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3 years ago

Find the parametric equations for the line that is tangent to the given curve at the given parameter (3cost)i (t^4 -3sint)j

Mathematics

1 answer:

ale4655 [162]3 years ago

5 0

Answer:

Following are the solution to this question:

Step-by-step explanation:

Please find the complete question in the attached file.

In the given equation, when the point t=0

So,

$\to r(0) = (3 \cos 0)i + (0^4 - 6 \sin 0)j + (2e^{3\times 0})k)$

$= (3 \times 1)i + (0 - 0)j + (2e^{0})k)\\\\ = 3i + 0j + (2 \times 1)k)\\\\ = 3i + 0j + 2k \\$

The value of the coordinates are $3, 0, 2$ . so, the equation of the line is:

$\to \frac{(x-3)}{3 \cos \ t} = \frac{(y-0)}{(t^{4}-6 \sin \ t)} = \frac{(z-2)}{2e^{3t}}=k$

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Assoli18 [71]

Answer:

The equation of line is y = 3 x - 1 , i.e option A .

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Step-by-step explanation:

Given as :

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Let The slope = m

Now, The slope is calculated in points form

So, Slope = $\dfrac{y_2-y_1}{x_2-x_1}$

I.e m = $\dfrac{2-(-7)}{1-(-2)}$

or, m = $\dfrac{9}{3}$

I.e m = 3

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Now, the equation of line in slope - point form can be written as

y - $y_1$ = m ( x - $x_1$ )

where m is the slope of line

i.e y - (-7) = ( 3 ) × ( x - (-2) )

or, y + 7 = 3 × (x + 2)

∴ y + 7 = 3 x + 6

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Hence, The equation of line is y = 3 x - 1 , i.e option A .

And The rate of change = m = 3 Answer

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3 years ago

Shelby found a tree branch that was 8 feet long.She chopped it into smaller pieces.If she wanted the wood pieces to be each have

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2 years ago

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Answer:

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So, for the statement given:

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3 years ago

What is the area of the square? 2 m square meters

Mariulka [41]

Answer:

Step-by-step explanation:

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2 years ago

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Harper knows he is 50 yards from school. The map on his phone shows that the school is 3/4 inch from his current location. How f

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Answer:

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Step-by-step explanation:

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2 years ago