Answer:-1/4
Step-by-step explanation:
Take the negative of the reciprocal for perpendicular lines. In the case of no slope (y=number) replace y with x
5/54 or approximately 0.092592593
There are 6^3 = 216 possible outcomes of rolling these 3 dice. Let's count the number of possible rolls that meet the criteria b < y < r, manually.
r = 1 or 2 is obviously impossible. So let's look at r = 3 through 6.
r = 3, y = 2, b = 1 is the only possibility for r=3. So n = 1
r = 4, y = 3, b = {1,2}, so n = 1 + 2 = 3
r = 4, y = 2, b = 1, so n = 3 + 1 = 4
r = 5, y = 4, b = {1,2,3}, so n = 4 + 3 = 7
r = 5, y = 3, b = {1,2}, so n = 7 + 2 = 9
r = 5, y = 2, b = 1, so n = 9 + 1 = 10
And I see a pattern, for the most restrictive r, there is 1 possibility. For the next most restrictive, there's 2+1 = 3 possibilities. Then the next one is 3+2+1
= 6 possibilities. So for r = 6, there should be 4+3+2+1 = 10 possibilities.
Let's see
r = 6, y = 5, b = {4,3,2,1}, so n = 10 + 4 = 14
r = 6, y = 4, b = {3,2,1}, so n = 14 + 3 = 17
r = 6, y = 3, b = {2,1}, so n = 17 + 2 = 19
r = 6, y = 2, b = 1, so n = 19 + 1 = 20
And the pattern holds. So there are 20 possible rolls that meet the desired criteria out of 216 possible rolls. So 20/216 = 5/54.
Answer:
a)
v=<400, 450+3t, 600-9.81t> m/s
r=<400t, 450t+3
/2, 15+600t-9.81/2> m/s
b) attach file
c) t=122.324s
d) z=18369.9854 m
Step-by-step explanation:
a)
The equation for velocity of each component is v=
+at, in this case the x-axis component has acceleration 0
, the y-axis component has acceleration 3 and the z-axis component has -g, where g=9.81.
The equation for position of each component is x=
+t+a/2,
with <, 
,
>=<0,0,15>.
c) This time is t when z=0, with positive sign.
d)Solving the equation 
=
+ 2*a*(z-) for z, with 
=0.
X - Ollie's age
8 is subtracted from Ollie's age = x-8
the result is the same as
subtracting 16 from 3 times his age = 3x-16
Ollie is 4 years old.
