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Answer:
Height of mound = 794 ft
Step-by-step explanation:
To illustrate the angle of elevation and distance, i have drawn it and attached below.
Now, from my diagram;
h = the height of the mound
At his first point of his trip to the foot of the mound, the angle of elevation is 40°, while the horizontal distance to the foot of the mound is "X"
So, by triangle definition,
tan(40°) = h/x
And so;
h = x tan40
h = 0.8391x - - - - (eq 1)
At his second point of the trip to the foot of the mound, Joe is now,
"(x - 450) ft" from the foot of the mound.
Thus, his angle of elevation is 40 + 18 = 58°.
So, by triangle definition,
tan(58°) = h/(x - 450)
h = (x - 450)•(tan(58°))
h = 1.6003(x - 450)
h = 1.6003x - 720.135 - - - - -(eq2)
To get the height(h) of the mound, let's equate (eq1) to (eq2).
0.8391x = 1.6003x - 720.135
1.6003x - 0.8391x = 720.135
0.7612x = 720.135
x = 720.135/0.7612
x = 946.0523 ft
Let's put this value for x in eq (1);
h = 0.8391 x 946.0523 = 793.83 ft ≈ 794ft
The number of possible groups or combination of three men can be formed from 10 is 120.
According to the given question.
Total number of men in a company, n = 10.
Number of men to be selected, r = 3
As we know that, What is a combination in math?
Image result for what is combination
A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
Therefore, the number of possible groups or combination of three men can be formed from 10
=
= 10!/ 3!7!
= 10(9)(8)/3(2)
= 5 × 3 × 8
= 120
The number of possible groups or combination of three men can be formed from 10 is 120.
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