Step-by-step answer:
Referring to the attached diagram, the resultant of two forces each with magnitude F and inclined to each other at 2a equals
Ra = 2Fcos(a) ..............................(1)
Similarly, the resultant of two forces each with magnitude F and inclined to each other at 2b equals
Rb = 2Fcos(b)..............................(2)
We are given that
Ra = 2Rb ....................................(3)
Substitute (1) & (2) in (3) gives
2Fcos(a) = 2(2Fcos(b))
Expand
2Fcos(a) = 4Fcos(b)
Simplify
cos(a) = 2 cos(b) QED
Note: Please note that you might have a faster response if you posted this question in the physics or the (new) Engineering section.
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Answer:
It must be longer than the original segment.
Step-by-step explanation:
Let analyse all the 4 answers:
- a. It divides the original segment into two equal pieces.
Yes because It finds the midpoint of the given line segment.
- b. Every point on the perpendicular bisector is the same distance from both end points of the segment.
Yes, because perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the segment's both endpoints.
- c. It must be longer than the original segment
Wrong, it can be shorter or equal to the original segment.
- d. It is perpendicular to (makes a 90 angle with) the original segment
True, because of it is one of the the properties of a perpendicular bisector of a segment
So we choose C.
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Answer:
Marcus position: -18 meters
Step-by-step explanation:
We establish a reference system where the zero height is on the sea surface. Then all height below the sea surface is negative.
~--~---~---~---~sea--~---~---~---~---~- 0 meters ---~---~----~---~---~---~---~--
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⊥ Marcus: - 18 meters
So the position of marcus is: -18 meters above sea level.
To return to the surface you must move 18 meters up.
False, it is on the horizontal.
1) Substituting into point-slope form, the equation of the line is y-6=⅓(x-3), which rearranges to:
So, we can now substitute in the coordinates of each of the options to see which point lies on the line.
- 3 = ⅓(6) + 5 -> 3 = 7, which is false.
- 6 = ⅓(7) + 5 -> 6 = 22/3, which is false.
- -3 = ⅓(-3) + 5 -> -3 = 4, which is false.
- 3 = ⅓(-6) + 5 -> 3 = 3, which is true.
So, the answer is (4) (-6, 3)
2) Substituting into point-slope form, the equation of the line is y - 5 = ¾(x-2), which rearranges to:
- y - 5 = 0.75x - 1.5
- y = 0.75x + 3.5
So, we can now substitute in the coordinates of each of the options to see which point lies on the line.
- 8 = 0.75(6)+3.5 -> 8 = 8, which is true.
- 9 = 0.75(5) + 3.5 -> 9 = 7.25, which is false.
- 1 = 0.75(-1) + 3.5 -> 1 = 2.75, which is false.
- 2 = 0.75(6) + 3.5 -> 2 = 8, which is false.
So, the answer is (1) (6, 8).
