the length of the escalator is 30 feet and the distance between the floors is 12 feet. find the distance from the base of the escalator to the point on the first floor directly below the top of the escalator.

Distance from the base of the escalator to the point on the first floor directly below the top of the escalator = 27.5 feet

Step-by-step explanation:

Given:

Length of escalator = 30 feet

Distance between the floors = 12 feet

To find the distance from base of escalator to the point on the first floor directly below the top of the escalator  we will create the figure for the situation.

From the figure we see that a triangle ABC is formed.

We see that the Δ ABC is a right triangle.

Applying Pythagorean theorem for right triangle ABC to find the missing side.

AB = 30 feet

BC = 12 feet

Plugging in values in the theorem.

Solving for AC.

Subtracting both sides by 144.

Taking square root both sides.

∴ feet.

∴ Distance from the base of the escalator to the point on the first floor directly below the top of the escalator = 27.5 feet

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.