Answer:
<em>Graph below</em>
Step-by-step explanation:
<u>Transformations</u>
Triangle ABC has coordinates A=(-4,2) B=(-2,6) C=(3,2)
We'll use the transformation (x,y) -> (2x, y+3) to map it to the triangle A'B'C'. Let's calculate the coordinates:
A'=(-8,5)
B'=(-4,9)
C'=(6,5)
The image below shows both triangles in the same grid
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.
