Una escalera de 30 pies de longitud está apoyada contra una pared de modo que su extremo superior se desliza hacia abajo con una velocidad de 1/2 pies/seg ¿cuál es la tasa de variación de la medida del ángulo formado por la escalera y el piso cuando el extremo superior está a 18 pies del piso?

dα /dt  = -  0.028 rad /sec     or  dα /dt  = - 1.59 °

El signo menos significa que el angulo va decresiendo

Step-by-step explanation:

La escalera, la pared vertical y el pié de la escalera y la pared forman un triangulo rectangulo. En ese triangulo

cos α   (  α  angulo que forma la escalera con el piso )

cos α =   x / L

Tomando derivadas con respecto al tiempo (L es constante ) se tiene:

- sen α  *  dα / dt   =  dx/ dt / L

Cuando  el extremo superior de la escalera está a 18 pies del piso, entonces  sen α  =  18 / 30  =  0.6

dx/dt = 1/2 pie/sec

dα/dt  = - (1/2)/ L* 0.6

dα /dt  = -  0.5 / 18

dα /dt  = -  0.028 rad /sec     or  dα /dt  = - 1.59 °

El signo menos significa que el angulo va decresiendo

i dont know if you cant find a way its best to actually add all of them start from 105 tho

step-by-step explanation:

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be