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mylen [45]
2 years ago
11

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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An independent-measures research study compares three treatment conditions using a sample of n = 5 in each treatment. For this s
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Answer: c. ​10

Step-by-step explanation:

Given : An independent-measures research study compares three treatment conditions using a sample of n = 5 in each treatment.

For this study, the three sample means are, M1 = 1, M2 = 2, and M3 = 3.

Grand mean = \overline{X}=\dfrac{M1+M2+M3}{3} [All sample have equal elements]

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For ANOVA,

SS_{between}=n\sum(M_i-\overline{X})^2 , where i= 1, 2 , 3

SS_{between}=5((1-2)^2+(2-2)^2+((3-2)^2)

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3 years ago
Jacob is asked to solve the follow problem: "Kayla is 9 years older than twice Hannah’s age. If the difference in their ages is
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Answer:

Step-by-step explanation:

k = 2h+9

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h+16=2h+9

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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.

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