En el año 2013 la empresa británica Biomatrix, diseñó un sistema ecológico de tratamiento de aguas contaminadas urbanas que logra recuperar la calidad del agua y revitalizar el paisaje a un costo bastante bajo. Este tratamiento consiste en cada 6 horas instalar un reactor que permite oxigenar el agua, cada 18 horas ubicar una colonia de bacterias que se alimentan de la contaminación y finalmente cada 12 horas, crear islas flotantes con diversas plantas que mejoran la circulación del rio. Si el día de hoy a las 00:00 horas se inicia el tratamiento, ¿Cuántas veces coincidirán las tres etapas a lo largo de 3 días?

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form

graph b

step-by-step explanation:

one solution- graph a (clear intercepting point.)

no solution- graph b (they're parallel, there will never be a point of interception.)

infinite solutions- graph c (all points intercept.)