<h2>Answer:</h2>
The Slope is 
<h2>Explanation:</h2>
Notice that both the points,
and
, are on the line. So we can use those points to calculate the slope. Recall that that slope of the line
can be calculated by
if we have the points,
and
.
<h3>Calculating for the slope of the line:</h3>
Given



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
In the given diagram:
measure angle DAB + measure angle BAC = 90 degrees
we are given that measure angle DAB = 10 degrees
Therefore:
measure angle BAC = 90 - 10 = 80 degrees
Now, triangle ABC is a right-angled triangle which means that we can use the trigonometric functions.
The function that we will use is:
cos theta = (adjacent) / (hypotenuse) where
theta = 80 degrees
adjacent = 500
hypotenuse is "x" that we want to calculate.
Substitute to get x as follows:
cos 80 = 500 / x
x = 500 / cos 80 = 500 / 0.1736 = 2879.4 m
Answer:
C
Step-by-step explanation:
5.1 + 2y + 1.2 = -2 + 2y + 8.3 ( subtract 2y on each side)
5.1 + 1.2 = -2 + 8.3 ( collect like terms)
6.3 = 6.3
If the equation ends with a true statement (ex: 2=2) then you know that there's infinitely many solutions or all real numbers.