Can somebody help with these.

Simplify (be sure to rationalize all denominators)
11. 3/[SQRT(5) - 2]
and
this..
Note: I only need help on the b part of the question..
15. Assume that a surveyor stands at the top of a mountain that is “h” feet tall. If the distance (in feet) that he can see is defined by d = 3200.2 SQRT(h), then answer the following. (a) How far can the surveyor see from the top of a 2000-foot mountain? (b) How tall is the mountain, if the surveyor can see 15 miles? (Note: 1 mile equals 5280 feet.)

11. Multiply numerator and denominator by sqrt(5) + 2. The denominator will become 5 - 4 = 1.

15. Use the formula you were given to solve for h, where d = 15x5280 = 79,200 feet

is that the answer for number 11?

and would the distance equal 79,200? and if so would I convert back to miles?

Thank you.

You have not completed #11. On #5, I gave you the distance in feet (79200). You solve for the altitude. We are here to help you, not to provide complete solutions for you to turn in

Ok yes i do ont want the answers but I want to know the next step in solving the equation....

once i have 5-4=1 as my dementaor what would i do?

Denominators of 1 can be ignored.

x/1 = x, no matter what x is

Sure! I'd be happy to help you with those problems.

11. To simplify the expression 3/(√5 - 2) and rationalize the denominator, we need to get rid of the square root in the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator. The conjugate of √5 - 2 is √5 + 2.

So, we have:
3/(√5 - 2) * (√5 + 2)/(√5 + 2)

Multiplying the numerators and denominators, we get:
(3 * (√5 + 2)) / ((√5 - 2) * (√5 + 2))

Expanding the denominator, we get:
(3 * (√5 + 2)) / (5 - 2√5 + 2√5 - 4)

Combining like terms, we have:
(3 * (√5 + 2)) / (1)

Therefore, the simplified expression is:
3√5 + 6

Now, let's move on to the second part of your question.

15. (b) To find the height of the mountain if the surveyor can see 15 miles, we can use the given formula: d = 3200.2√h, where d is the distance that the surveyor can see and h is the height of the mountain.

First, convert 15 miles to feet. Since 1 mile equals 5280 feet, we have:
15 miles = 15 * 5280 feet = 79,200 feet

Now, we can substitute this value into the formula:
79,200 = 3200.2√h

Next, we need to isolate the square root term. Divide both sides of the equation by 3200.2 to get:
√h = 79,200 / 3200.2

Simplifying the right side, we have:
√h ≈ 24.747

To get rid of the square root, we square both sides of the equation:
(√h)² = (24.747)²

This gives us:
h ≈ 611.089

Therefore, the height of the mountain is approximately 611.089 feet if the surveyor can see 15 miles.

I hope this helps! Let me know if you have any further questions.