During the production of biodiesel, glycerin is a waste product and is collected by gravity separation because its sg (1.26) is much higher than that of biodiesel. glycerin is withdrawn from the bottom of the separation tank through a pipe that has p1 = 350 kpa gage, where d = 70 cm and the flowrate is 680 l/s. find the pressure at section 2, which is 0.8 m higher and where the diameter has been reduced to d = 35 cm. assume the flow is inviscid. (gravity acceleration: g = 9.81 m/s2)

the small 0.38-kg slider is known to move from position a to position b along the vertical-plane slot. determine (a) the work done on the body by its weight and (b) the work done on the body by the spring. the distance r = 0.70 m, the spring modulus k = 154 n/m, and the unstretched length of the spring is 0.53 m

explanation:

-reverse card

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .