Jonathan took a 35 questions test and
2 answers:
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Answer:
Explanation:
Highlight the first digit on the very left (2). The 7 right next to it means we'll round that 2 up to a 3. Every other digit becomes a zero.
The number 27,895,168,401,112 rounds to 30,000,000,000,000 which is the number 30 trillion.
It converts to the scientific notation because we basically start with 3.0 and move the decimal point 13 spots to the right to arrive at 30 trillion as shown above.
Based on the information provided, = at a bearing angle of = 59.88° .
We are requested to calculate the overall displacement of the ship, both in magnitude and direction, once it departs the harbor under the stated parameters. First, let's define a bearing.
<h3>What is bearing in the context given above?</h3>Angles are generally measured anticlockwise from the positive x-axis, whereas bearing angles are evaluated clockwise from the positive y-axis. A bearing is NOT a standard angle measuring tool.
Therefore, a bearing of 44.0° indicates that this is an angle 90.0° - 44.0° = 46°. This is the angle to be used in the calculations.
We're given that the first displacement is 11.4° at an angle of 46° (which was computed earlier).
Step 1 - Split the above into components
x1 = 11.4 Cos 46°
= 7.92m
y1 = 11.4Sin 46.0°
= 11.4 * 0.71933980033
= 8.2m
The second displacement is a simple 6.2mi due east, that is, the positive
x-direction. The components are thus:
Δx = x1 + x2
= 7.92 + 6.2
= 14.12mi
Δy = 1 + y2
= 8.2 + 0
= 8.2
r = √(x total)² + (y total)²
=√[(14.21)²+(8.2)²]
= √(201.9241 +67.24)
= √269.1641
= 16.4mi
The direction of the displacement vector is given by:
tan Ф = (Δy)/(Δx)
= arctan (8.2/14.12)
= arctan (0.5807365439)
= 30.12°
Recall that we were asked for the bearing angle. The bearing angle is what we get when we subtract 30.12° from 90°.
That is:
= 90 - 30.12
= 59.88°
Learn more about bearing angle:
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