From the astronaut to the horizon is a tangent line to the curvature of the earth. And from that point on the horizon to the center of the earth is at a right angle to the tangent and is equal to the radius of the earth...so we can say
cosα=r/(r+h) where r is the radius of the earth and h is the height above the surface of the earth...
α=arccos(r/(r+h))
now tanα=d/r where d is the distance from the astronaut to the point on the horizon so:
tan(arccos(r/(r+h))=d/r
d=rtan(arccos(r/(r+h))) and using r≈4000 and h=50 we get:
d=4000tan(arccos(4000/(4050)))
d≈634.42mi
d≈634 mi (to nearest mile)
Answer:
A) 3; B) 1116 m²; C) 24 m³; D) 1/27
Step-by-step explanation:
A) Scale factor
The scale factor is the ratio of the heights of the two pyramids.
h₂/h₁ = 24/8 = 3
B) Surface area
The ratio of the surface areas is the square of the scale factor.
A₂/A₁ = 3²
A₂/124 = 9
A₂ = 124 × 9 = 1116 m²
The volume of the larger pyramid is 1116 m².
C) Volume
The ratio of the volumes is the cube of the scale factor.
V₂/V₁ = 3³
648/V₁ = 27
648 = 27V₁
V₁ = 648/27 = 24 m³
The volume of the smaller pyramid is 24 m³.
D) Volume ratio
V₁/V₂ = 24/648 = 1/27
The volume ratio is 1/27.
Answer:
4^7
Step-by-step explanation:
4^2 + 4^5
=> 4^ 2+5
=> 4^7
