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iren [92.7K]
3 years ago
8

A red balloon starts at 7.3 meters off the ground and rises at 2.6 meters per second. A blue balloon starts at 12.4 meters off t

he ground and rises at 1.5 meters per second. Write and solve an equation to determine when the balloons are at the same height.
Mathematics
1 answer:
nexus9112 [7]3 years ago
6 0
This problem is an example of solving equations with variables on both sides. To solve, we must first set up an equation for both the red balloon and the blue balloon. 

Since the red balloon rises at 2.6 meters per second, we can represent this part of the equation as 2.6s. The balloon is already 7.3 meters off of the ground, so we just add the 7.3 to the 2.6s: 

2.6s + 7.3

Since the blue balloon rises at 1.5 meters per second, we can represent this part of the equation as 1.5s. The balloon is already 12.4 meters off of the ground, so we just add the 12.4 to the 1.5:

1.5s + 12.4

To determine when both balloons are at the same height, we set the two equations equal to each other: 

2.6s + 7.3 = 1.5s + 12.4

Then, we solve for s. First, the variables must be on the same side of the equation. We can do this by subtracting 1.5s from both sides of the equation: 

1.1s + 7.3 = 12.4

Next, we must get s by itself. We work towards this by subtracting 7.3 from both sides of the equation: 

1.1s = 5.1

Last, we divide both sides by 1.1. So s = 4.63. 

This means that it will take 4.63 seconds for both balloons to reach the same height. If we want to know what height that is, we simply plug the 4.63 back into each equation: 

2.6s + 7.3
= 2.6 (4.63) + 7.3
= 19.33

1.5s + 12.4
= 1.5 (4.63) + 12.4
= 19.33

After 4.63 seconds, the balloons will have reached the same height: 19.33 meters.
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Answer:

720

Step-by-step explanation:

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Height of the kite is = 36 inches.

Width of the kite is = 30 inches

One of the ways to find the area is to draw a vertical line to break the kite into two equal triangles. Mark the base as 36 inches and height as 15 inches .

Now we will use the formula area=\frac{1}{2}*base*height to find the area of each triangle. Then we will add both the areas to find the area of the kite.

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Area of the 2nd triangle is also = 270 square inches

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Answer:

\theta \approx 6.28n + 2.38,  \quad  n \in \mathbb{Z}

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Considering \theta \in (0, 2\pi]

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Step-by-step explanation:

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We have:

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