers

Answer:

Yes! Great job!

Hope that helps!

yes it is correct!!!!!!!!!!!!!!!!!!!!!!

If y = 3x - 5 and x = 3y - 5, then what are x and y?

Answers

Answer:

2?

Step-by-step explanation:

Answer:

x nang iwan at y naman ganon

Solve the quadratic equation x^2- 11x = 12 using any method. Describe the method you chose and why you chose it.

Answers

Answer:

12, -1 its the answer

Step-by-step explanation:

1. subtract 12 from both sides

2. simplify which looks like this x^2- 11x - 12=0

3.solve with the quadratic formula

4.separate the solutions

and there you go

The length of an alligator in a zoo is 14 5/6 feet. The Everglades National Park lists the longest alligator ever recorded in Florida at 17 5/12 feet. Which is the difference in their lengths? a 2 3/4 feet b 2 7/12 feet c 3 5/8 feet d 3 5/6 feet

Answers

9514 1404 393

Answer:

  b)  2 7/12 ft

Step-by-step explanation:

The difference is ...

  (17 5/12 ft) - (14 5/6 ft) = (17 -14) ft + (5/12 -5/6) ft

  = 3 ft + (5/12 -10/12) ft = 3 ft - 5/12 ft

  = 2 7/12 ft

I did this myself, but I kept getting negative numbers can someone else try and do this and see what you get ​

Answers

Answer:

6

Step-by-step explanation:

Answer:

67

Step-by-step explanation:

4x = 2x + 12

4x - 2x = 2x - 2x + 12

2x = 12

2x ÷ 2 = 12 ÷ 2

X = 6

Plug into HI

9 × 6 + 13 = 67

Find the values of the variables and the lengths of the sides of this kite.

Answers

Answer:

option D

Step-by-step explanation:

option D is the correct answer of this question .

plz mark my answer as brainlist.

hope this will be helpful to you.

Answer:

D

Step-by-step explanation:

pls help this is due soon check 2 that apply

Answers

Answer:

I am pretty sure it is option a and c

Sorry if i am wrong

If 8 model airplanes cost $24, what is the unit price of the model airplanes? The unit price of the model airplane.​

Answers

Answer:

3 dollars per airplane

Step-by-step explanation:

24/8 is 3, where 8 is airplanes and 24 is cost in total

Do Ilboe.org bookmarks
Lesson 2 Review...
< Exit
Topic 5 Assessment
IMPLAYER
Drag each expression to its equivalent expression. Each expression may be used only once.
+ 1
4
1
X +
+1
3
Expression
Equivalent Expression
-
3
4
1
4
+
3
+
3
4
See

Answers

You can do this just believe in your self
It A

A submarine travels 12 km due West from its base and then turns and travels due South for 14.8 km. How far away is the submarine from its base? .

Answers

Answer:

the submarine travels 26.8 km. from its base

Answer:

The answer is 19.1

Step-by-step explanation:

[tex]z = \sqrt{ {x}^{2} + {y}^{2} } = \sqrt{ {12}^{2} + {14.8}^{2} } = 19.1[/tex]

Can you plz help me!

Answers

The integer is -56. The word “lost” represents negative.

The weights of four puppies are shown in pounds

9.5 9
9.125 9


Which list shows these weights in order from greatest to least?

Answers

Answer:

9.125 9, 9.59

Step-by-step explanation:

Sarah is conducting a science experiment where she initially has a population of 4 fruit flies. Every week the population triples. She writes the function f(x)=4(3)x to predict the population growth. Which rule can also model the function?

Answers

Answer and explanation:

Given that initial population of fruit flies = 4

And population of fruit flies triple every week

If population of fruit flies triple every week then let x represent number if weeks

Therefore function can be modelled thus :

f(x)= 4 + 3x

To demonstrate that the function is correct, we use an example. Now assume population grows for two weeks, using the function:

f(2)= 4+3×2

f(2)= 10

Therefore population grows to 10 fruit flies in 2 weeks based on our function

please help asap!!!!

Answers

Answer:

primeter 34.ft

area.30 ft

Step-by-step explanation:

Please help me again!

Answers

Answer:

144

Step-by-step explanation:

First subtract 180 from 20% of 180.

180 - (20/100 x 180) = 180-36 = 144

geometry, write statement and reason

Answers

when i do proofs, i always have notes that tell me the answer. maybe look in your book, sometimes they r in there! hope this helps
AB is parallel to DC (given).
AB is congruent to DC (given).
Both triangles share line AC...so you can start there and say that AC is congruent to AC (reflexive property).
Since AB and DC are parallel, and they are cut by a transversal (line AC), you can say that angle DCA is congruent to angle BAC (alternate interior angles theorem).
Since you have 2 sides and the included angle congruent on these 2 triangles, you can say that triangles ABC and CDA are congruent by the SAS (Side-Angle-Side) theorem...or just “SAS”

7x-3=12 help me please

Answers

Answer:

x=15/7

Step-by-step explanation:

7x-3=12

+3=+3

7x=15

/7=/7

x=15/7

(3x - 2)³=
gives the solution pls.​

Answers

Answer:

27x^3 - 54x^2 + 36x - 8

Step-by-step explanation:

(3x - 2)^3

= (3x - 2) (3x - 2) (3x - 2)

= 27x^3 - 54x^2 + 36x - 8

Hope this helps :)

Let me know if there are any mistakes!!

