The maximum grade allowed between two stations in a rapid-transit rail system is 3.5%. Between station A and station B, which are 270 ft apart, the tracks rise 8 and one half 8 1 2 ft. What is the grade of the tracks between these two stations? Round the answer to the nearest tenth of a percent. Does this grade meet the rapid-transit rail standards?

x = 3.1 %

Step-by-step explanation:

Let x be the slope the track.

Given:

Distance between station A and B = 270 ft

Track rise =

We need to find the slope of the railway track between station A an B.

Solution:

The maximum grade allowed between two stations in a rapid-transit rail system is 3.5%.

We know that slope of the railway track is equal to gradient of the tracks.

So. the slope of the railway track is defined as the ratio of the distance between the stations and track rises.

x = 3.1 %

So x = 3.1 % less than the maximum grade allowed between two stations in a rapid-transit rail system is 3.5%.

Therefore, x = 3.1 % meets the rapid-transit rail standards.

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places