We are going to fence in a rectangular field that encloses 200m2. If the cost of thematerial for of one pair of parallel sides is $3 per meter and cost of the material for theother pair of parallel sides is $8 per meter determine the dimensions of the field thatwill minimize the cost to build the fence around the field.

Step-by-step explanation:

Let be x and y the length and width of the rectangular field, whose area and perimeter are, respectively:

Building cost is minimum when perimeter is minimum, then equation system must be reduced and critical values have to be found:

Then,

Now, critical values are determined by First and Second Derivative Tests:

FDT

(As length is a positive number)

SDT

(which means that critical point leads to a minimum).

Now, the value of the other variable is:

Lastly, the cost of building the fence is:

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.

about 168 miles

step-by-step explanation: