In construction, floor space must be planned for stair cases. If the vertical distance between the first and second floors it's 3.6 m and a contractor is using the standard step pattern of 28 cm wide for 18 cm high and how many steps are needed to get the first to the second floor and how much linear distance( ie "width" or "base" ) Will be needed for the staircase? What is the length of the railing that would be attached to these stairs

665.73 cm or 6.65 m

Step-by-step explanation:

The first thing is to pass the distance in meters to centimeters, knowing that 1 meter equals 100 centimeters:

3.6m * 100cm / 1m = 360cm

Now we calculate the number of steps:

360 cm / 18 cm = 20 steps

Now each step measures 28 cm, therefore:

20 * 28 = 560 cm

To calculate the length of the ladder, we must apply Pythagoras:

c ^ 2 = a ^ 2 + b ^ 2

a = 360; b = 560

replacing:

c ^ 2 = 360 ^ 2 + 560 ^ 2

c ^ 2 = 443200

c = 665.73

665.73 cm in meters would be 6.65 meters.

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true