As Artemis Fowl's private jet approaches Heathrow airport, its horizontal distance from the airport is 22 miles when his altitud
e is 2.2 miles. To the nearest degree, what is the angle of descent of Artemis' plane?
2 answers:
Answer:
The angle of descent of Artemis' plane is 6°
Step-by-step explanation:
Let
x -----> the angle of descent of Artemis' plane
we know that
The tangent of angle x is equal to divide the opposite side to angle x (altitude) by the adjacent side to angle x (horizontal distance)
see the attached figure to better understand the problem
so
tan(x)=2.2/22
x=arctan(2.2/22)=5.71°
Round to the nearest degree
x=6°
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Answer:
2670 square feet. Option e.
Step-by-step explanation:
Dan and Betty can paint 2,400 square feet in 4 hours.
They can paint in one hour = 600 square feet.
Since given that Betty paints twice as fast as Dan. Let us take an equation:
Let Betty = B, Dan = D and Sue = S
B = 2D
4(B+D) = 2400
4B + 4D = 2400
12D = 2400
D = 200 sq. ft.
B = 2D = 400 sq. ft.
Therefore, Dan can paint 200 square feet in 1 hour and Betty paints twice 400 square feet in 1 hour.
Now given three of them can paint 3,600 square feet in 3 hours.
3( B+D+S) = 3600
3B + 3D + 3S = 3600
3(400) + 3(200) + 3(S) = 3600
1200 + 600 + 3S = 3600
S = 600 Sq. ft.
Sue can paint 600 square feet in one hour.
So sue can paint in 4 hours and 27 minutes.
× 600
= 2670 square feet. Option e.
Answer:
The distance from the ground to the top of the ladder = 18.7 feet
Step-by-step explanation:
The distance from the ground to the top of the ladder is 9 feet more than the distance from the building to the base of the ladder.
distance from the building to the base of the ladder.= X
The distance from the ground to the top of the ladder = 9+x
Solving the triangle using Pythagorean theorem
X² +(x+9)²= 21²
X² + x² + 18x +81= 441
2x² +18x -360 = 0
X² +9x -180 = 0
X= (-9-28.3)/2 or (-9+28.3)/2
Definitely x is going to be a positive number
So
X= (-9+28.3)/2
X=9.65 feet
The distance from the ground to the top of the ladder = 9+x
The distance from the ground to the top of the ladder = 9+9.65
The distance from the ground to the top of the ladder = 18.65
The distance from the ground to the top of the ladder = 18.7 feet
Let , coordinate of points are P( h,k ).
Also , k = 3h + 1
Distance of P from origin :
Distance of P from ( -3, 4 ) :
Now , these distance are equal :
Solving above equation , we get :
Hence , this is the required solution.