The orthocenter is the point where the three altitudes meet.
sketch the graph and you will see that AB is a horizontal line, the altitude is a vertical line through the point (1,3), so the equation of this altitude is x=1
next, find another altitude. I'll use the altitude of BC.
the slope of BC is (6-3)/(4-1)=1, so the slope of the altitude, which is perpendicular to BC going through the point A (0,6), is -1, the equation of the altitude of BC is y=-x+6
the system of equation : x=1
y=-x+6
has a solution (1, 5)
the solution is where the two lines meet, the meeting point is the orthocenter.
Double check by find the equation for other altitude:
slope of AC: (3-6)/(1-0)=-3
slope of altitude of AC: 1/3
equation of altitude of AC: y=(1/3)x+b
the altitude of AC goes through point B (4,6), so we can find out b by plug x=4, y=6 in the equation: 6=(1/3)*4+b, b=14/3
y=(1/3)x+14/3
Is (1,5) also a solution to this equation? Plug x=1 in the equation, we get y=5, so yes, (1,5) is a point on the third altitude.
Answer:
6/25 x 3/4 = 18/100 % 16/5 = 18/100 x 5/16 = 90/1600 or 0.05625
Can also be simplified to 9/160
Answer:
Approximately
, assuming that
.
Step-by-step explanation:
Initial kinetic energy of the sled and its passenger:
.
Weight of the slide:
.
Normal force between the sled and the slope:
.
Calculate the kinetic friction between the sled and the slope:
.
Assume that the sled and its passenger has reached a height of
meters relative to the base of the slope.
Gain in gravitational potential energy:
.
Distance travelled along the slope:
.
The energy lost to friction (same as the opposite of the amount of work that friction did on this sled) would be:
.
In other words, the sled and its passenger would have lost (approximately)
of energy when it is at a height of
.
The initial amount of energy that the sled and its passenger possessed was
. All that much energy would have been converted when the sled is at its maximum height. Therefore, when
is the maximum height of the sled, the following equation would hold.
.
Solve for
:
.
.
Therefore, the maximum height that this sled would reach would be approximately
.
Greetings! Hope this helps!
Answer:
"Hecto" Is a meaning for 100, So your answer would be A.) Hecotmeter
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