Answer:
The Pythagorean Theorem leads to a simple proof of the Pythagorean Identity using only the basic definitions of trig functions. The Pythagorean Theorem on a right triangle with legs a,b and hypotenuse c gives us: a2+b2=c2. Dividing through by c2 gives: (ac)2+(bc)2=1.
The answer would be 2x^2+2x-4
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
Answer:
Step-by-step explanation:
84/100 = x/125
x = 105 points
