3.A pilot is flying over a straight highway. He determines the angles of depressions to two mileposts that are 3.8 km apart, to be 58 and 30. Find the distance from the plane to point A.

2.1 km

Step-by-step explanation:

Let's say the distance between the plane and the ground is y.

The horizontal distance between the plane and A is:

tan 58° = y / x₁

x₁ = y / tan 58°

x₁ = 0.625 y

The horizontal distance between the plane and B is:

tan 30° = y / x₂

x₂ = y / tan 30°

x₂ = 1.732 y

The difference between them is 3.8 km.

x₂ − x₁ = 3.8

1.732 y − 0.625 y = 3.8

1.107 y = 3.8

y = 3.432

The horizontal distance between the plane and point A is therefore:

x₁ = 0.625 × 3.432

x₁ = 2.145

Rounded, the plane is 2.1 km from point A.

Question:

complete the table below to solve the equation

f(x) = 2.5x – 10.5 g(x) = 64(0.5^x)

x = 2, 3, 4, 5, 6

The completed table is attached below

Solution:

Given that,

Substitute the x = 2 in f(x)

Substitute the x = 3 in f(x)

Substitute the x = 4 in f(x)

Substitute the x = 5 in f(x)

Substitute the x = 6 in f(x)

Also given that,

Substitute the x = 2 in g(x)

Substitute the x = 3 in g(x)

Substitute the x = 4 in g(x)

Substitute the x = 5 in g(x)

Substitute the x = 6 in g(x)