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
Kryger [21]
3 years ago
6

Find the equation of the tangent line at the point where the curve crosses itself. x = t^3-6t, y = t^2.

Mathematics
1 answer:
den301095 [7]3 years ago
8 0

Here is the solution for this specific problem:

<span>Based from the graph, the curve will intersect itself at the y-axis, i.e. x = 0. </span><span>

</span><span>t^3 - 6t = 0 </span><span>
<span>t(t^2 - 6) = 0 </span>
<span>t = 0 or t = ± √6 </span>

<span>dx/dt = 3t^2 - 6 </span>
<span>dy/dt = 2t </span>

<span>dy/dx = 2t/(3t^2 - 6) </span>

<span>@ t = 0, dy/dx = 0. </span>
<span>x = 0, y = 0 </span>

<span>y = 0 </span>

<span>@ t = √6, dy/dx = 2√6/12 = √6/6 </span>
<span>x = 0, y = 6 </span>

<span>y - 6 = (√6/6) x </span>
<span>y = (√6/6)x + 6 </span>

<span>@ t = -√6, dy/dx = -2√6/12 = -√6/6 </span>
<span>x = 0, y = 6 </span>

<span>y - 6 = (-√6/6) x </span>
y = (-√6/6)x + 6</span>

So the equations of the tangent line at the point where the curve crosses itself are: <span>y = (√6/6)x + 6 and </span>y = (-√6/6)x + 6. I am hoping that these answers have satisfied your queries and it will be able to help you in your endeavors, and if you would like, feel free to ask another question.

You might be interested in
Consider the lines y=8x+1, y=-8x+1 and y=2x+1. How are these lines the same, if at all? How do their slopes compare? Is there a
vivado [14]

Answer: the answer is blue

Step-by-step explanation:

8 0
2 years ago
HELP MEEE PLEASE ILL MARK BRIANLIST!!!!
Aleksandr-060686 [28]
The points in order from top to bottom are :

F
E
C
H
I
5 0
3 years ago
Read 2 more answers
What is 1 1/4÷ by 3 4/5
spin [16.1K]

let's firstly convert the mixed fractions to improper fractions and then divide.

\bf \stackrel{mixed}{1\frac{1}{4}}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}}~\hfill \stackrel{mixed}{3\frac{4}{5}}\implies \cfrac{3\cdot 5+4}{5}\implies \stackrel{improper}{\cfrac{19}{5}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{5}{4}\div\cfrac{19}{5}\implies \cfrac{5}{4}\cdot \cfrac{5}{19}\implies \cfrac{25}{76}

4 0
3 years ago
Read 2 more answers
Jack wanted to measure the weight of his luggage at the airport before departure. He was surprised to see that it weighed 23.6 k
Alex

Answer:

25.7 is how much his luggage weighs.

Step-by-step explanation:

4 0
2 years ago
Need help with this​
Vanyuwa [196]

Answer:

Slope-int form: y = 3x+5

Standard form: y - 3x = 5.

Step-by-step explanation:

(reminder: slope-intercept form is expressed as y=mx+b, and standard form is expressed as ax+bx=c.)

Since the slope is 3, the coefficient of x is also 3, which makes the equation y=3x.

But the y coordinate of the equation at x = -2 is -6, so we need to add 5 to the end of the equation, leaving you with:

y=3x+5.

To convert it to standard form, subtract 3x from both sides:

y - 3x = 5.

I hope this helped you.

4 0
3 years ago
Other questions:
  • Need help 16=-2(k+9)
    9·2 answers
  • A card is drawn from a standard deck of 52 cards. what is the probability that it is a heart? type in your answer to two decimal
    13·2 answers
  • Help math whats the answer will give brainliest
    14·1 answer
  • What is the sum? 3k/k^2+k-7/4K
    7·1 answer
  • The measure of an angle is 8 degrees less than three times the measure another angle. If the two angels are supplementary, what
    13·2 answers
  • 8/t; t=4 rkrrkrkkrkrkrkrkr
    13·1 answer
  • Alex wants to rent a car. The charge is $18 plus $0.12 per mile.
    5·1 answer
  • SOS ANSWERRRRR PLZZZZZ
    11·1 answer
  • PLEASE HELP (30 POINTS)
    14·1 answer
  • Solve the equation: 3y + 20 = 3 + 2y
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!