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REY [17]
3 years ago
5

Trina earns $28.50 tutoring for 3 hours. Write an equation relating her earings m to the number of hours h she tutors. Assuming

the situation is proportional, how much would Trina earn turtoring for 2 hours? 4.5 hours?

Mathematics
2 answers:
777dan777 [17]3 years ago
8 0
28.50÷3= 9.50/ hr


2 hours would be
2×9.50= $19


4.5 hours would be
4.5×9.5=42.75
atroni [7]3 years ago
6 0

Answer:

Equation forms : m=9.5h

Step-by-step explanation:

Trina earns $28.50 tutoring for 3 hours.

So, per hour earnings of Trina are = \frac{28.50}{3}= 9.5 dollars

Let her total earnings be m

Let the number of hours she tutors be h

To establish an equation multiply the hourly rate by h.

m=9.5h

And when h = 2 hours;

m=9.5(2)

m = $19.

When h = 4.5 hours;

m=9.5(4.5)

m = $42.75

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Charlie is watching hot air balloons. balloon a has risen at a 50° angle. balloon b has risen at a 78° angle. if the distance fr
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The distance from Balloon A to Balloon B, d ≈ 1,052 feet

What is distance ?

  • Distance is defined to be the magnitude or size of displacement between two positions.
  • Note that the distance between two positions is not the same as the distance traveled between them.
  • Distance traveled is the total length of the path traveled between two positions. Distance traveled is not a vector.

The given parameters are;

The angle at which Balloon A rises, x° = 50° above horizontal

The angle at which Balloon B rises, y° = 78° above horizontal

The (vertical) distance of Balloon A to the ground, h = 1,000 ft.

The required parameter;

The distance from Balloon A to Balloon B, d

We find the distances of the balloons from Charlie and the angle between the balloon strings, θ, then apply cosine rule

Let,

The height of the balloon strings are equal

The distance of Balloon A to the ground, h₁ = The distance of Balloon B to the ground, h₂ = 1,000 ft.

The distance of the Balloon A  from Charlie, l₁, is given as follows;

l₁ × sin(x°) = h₁

∴ l₁ = h₁/(sin(x°))

Which gives;

l₁ = 1,000 ft./(sin(50°)) ≈ 1,305.41 ft.

l₁ ≈ 1,305.41 ft.

For Balloon B, we get;

h₁ = h₂ = 1,000 ft.

∴ l₂ = 1,000 ft./(sin(78°)) ≈ 1,022.34 ft.

l₂ ≈ 1,022.34 ft

The angle between the balloon strings, θ = 180° - (x° + y°)

∴ θ = 180° - (50° + 78°) = 52°

The angle between the balloon strings, θ = 52°

By cosine rule, we have;

d = √(l₁² + l₂² - 2 × l₁ × l₂ × cos(θ))

∴ d = √(1,305.41² + 1,022.34² - 2 × 1,305.41×1,022.34 × cos(52°)) ≈ 1,052 feet

Therefore, the distance from Balloon A to Balloon B, d ≈ 1,052 feet

Learn more about distance

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