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:
The chance of a girl being picked is an 18/35 chance.
Step-by-step explanation:
Answer:
Yes.
Step-by-step explanation:
The relation would be 3 = k*9 as there is a direct proportional relationship.
So k = 3/9 = 1/3 and we can write the relation as d = 1/3 t where d=distance and t = time.
So if we double the time t we have:-
d = 1/3 * 18
= 6 kilometers.
So the distance is doubled.
The answer is infinitely many solutions
If you divide the 2nd equation by 3, you get the first equation, meaning they are identical. That means that any value of x will be true, which means there are infinite solutions
To find the area of any regular (regular means all sides are = and all angles are =) poylgon when you know the length of the apothem and the length of the side you can use the formula:
A = (1/2)ap where a = the length of the apothem and p = the perimeter of the polygon. You can also use n*s in place of p where n = the number of sides of the polygon and s = the length of the side.
A= (1/2)(16)(19*8) (An octagon has 8 sides.)
A = 1216 in^2
