Angles that are opposite to each other when two lines cross are equal, therefore angle 1 is equal to angle 4. This also implies that angle 1 = angle 5. When a line crosses two parallel lines, the angles corresponding to each other are equal. So, if r and s are parallel, the angles that are formed when line l intersects line r are equal to those when l intersects line s. Thus, we have angle 1 = angle 5, angle 2 = angle 6, and so on. Hence, since angle 1 is equal to angle 5, we deduce that lines r and s are parallel.
To address this problem, let's start by formulating the general motion equation along the vertical direction.
This gives us:
Where,
- g: gravitational acceleration
- vo: initial velocity
- h0: starting height
For the first individual:
For the second individual:
When both individuals reach the identical altitude, the following holds:
Rearranging results in:
Solving for time:
Result:
The two window washers reach the same height after 18.31 seconds.
<span>The system becomes inconsistent when a equals 3 but b is not 5, as this results in parallel lines. If a equals 3 and b equals 5, the system is both consistent and dependent, since both equations represent the same line.</span>
Response:
To settle their disagreement over who does the dishes, flip a fair coin. There is an equal 50% probability of it showing heads or tails, hence the choice will be random.
