The variable a is the length of the ladder. The variable h is the height of the ladder's top at time t, and x is the distance from the wall to the ladder's bottom. Suppose that the length of the ladder is 5.0 meters and the top is sliding down the wall at a rate of 0.4 m/s. Calculate dx dt when h = 3.1.

Answer:dx/dt= 0.2608 at  h= 3.1 m Step-by-step explanation: a is the length of the ladder. a=5by pythagorus theorem [tex]x^2 = a^2-h^2[/tex]differentiating with respect to t we get [tex]x\frac{dx}{dt} = -h\frac{dh}{dt}[/tex]......1The variable h is the height of the ladder's top at time t, and x is the distance from the wall to the ladder's bottomAt h= 3.1 x^2= 6^2-3.1^2 = 9.1×2.9x= 5.1371 m given [tex]\frac{dh}{dt} =-0.4[/tex]putting values in 1 to get dx/dt[tex]5.1371\frac{dx}{dt} = 3.1×04[/tex].dx/dt= 0.2608 at  h= 3.1 m