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2 years ago

Please anyone to show me how this mathematics question is done..please

Mathematics

1 answer:

irinina [24]2 years ago

5 0

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

(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

(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.

_____

<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.

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PLEASEEEEEEEEEEEEEEEEEE URGENT

jeyben [28]

Option C:

f(x) = 5x + 7 is the function of the input-output table.

Solution:

Option A: f(x) = 6x + 9

Input x = 1 in the above equation.

f(1) = 6(1) + 9

= 6 + 9

f(1) = 15

But the output is 12 in the table.

So, it is not the function of the table.

Option B: f(x) = 7x + 5

Input x = 1 in the above equation.

f(1) = 7(1) + 5

f(1) = 12

Input x = 5 in the above equation.

f(5) = 7(5) + 5

f(5) = 40

But the output is 32 in the table.

So, it is not the function of the table.

Option C: f(x) = 5x + 7

Input x = 1 in the above equation.

f(1) = 5(1) + 7

f(1) = 12

Input x = 5 in the above equation.

f(5) = 5(5) + 7

f(5) = 32

Input x = 10 in the above equation.

f(10) = 5(10) + 7

f(10) = 57

Input x = 5 in the above equation.

f(15) = 5(15) + 7

f(15) = 82

All outputs are correct for the given input.

Hence it is the function of the table.

Option D: f(x) = 12x + 1

Input x = 1 in the above equation.

f(1) = 12(1) + 1

f(1) = 12

Input x = 5 in the above equation.

f(5) = 12(5) + 1

f(5) = 61

But the output is 32 in the table.

So, it is not the function of the table.

Hence Option C is the correct answer.

f(x) = 5x + 7 is the function of the input-output table.

4 0

3 years ago

A Cab charges $1.75 for the flat fee and $0.25 for each mile. Write and solve an inequality to determine how many miles Eddies c

NemiM [27]

1.75 + 0.25x ≤ 15
where x is equal the number of miles.

The key to solving an inequality is just temporarily making the ≤ symbol a =. Then solve for x like any other algebraic equation. Once you find the value of x, you will have solved the inequality. Make sure to add back the ≤ when you are done.

15 - 1.75 = 13.25
13.25/0.25 = x
x = 53
add back the ≤
x ≤ 53
This means Eddies can travel up to 53 miles with his $15.

4 0

3 years ago

A. Write 60,000,000 in words.

Vitek1552 [10]

Answer:

The answer is sixty million.

5 0

3 years ago

If 1/5 of the remaining blueberries is used to make muffins how many pounds of blueberries are left in the container

nlexa [21]

Answer:

4/5.

Step-by-step explanation:

would you mind looking at my question :)

3 0

3 years ago

Hey! i’ll give brainliest please help

Ahat [919]

Answer:

I think it's D but im not sure

hope this helps

have a good day :)

Step-by-step explanation:

6 0

2 years ago