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
Using trigonometric identities, sin^2(y) = 1 - cos^2(y).
If you substitute that in, you get 1- cos^2(y)/(1-cos(y)).
You can factorise 1 - cos^2(y) to be (1-cos(y))(1+cos(y)).
This means that the answer is 1 + cos(y) as the 1 - cos(y) will cancel.
Answer:
2/3
Step-by-step explanation:
17/21-1/7
17/21-3/21
14/21=2/3
Uhh... what are the options?
Here's some possible ones:
0.2
1/5
Answer:
The answer is option D.
Step-by-step explanation:
Because -3/-5 = 3/5 since the negative sign cancel each other.
Hope this helps you
