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Lubov Fominskaja [6]
2 years ago
14

8) Eugene wrote a riddle: A positive number is 5 less than another positive number. Six times the lesser number minus 3 times th

e greater number is 3. Find the two positive numbers.
Mathematics
1 answer:
Gala2k [10]2 years ago
3 0

Answer: the two numbers are 6 and 11.

Set up the individual equation according to the verbal statements:

<em>A positive number is 5 less than another positive number:</em>

a = b - 5       (this also implies that a<b)

<em>Six times the lesser number minus 3 times the greater number is 3. </em>

6  a -3 b = 3

<em>Find the two positive numbers.</em>

This is a system of linear equations - solve for a and b:

<em>6(b-5)-3b=6b-30-3b=3b-30=3\\3b=33\\b=11\\\rightarrow a=11-5 = 6</em>

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An observer in tower A sees a boat 1538 yd away at an angle of depression of 35°. To the nearest yard, how far is the boat away
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From my own solution, my answer is closest to D<span>. 1951 yd; 27°
</span><span>
The boat is 1951 yards away from the observer in tower B. The angle of depression to the boat from Tower B is 27</span>°.<span>

Pls. see my attachment. 

In it I divided the big triangle into two small right triangles. 
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sin 35</span>° = opposite / 1538 yd
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From there, I used the Pythagorean theorem to solve for the missing side which is part of the 3,000 yd measure.

I got the measure of 1,259.86 yards. The remaining measure of 1,740.14 is the side of the other right triangle. 

Still using Pythagorean Theorem, I used the measurement of the known side of the 2nd right triangle to solve for its hypotenuse which was 1,950.97 or 1,951 yards.

With regards to the angle of depression, I used this formula:

tan(y) = opposite / adjacent
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tan(y) = 0.513
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</span>

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