Find the instantaneous rate of change of the surface area s ! 6x2 of a cube with respect to the edge length x at x ! a

The instantaneous rate of change is simply equivalent to the first derivative of the equation or function. We are given the equation of Surface Area (A) with respect to side (x):

A = 6 x^2

Taking the first derivative of the equation:

dA = 12 x dx

dA / dx = 12 x

Now the term dA / dx is the instantaneous rate of change in the surface area with respect to the side length. To get the rate of change when the side x = a, simply plug this in into the equation:

rate of change = dA / dx = 12 x

so when x = a:

rate of change = 12 a

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.