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Nesterboy [21]
3 years ago
13

Find an equation of the tangent line to the curve at the given point. y = x3 − 3x + 2, (3, 20)

Mathematics
1 answer:
lisov135 [29]3 years ago
8 0

Answer:

y - 20 = 24(x - 3)

Step-by-step explanation:

Equation of a line:

The equation of a line, in point-slope form, has the following format:

y - y_0 = m(x - x_0)

In which the point is (x_0,y_0) and the slope is m.

(3, 20)

This means that x_0 = 3, y_0 = 20. So

y - y_0 = m(x - x_0)

y - 20 = m(x - 3)

Slope:

The slope is the derivative of the function at the point:

The function is:

y = x^3 - 3x + 2

The derivative is:

y^{\prime}(x) = 3x^2 - 3

At the point, we have that x = 3. So

m = y^{\prime}(3) = 3*3^2 - 3 = 27 - 3 = 24

So the equation to the tangent line to the curve a the point is:

y - 20 = 24(x - 3)

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Step-by-step explanation:

using the sine/ cosine ratios in the right triangle and the exact values

cos30° = \frac{\sqrt{3} }{2} , sin30° = \frac{1}{2} , then

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x = 30

and

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Step-by-step explanation:

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Can some explain how to do this?
zepelin [54]

Answer:

  • Exact Area = 210.25pi - 210
  • Approximate Area = 450.185

The units for the area are in square inches or in^2. The approximate value shown above is when using pi = 3.14

=============================================================

Explanation:

Use the pythagorean theorem to find the length of the hypotenuse

  • a = 20
  • b = 21
  • c = unknown

a^2 + b^2 = c^2

20^2 + 21^2 = c^2

400 + 441 = c^2

c^2 = 841

c = sqrt(841)

c = 29

The hypotenuse is 29 inches long. This is the diameter of the circle. Half of that is the radius at r = d/2 = 29/2 = 14.5 inches.

The area of the circle is...

A = pi*r^2

A = pi*(14.5)^2

A = pi*210.25

A = 210.25pi

Which is exact in terms of pi

We'll subtract off the triangular region as this isn't shaded in. The area of the triangle is base*height/2 = 20*21/2 = 420/2 = 210 square inches.

So the shaded region is therefore 210.25pi - 210 square inches

This approximates to 210.25*3.14 - 210 = 450.185 when using the approximation pi = 3.14; use more decimal digits of pi to get a more accurate value.

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