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.
Roots test tells us to take the factors of the 20 divided by the factors of the coefficient of the the first.
factors of 20 are 1,2,4,5,10,20
factors of 1 are 1
so plus or minus 1/1, 2/1, 4/1, 5/1, 10/1, 20/1 are all possible rational zeros
The expression x-4 will come out to be a negative integer. That means X <em>has to be </em>something that when 4 is taken away from it, the answer is still negative.
Let's try 5.
5-4 is 1. Is 1 negative? No, so that doesn't work.
4-4 is 0. 0 isn't negative either, so that doesn't work.
3-4 is -1. Is -1 negative? YES! Let's try it for 2 as well, just to be safe.
2-4 is -2. Still negative.
X can be anything less than 4.
Answer:
12:50 PM.
Step-by-step explanation:
We have been given that Craig’s school has 4 lessons in the morning and lesson 1 starts at 8:35. Each lesson is 60 minutes long. There is a break of 15 minutes between lesson 2 and 3.
We can see that lesson 1 will end at 9:35 AM and second lesson will end at 10:35 AM.
We have been also given that there is a break for 15 minutes between lesson 2 and 3. So third lesson will start at 10:50 AM as lunch break will end at 10:50 AM.
Third lesson will end 60 minutes after 10:50 AM that is 11:50 AM and fourth lesson will end 60 minutes after 11:50 AM that is 12:50 PM.
Therefore, 4th lesson will end at 12:50 PM.
18miles/6mph = 3hrs
3 hours
