At point of intersection the two equations are equal,
hence, 6x³ =6x²
6x³-6x²=0
6x²(x-1)=0 , the values of x are 0 and 1
The points of intersection are therefore, (0,0) and (1,6)
To find the slopes of the tangents at the points of intersection we find dy/dx
for curve 1, dy/dx=12x, and the other curve dy/dx=18x²
At x=0, dy/dx=12x =0, dy/dx=18x² = 0, hence the angle between the tangents is 0, because the tangents to the two curves have the same slope which is 0 and pass the same point (0,0) origin.
At x=1, dy/dx =12x = 12, dy/dx= 18x² =18, Hence the angle between the two tangents will be given by arctan 18 -arctan 12
= 86.8202 - 85.2364 ≈ 1.5838, because the slope of the lines is equal to tan α where α is the angle of inclination of the line.
Answer:
y + 4x - 6 = 0
Step-by-step explanation:
Rearranging the given equation:-
4y = x + 24
y = 1/4 x + 6
This has a y intercept of (0, 6) and a slope of 1/4.
Thus, the other line has a slope of -4 and passes through the point (0,6) also.
Using the Point-slope form of a straight line:-
y - y1 = m(x - x1)
y - 6 = -4(x - 0)
y + 4x - 6 = 0 is the required equation
Answer:
d
Step-by-step explanation:
3x+6=21
-6+21= 15
15÷3=5
Answer:
8.025
Step-by-step explanation:
If you count the zeros in 1000, it's three. Count three starting from the back of 25. Add 0 in front of 25 to make it a three digit number. You then put the decimal point with the whole number.