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2 years ago

Find the equation of the normal to the curve y=x^2-2x^2-4x+1 at thepoint (-1,2)

Mathematics

1 answer:

balandron [24]2 years ago

5 0

Answer:

$y=-\frac{1}{3}x+\frac{5}{3}$

Step-by-step explanation:

Assuming that the first exponent in the formula for the curve should be 3, not 2...

$y=x^3-2x^2-4x+1$

The derivative is

$y'=3x^2-4x+4$

The slope of the tangent line at the point (-1, 2) is the value of the derivative at x = -1.

$y'|_{x=-1} = 3(-1)^2-4(-1)+4=3-4+4=3$

The slope of the normal line is the opposite reciprocal of the slope of the tangent line.

$m_{\text{normal} = -\frac{1}{3}$

Using the Point-Slope form of a linear equation, the normal line is

$y-2=-\frac{1}{3}(x-(-1))\\y-2=-\frac{1}{3}(x+1)\\y=-\frac{1}{3}x-\frac{1}{3}+2\\y=-\frac{1}{3}x+\frac{5}{3}$

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3 years ago

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3 years ago

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Step-by-step explanation:

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3 years ago

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The ratio of the length of each side of the triangle to that of the hexagon is

<h3>What is equilateral triangle?</h3>

The triangle which has all the three sides equal in dimension is called the equilateral triangle.

According to the question,

Area of triangle = Area of rhombus = Area of hexagon

1/2 base x height = 1/2 diagonal1 xdiagonal2 = (3√3 / 2) side²

The triangle has equal base and height = a.

The hexagon has each side measuring b.

1/2 a² = (3√3 / 2) b²

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a²/b² = 3√3

a/b = √ 5.19615

a/b = 2.2795

Thus, the ratio of each side of the triangle to that of the hexagon is 2.2795.

Learn more about equilateral triangle.

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1 year ago

Find the equation of the normal to the curve y=x^2-2x^2-4x+1 at thepoint (-1,2)​

Find the equation of the normal to the curve y=x^2-2x^2-4x+1 at thepoint (-1,2)