Mathematics, 20.07.2019 17:00 gabriellarenolp5x7c0

Vectors and angles a ship is sailing through the water in the english channel with a velocity of 22 knots along a bearing of 157° (knots being a unit used to measure the speed of aircrafts and boats). the current has a velocity of 5 knots along a bearing of 213°. find the resultant velocity and direction of the ship. (remember that bearing is measured clockwise from the north axis). 1) 25 knots at 166.5 degree 2) 27 knots at 350 degree 3) 166.5 knots at 25 degree 4) 350 knots at 27 degree

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The velocity of the ship = 22 ∠157° = (22 cos 157°) i+ (22 sin 157°) j

The velocity of current = 5 ∠213° = (5 cos 213°) i+ (5 sin 213°) j

So, the resultant velocity = 22 ∠157° + 5 ∠213°
= (22 cos 157°) i+ (22 sin 157°) j + (5 cos 213°) i+ (5 sin 213°) j
= (22 cos 157° + 5 cos 213°) i + (22 sin 157° + 5 sin 213°) j
= -24.444 i + 5.873 j
= 25.14 ∠166.5°

The correct answer is option (1)
1) 25 knots at 166.5 degree

Answer from: Quest

step-by-step explanation:

Answer from: Quest

the range of a function is the range of y-values for which it is defined, or exists. given that we are only looking at the y-values, we can already discount the first two answers as they deal with the domain of the function (range of x-values).

now, what we need to do is find the smallest and highest y-values for which the function is defined. if you'd like, you could take a ruler and start at the very bottom of the graph, find the lowest point, then move the ruler higher and higher until you reach the highest point. doing so either in your head or with an actual ruler, we can see that the lowest y-value is -5 and the highest y-value is -1.

the question now remains as to whether they are included in the range (fourth answer) or excluded (third answer). the key here is to recognise whether they are marked with an open or a closed circle. since both (-2, -5) and (2, -1) are marked with a closed circle, they are points that exist on the graph and are thus included in the range (note that if they were marked with an open circle like (4, -2) then that would signify that there is a break in the graph at that point).

thus, the fourth answer, (y | -5 ≤ y ≤ -1), is correct.

also note that usually it is good practice to scan your eye inbetween the highest and lowest point for any breaks in the graph - we do have one here at (4, -2), however -2 is still included in the range because there is another point that is included in the graph with the same y-value, ie. point (1, -2).

i hope that but if you require any further explanation don't hesitate to comment below.

Me if you can and if you finished this lesson on edg- comment you.

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Vectors and angles a ship is sailing through the water in the english channel with a velocity of 22...