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spin [16.1K]
3 years ago
14

How to find (a) and (b)?​

Mathematics
1 answer:
rodikova [14]3 years ago
3 0

Answer:

A) Gradient = -3

B) 3y - x = 7

Step-by-step explanation:

The curve has the equation;

y = x³ - 6x² + 9x + 1

We are given the pints it passes through as;

A(2,3) and P(3, 1)

A) to find the gradient, we will find the derivative of the given equation.

Thus;

Gradient = y' = 3x² - 12x + 9

At point A, x = 2. Thus;

Gradient = 3(2²) - 12(2) + 9

Gradient = 12 - 24 + 9

Gradient = -3

B) since the gradient of the tangent = -3, it means the gradient of the normal will be; -1/-3 = 1/3

Thus, equation of the normal to the curve at point A will be;

(y - 3) = ⅓(x - 2)

Multiply both sides by 3 to get;

3y - 9 = x - 2

3y - x = 9 - 2

3y - x = 7

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Find the (LCD) 5/6 and 11/8
eduard

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8 0
3 years ago
Read 2 more answers
What expression represents the volume of the cone, in
denis23 [38]

The expression that represents the volume of the given cone, in cubic units is 2/3 πx³.

<h3>How to calculate the volume of the cone?</h3>

The volume of a cone with radius 'r' and slant height 'h' is

V = 1/3 π r² h

Unit: cubic units

<h3>Calculation:</h3>

The given cone has radius r = x and height h = 2x

Then, the volume of the cone is calculated by

V = 1/3 π r² h

   = 1/3 π x² (2x)

   = 2/3 π x³ cubic units

Therefore, the volume of the given cone is V = 2/3 π x³ cubic units.

So, option A is correct.

Learn more about the volume of a cone here:

brainly.com/question/13677400

#SPJ9

Disclaimer: The given question on the portal is incomplete. Here is the complete question.

Question: What expression represents the volume of the cone, in cubic units?

A) 2/3 πx³

B) 4/3 πx²

C) 2πx³

D) 4πx³

8 0
2 years ago
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