Mathematics, 03.04.2020 01:09 dlewis9632

In order to meet ADA (Americans with Disabilities Act) requirements, a wheelchair ramp must have an angle of elevation of no more than 4.8°. A builder needs to install a ramp to reach a door that is 2.5 feet off the ground.

Is 35 feet long enough for the straight line distance of the ramp to meet the requirements?

What angle of elevation will this ramp have?

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Answer from: Domi0129

Yes, 35 feet is enoughThe angle of elevation is 4.1º

Explanation:

The ramp, its vertical elevation, and the ground make a right triangle, with the length of the ramp being the hypotenuse, the vertical elevation one leg, and the horizontal distance (ground) the other leg.

The angle of elevation of a ramp is related with the hypotenuse and the opposite leg by the trigonometric ratio named sine:

sine (α) = opposite leg / hypotenuse

In this problem, the length of the ramp. i.e the straight line distance of the ramp, is the hypotenuse, the distance the door is off the ground (the height of the ramp) is the opposite leg, and the angle α is the angle of elevation of the ramp.

Then:

sine (α) = opposite leg / hypotenuse = 2.5 feet / 35 feet ≈ 0.07142857α = arcsine(0.07142857) = 4.1º.

Thus, the ramp will have an angle of elevation of 4.1º and you conclude that the 35 feet long is enough because the angle is smaller than the limit of 4.8º.

Answer from: Quest

a) 7x=7

step-by-step explanation:

Answer from: Quest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

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