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matrenka [14]
3 years ago
5

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:
Sphinxa [80]3 years ago
4 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.

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Answer:

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Step-by-step explanation:

Divide by the coefficient of the variable. Since it is negative, the direction of the comparison must be reversed.

(-4a)/(-4) > (-32)/(-4)

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Determine if b is a linear combination of a1 a2, and a3. a1 = [ 1 -2 0 ], a2 = [ 0 1 3 ], a3 = [ 6 -6 18 ], b = [ 2 -2 6 ] Choos
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Answer: Vector b is not a linear combination

Step-by-step explanation:

First of all we put the vectors in terms of different variables, such as:

a1(1,-2,0)=(a,-2a,0);

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a3(6,-6,18)=(6c,-6c,18c);

To know that a vector is a linear combination we need to express it like a sum of other different vectors.

(2,-2,6)=(a,-2a,0)+(0,b,3b)+(6c,-6c,18c)

(2,-2,6)=(a+0+6c,-2a+b-6c,0+3b+18c)

We express this sum like a system of equations.

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We solve this system of equations and we can note that the system don't have a solution, so the vector b is not a linear combination of a1, a2, and a3.

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Read 2 more answers
Soire 4(x + 1) + 8 = 24. (I point)<br> оа<br> A 3.75<br> B -2<br> C 5<br> D 3
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Answer:

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Step-by-step explanation:

4(x + 1) + 8 = 24

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4(x + 1) + 8-8 = 24-8

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4(x+1)/4 = 16/4

x+1 = 4

Subtract 1

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Answer:

x=5

Step-by-step explanation:

I just rounded up my answer but if this is not correct then it is a decimal of 4.7

7 0
3 years ago
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