1) slope of the line = derivative of the of the function at the given point.
y' = cosx - x cosx
Evaluate for x = pi => y' = cos(pi) - pi*cos(pi) = -1 - (pi*cos(pi)) = -1 + pi
Then slope = -1 + pi
Given point: (pi, -pi)
Equation:
y - (-pi) = [-1+ pi] (x - pi)
y + pi = -x +pi + xpi -pi^2
y = (pi-1)x - pi^2 .... this is the answer
Hello here is a solution :
Answer:
C and D
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Calculate m using the slope formula
m = 
with (x₁, y₁ ) = (- 3, - 6) and (x₂, y₂ ) = (9, 3) ← 2 points on the line
m = 
= 
= 
Using (a, b ) = (9, 3 ) , then
y - 3 = (x - 9) → C
Using (a, b ) = (- 3, - 6 ), then
y - (- 6) = (x - (- 3) ) , that is
y + 6 = (x + 3) → D
The system of equations has No solution.
<u>Step-by-step explanation</u>:
step 1 :
The given system of equations are
4x-8y=-16 -------- (1)
x-2y=-8 ----------- (2)
step 2 :
Taking 4 as common from equation (1)
4(x-2y) = 4(-4)
The equation (1) becomes x-2y = -4
- Now, equations (1) and (2) have same x and y terms and only constant is different.
- Therefore, the system of equations cannot be solved for x and y values. It has no solution.
step 3 :
From equation (2), find the value for x
x-2y = -8
x = 2y-8
step 4 :
Substitute x = 2y-8 in equation (1)
4x-8y = -16
4(2y-8) -8y = -16
8y - 32 -8y = -16
8y-8y = 32-16
It cannot be solve for x and y values.
∴ The system of equations has No solution.
X int can be found by subbing in 0 for y and solving for x
9x - 7y = 21
9x - 7(0) = 21
9x = 21
x = 21/9 which reduces to 7/3...so the x int is 7/3 or (7/3,0) <==
to find the y int, sub in 0 for x and solve for y
9x - 7y = 21
9(0) - 7y = 21
-7y = 21
y = -21/7
y = -3....so the y int is -3 or (0,-3) <==
