Answer:
1,809.98 lb*m/s^2
Step-by-step explanation:
First, we want to know how much weight of the boulder is projected along the path in which the boulder can move.
The weight of the boulder is:
W = 322lb*9.8 m/s^2 = (3,155.6 lb*m/s^2)
This weight has a direction that is vertical, pointing downwards.
Now, we know that the angle of the hill is 35°
The angle that makes the direction of the weight and this angle, is:
(90° - 35°)
(A rough sketch of this situation can be seen in the image below)
Then we need to project the weight over this direction, and that will be given by:
P = W*cos(90° - 35°) = (3,155.6 lb*m/s^2)*cos(55°) = 1,809.98 lb*m/s^2
This is the force that Samuel needs to exert on the boulder if he wants the boulder to not roll down.
Most likely more than the number of guests.
2 lines are skew if they are neither parallel, nor intersecting.
If 2 lines are parallel or intersecting, they form a plane, so they are coplanar. So "skew" is the opposite or complement of "coplanar".
i) a and b: are both on M so coplanar, not skew
ii) b is in M, c is in N and they have no common point, so skew. (if they had a common point that would be a point in the line d of intersections of planes M and N, but they dont meet at such a point)
iii) b and e: are both on M so coplanar, not skew
iv) e and c : skew, same argument as ii.
v) a and e : are both on M so coplanar, not skew
vi) a and c: a is in M, c is in N. If they met, they would met at a point on line d, the only set of points common to planes M and N, but they dont. so skew
Answer:
Step-by-step explanation:
x
=
π
n
,
2
π
3
+
2
π
n
,
4
π
3
+
2
π
n
x
=
π
n
,
2
π
3
+
2
π
n
,
4
π
3
+
2
π
n
, for any integer
n
n
f(x) = ¹/₂x - 2
f(14) = ¹/₂(14) - 2
f(14) = 7 - 2
f(14) = 5
