The graph of an exponential function of the form y = f(x) = a^x passes through the points and . The graph lies the x-axis.
1 answer:
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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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Answer:
C = 68.667°
a = 123.31 yd.
c = 114.90 yd.
Step-by-step explanation:
The missing image for the question is attached to this solution.
In the missing image, a triangle AB is given with angles A and B given to be 88° 35' and 22° 45' respectively
We are them told to find angle C and side a and c given that side b = 47.7 yd.
A = 88° 35' = 88° + (35/60)° = 88.583°
B = 22° 45' = 22° + (45/60)° = 22.75°
The sum of angles in a triangle = 180°
A + B + C = 180°
C = 180° - (A + B) = 180° - (88.583° + 22.75°) = 68.667°
The sine law is given as
(a/sin A) = (b/sin B) = (c/sin C)
Using the first two terms of the sine law
(a/sin A) = (b/sin B)
a = ?
A = 88.583°
b = 47.7 yd.
B = 22.75°
(a/sin 88.583°) = (47.7/sin 22.75°)
a = (47.7 × sin 88.583°) ÷ sin 22.75°
a = 123.31 yd.
Using the last two terms of the sine law
(b/sin B) = (c/sin C)
b = 47.7 yd.
B = 22.75°
c = ?
C = 68.667°
(47.7/sin 22.75°) = (c/sin 68.667°)
c = (47.7 × sin 68.667°) ÷ sin 22.75°
c = 114.90 yd.
Hope this Helps!!!
Answer:
Step-by-step explanation:
We are given the following in the question:
A(1, 1), B(2, 4), C(4, 2)
i) Slope of AB
Thus, slope of AB is 3.
ii) Point slope form
The point slope form of a line can be written as:
The point intercept form of line can be written as:
The line is parallel to AB and contains point C(4, 2). Since line p is parallel to AB, line p will have the same slope as line AB
Putting values, we get,
which is the required slope intercept equation of line p.