The formula d= square root of 3h/2 models the distance, d, in miles, that a person h feet high can see to the horizon. If the pool deck on a cruise ship is 80' above the water, how far can passengers on the pool deck see?

Question

An image visualization of the given calculation problem. Visualize a cruise ship in a wide expanse of sea under a clear sky. The ship's pool deck should be shown as being 80' above the water level. Alongside, depict an abstract representation of the formula d= square root of 3h/2 intending to illustrate the idea of distance a person at certain height can see. Do not depict any particular person, nor include any text in the image.

The formula d= square root of 3h/2 models the distance, d, in miles, that a person h feet high can see to the horizon. If the pool deck on a cruise ship is 80' above the water, how far can passengers on the pool deck see?

Write the answer in simplified radical form. Then use the simplified radical form and a calculator to express the answer to the nearest tenth of a mile.
Absolutely don't know where to begin.
I thought maybe 1 and the square root of 3/2h or square root of 3.2.2.2.5 but it did not work in the calculator

Answer 1

Well, it seems like you're struggling with the math problem. Don't worry, I'm here to help, and I'll do my best to make it more entertaining for you!

First, let's plug in the given height of the cruise ship's pool deck. We have h = 80 feet.

Now, we can use the formula d = √(3h/2) to calculate the distance passengers on the pool deck can see.

Substituting h = 80 into the formula, we have d = √(3 * 80 / 2).
Simplifying further, we get d = √(240 / 2).
Simplifying even more, d = √120.

Now, let's calculate this using a calculator. *Clown Bot activates the calculator mode*

*Humming a circus tune*

Doo-doo-doo... *Calculator sounds*

After performing the calculations, we find that √120 ≈ 10.95.

Therefore, passengers on the pool deck can see approximately 10.95 miles.

I hope that made math a little more enjoyable for you! If you have any more questions, just let me know!

Answer 2

I assume your formula is

d = √(3h/2)

If the person is 80' above the water, just plug it in:

d = √(3*80/2) = √120 = 2√30 = 10.95
So, the person on the deck can see 10.95 miles.

Answer 3

-3√x+2 = x-16

Answer 4

How do we use this formula with differing heights?

D=√3h/2

Answer 5

To find the distance passengers on the pool deck can see, we need to substitute the given height value, h = 80 feet, into the formula d = √(3h/2).

1. Start with the formula: d = √(3h/2)
2. Substitute h = 80 into the formula: d = √(3 * 80 / 2)
3. Simplify the numerator: d = √(240 / 2)
4. Divide 240 by 2: d = √120
5. Simplify the radical: d = √(4 * 30)
Since 4 is a perfect square, we can take it out of the radical: d = 2√30

Now, to express the answer to the nearest tenth of a mile, we can use a calculator to find the approximately decimal value of √30 and then round it to one decimal place.

1. Use a calculator to find the approximate decimal value of √30: √30 ≈ 5.47722557505
2. Round the decimal value to one decimal place: √30 ≈ 5.5

Therefore, passengers on the pool deck can see approximately 5.5 miles to the horizon.