Which of the following is the product of the rational expressions shown below? 7x/x-4•x/x+7
1 answer:
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9514 1404 393
Answer:
(i) 55.59 km/h
(ii) 3600 nautical miles ≈ 6670.8 km
(iii) 30°N 29.3°E
Step-by-step explanation:
(i) The speed in km/h requires a units conversion.
(30 kt/h)(1.853 km/kt) = 55.59 km/h
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(ii) Here, we assume we're interested in the <em>distance traveled</em>. If the course is "due east", we presume that means it follows the 30° latitude line, so is not the shortest route between A and B. That is, the distance from A to B will be different from the distance traveled. (The shortest route from A to B is along a great circle.)
distance = speed × time
distance = (30 kt/h)(120 h) = 3600 nautical miles
= (55.59 km/h)(120 h) = 6670.8 km
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(iii) The radius of the 30° latitude line is ...
(6370 km)(cos(30°)) = 3185√3 km ≈ 5516.58 km
The relationship between arc length (s) and central angle (α) is ...
s = rα
So, the change in the vessel's longitude is ...
α = (6670.8 km)/(5516.58 km) ≈ 1.20923 radians ≈ 69.28°
Then town B has longitude ...
40°W -69.3° = -29.3°W = 29.3°E
The position of town B is about 30°N 29.3°E.
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<em>Additional comment</em>
The route supposedly taken by this sea vessel is from the middle of the North Atlantic to a town in northern Egypt, through the northern Sahara desert. The eastern end point is shown in the attachment.
Some spherical trigonometry is involved if you want to find the end point of the great-circle route of the same length.
Answer:
The equation of line passing through point (3 , 10) with slope 2 is y = 2 x + 4 .
Step-by-step explanation:
Given as :
The slope of a line = m = 2
The line is passing through point = ,
= 3 , 10
Now, <u>Equation of line in point- slope form</u>
y - = m × (x -
)
Or, y - 10 = 2 × (x - 3)
Or, y - 10 = 2 × x - 2 × 3
Or, y - 10 = 2 x - 6
Or, y = 2 x - 6 + 10
Or, y = 2 x + 4
So, The equation of line y = 2 x + 4
Hence, The equation of line passing through point (3 , 10) with slope 2 is y = 2 x + 4 . Answer
We have these system of inequalities:
In this way, we have two straight lines that can be solved as follows:
This two lines has been plotted in the Figure below and the region of the inequality is indicated in gray color. Therefore, each point in this region satisfies the system of inequalities. To illustrate this, let's take a point within the gray region, say (0, 0):
