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:
9.2
Step-by-step explanation:
So the 14 can be divided equally on both sides by the fact that the line cutting it at right angle bisects it.
Thus having 6 and 7 as the two shorter sides of a right angled triangle will help us get the radius( hypotenuse in this case) using the square root of the sum of the squares of both six and 7, the Pythagoras theory.
this leads to 9.2 as our answer
Answer:
y = 3x + 6
Step-by-step explanation:
Since the line is parallel, it has the same slope -- 3
y = 3x + b, sub point (1, 9)
9 = 3(1) + b
9 = 3 + b
b = 9 - 3
b = 6
y = 3x + b -- y = 3x + 6
Hi there!
We can find the answer by factoring the equation, then setting them up equal to zero.
x² - 7x + 12 = 0
(x - 3)(x - 4) = 0
x - 3 = 0 x - 4 = 0
x = 3 x = 4
So you have two real solutions for the equation x² - 7x + 12 = 0.
Hope this helped! :)
Answer:
n ≥ 29
She needs to do more than 29 pushups on the sixth day.
Step-by-step explanation:
First, we need to use the formula for finding the average. We currently have numbers for the first 5 days.
(22+26+21+25+27+n)/6 = 25
Multiply both sides by 6.
25*6 = 150
150-27-25-21-26-22=x
x=29
Since it is an inequality, Sarah needs to do more than 29 pushups on the sixth day.
