Answer:
4,486.93 ft
Step-by-step explanation:
Let 'h' be the height of the mountain and 'x' be the horizontal distance between the first position measured and the top of the mountain.
Two right triangles can be modeled such that their tangent relationships yield:
Solving the linear system:
The mountain is 4,486.93 ft high.
-4^3 is -64. so 64 is the opposite of -64
Answer:
a^2 + b^2 = c^2 (pythagorean theorem)
a^2 + 40^2 = 41^2 (plug in the known values)
a^2 + 1,600 = 1681 (simplify what you can)
a^2 = 81 (subtracted 1600 from both sides)
a= (81 under a radical) (I think this is what your answer will be, based on the problem)
a=9 (what the fully simplified answer is)
The least amount of money that should be budgeted to paint the monument is $1692.
<h3>Least amount of money that should be budgeted</h3>
First step
Using Pythagorean theorem to find the surface area
Since POR is a right triangle
Hence:
PO=20
BR=12
OR=12
PR=√20²+12²
PR=400+144
PR=544
Area of PBC=1/2×24×√544
Area of PBC=12√544
Lateral surface area=4×12√544
Lateral surface area=48√544
Lateral surface area=1119.54²ft
Second step
Since regular paint is 2 coats 200 sq. ft per gallon
Hence:
Number of gallons=1119.54×2/200
Number of gallons= 11.2 gallons
11.2×35= 392
1119.54/80=13 gallons
13×100 =1300
Last step
Least amount=392+1300
Least amount= $1692
Therefore the least amount of money that should be budgeted to paint the monument is $1692.
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Answer: 95040
Step-by-step explanation:
It is important to note that selection and arrangement are two different things in permutation and combination study. In the scenario above, we have 12 books, out of which 5 is to be arranged on a shelf. The answer prescribed by 12C5 which gives 792, only solves the selection process of choosing 5 books from a total of 12. Every 5 books picked will also have to be arranged on the shelf which is solved as n!(number of ways of arranging n different objects)
Hence, to arrange 5 books from a total of 12 books on a book shelf is
nCr * r!
12C5 * 5!
792 * 120
= 95040
