Find the angles thetaθ (with respect to the positive x-axis) associated with the directions of maximum increase, maximum decrease, and zero change. what angle(s) is/are associated with the direction of maximum increase?

Step-by-step explanation:

A line or ray pointing straight upward will be pointing in the direction of maximum increase. It will make an angle of 90° with respect to the x-axis.

A line or ray pointing straight downward will be pointing in the direction of maximum decrease. It will make an angle of -90° with respect to the x-axis.

A horizontal line will be associated with zero change. It makes an angle of 0° with respect to the x-axis.

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.