Answer:

1x

Step-by-step explanation:

A coupon book has a coupon for 40% off of a lift ticket at Mt. Woodstock. A lift ticket usually costs $70. How much would a skier save?

Answers

Answer:

The Skier would save $28 dollars

Step-by-step explanation:

The answer is 28 because 40% of 70 is 28.

Hope this helps! :)

Answer:

The skier would spend $48 and save $28

Step-by-step explanation: In the attachment

please help! I will give brainlist​

Answers

Answer:

A= Yes, it's the equation

B= it's what the problem equals

Step-by-step explanation:

I think this is right I'm not to sure but I think it is

hope this helps :)

Step-by-step explanation:

the process shown in the picture.

COULD I GET GET SOME HELP PLZ? REWARD BRAINLIEST

Answers

Answer:

1. D) -4/3 or 4/3

2. A) -6 or 8

Step-by-step explanation:

Answer:

x=4/3 or -4/3

x=8,-6

Step-by-step explanation:

What is the answer to 2 + n = 16

Answers

Answer:

Original Equation: 2+n=16

Subtract 2 from both sides: 2+n-2=16-2

Simplify: n=14

Hope this helps!

n = 14
14 + 2 = 16
To do this correctly, subtract 2 on both sides. This cancels out the 2 on the left, leaving you with n = 16-2. 16-2=14

Solve for xxx. Your answer must be simplified. x/3 ≥ −33

Answers

we can reduce it by multiplying 3 with -33
X>=-99 that’s your final answer!! I’m sorry about the sign. I couldn’t type it here

Answer:

x ≥ -99

Step-by-step explanation:

Its on khan academy

Other Questions
A satellite is orbiting the earth at an altitude where the acceleration due to gravity is 8.70 m/s2. What is its speed?7.45x10^(3) m/s2.65x10^(3) m/s7.91x10^(3) m/s7.68x10^(3) m/s Suppose a corporation issues 5,000 shares of $I par common stock for $30 per share. In addition to the increase in cash, what effect does this transaction have on the accounting equation? Retained earnings increases $150,000. uld n os 0 Common stock increases $1.50,000. O Gain on stock issuance increases $145,000 earnings per share (eps) may be determined by ______. (check all that apply.) Your RL circuit has a characteristic time constant of 20.0 ns, and a resistance of 5.00 M. (a) What is the inductance of the circuit? (b) What resistance would give you a 1.00 ns time constant, perhaps needed for quick response in an oscilloscope? Each marble bag sold by dantes marble company contains 5 yellow marbles for every 8 orange marbles. If a bad has 35 yellow marbles, how many marbles does it contain? Forensic chemists are analyzing blood samples taken from a murder victim. They run tests for any trace of substances that do not naturally occur in the bloodstream. Nothing odd registers but they do find extremely high levels of caffeine. What does this most likely indicate about the murder victim? They drank a lot of coffee. They worked on a coffee bean plantation. They were poisoned with powdered caffeine. Someone put arsenic in their coffee Find the net signed area between the curve of the function f(x)=x1 and the x-axis over the interval [7,3]. Do not include any units in your answer. Recently, u.s. dairies, struggling to increase milk sales, tried to change the way adults thought about milk. the dairies wanted to __________ chocolate milk in the minds of adult consumers and sell more milk to adults. A patient undergoing radiation therapy for cancer receives a 225 rad dose of radiation. Assuming the cancerous growth has a mass of 0.17 kg and assuming the growth to have the specific heat of water, determine its increase in temperature. leeks company's product has a contribution margin per unit of $17.15 and a contribution margin ratio of 24.5%. what is the selling price of the product? After testing a hypothesis regarding the mean, we decided not to reject H0. Thus, we are exposed to:a.Type I error.b.Type II error.c.Either Type I or Type II error.d.Neither Type I nor Type II error. The program of Figure 11-8 is used to convert the 9-1. Celsius temperature indicated by the thumbwheel switch to Fahrenheit values for display. Answer each of the questions with reference to this program, assuming a thumbwheel switch setting of 25C. The value of the number stored in 1.012 is: a) 25. b) 30. c) 35. d) 40 What is the temperature dependence for the spontaneity of the following reaction?CH3OH(g)+O2(g)CO2(g)+H2O(g)H=434 kJ mol1, S=43 J K1mol1 ____________________________are the two economic factors that reflect the country's attractiveness as a market. Refer to Exhibit 8.13 for a perfectly competitive market. Area B represents _____a) the consumer surplus.b) the producer surplus.c) a public good.d) the ceiling.e) the floor. what is an example of a symptom or effect of an illness that would likely lead to impaired digestion and absortion? (1 point) find the centroid (x,y) of the region that is contained in the right-half plane {(x,y)|x0}, and is bounded by the curves: y=6x2 9x, y=0, x=0, and x=8 What length should a bagpipe pi ends and is being played at room temperature. pe have to produce a fundamental frequency of 131 Hz ? Assume the pipe is open at both The following information is provided for Cullumber Company and Pharoah Corporation. in $ millions) Cullumber Company Pharoah Corporation Net income 2022 $135 $415 1715 4540 Net sales 2022 Total assets 12/31/20 1050 2200 1215 3160 Total assets 12/31/21 1080 4050 Total assets 12/31/22 What is Cullumber's return on assets for 2022? (Round answer to 1 decimal place, e.g. 15.2.) O 11.1% O 11.8% O 118.0% 12.5% Construct a circuit that has a switch for each lightbulb (one battery)(Best answer gets brainliest)