Two forces, one of 120 pounds and the other of 200 pounds, act on the same
1 answer:
9514 1404 393
Answer:
-8.21°
Step-by-step explanation:
The horizontal and vertical components of the forces are ...
(120; 30°) = (103.923, 60}
(200; -30°) = (173.205, -100}
Then the resultant is ...
(103.923 +173.205, 60-100) = (277.128, -40)
and the resultant direction is
arctan(-40/277.128) = -8.21°
_____
The polar coordinates (A; β) can be translated to rectangular coordinates by ...
(A; β) = (A·cos(β), A·sin(β))
__
<em>Additional comment</em>
The semicolon in (A; β) signifies the ordered pair is polar coordinates (magnitude; angle). The comma in (x, y) signifies the ordered pair is rectangular (Cartesian) coordinates. This notation is borrowed from the GeoGebra app, a geometry graphing/calculating program. It avoids some confusion. Personally, I prefer the notation A∠β to signify a magnitude and direction in polar coordinates.
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Answer:
y ≥ 3x - 1
y <
Step-by-step explanation:
Let the equation of the solid line passing through (x', y') given in graph is,
y = mx + b
Here m = slope of the line
b = y-intercept
Slope of the solid line =
m =
m = 3
y - intercept 'b' = -1
Therefore, equation of the line will be,
y = 3x - 1
Since, shaded (blue) area is above the line, inequality that will represent the solution area will be,
y ≥ 3x - 1
For the dotted line,
Slope of the line (m) =
=
=
y-intercept (b) = 2
Equation of the dotted line → y =
Since, shaded (grey color) area is below the dotted line,
Inequality representing the solution area will be,
y <