Asupermarket is to be designed as a rectangular building with a floor area of 14,400 square feet. the front and back of the building will be mostly glass and will cost $81 per running foot. the other two walls will be constructed of brick and cost $64 per running 1 foot. find the dimensions of the base of the building that will minimize cost.

Step-by-step explanation:

These problems are easily solved if you start with the knowledge that the solution makes the front/back cost equal to the side cost.

Suppose we define the length of the front as x. Then the total cost of the front and back is (2x)(81) = 162x.

If y is the length of the side of the building, then (2y)(64) = 128y is the total cost of the sides of the building. When these costs are equal, we have ...

  162x = 128y

  y = (162/128)x

The floor area is ...

  xy = 14400 = x(162/128)x

  x = √(14400·128/162) = √(11377 7/9) = 106 2/3

  y = (162/128)x = 135

The front/back of the building measure 106 ft 8 inches; the sides measure 135 feet.

Solution using derivatives

Using the above variable definitions, we can find the side length as ...

  y = 14400/x

so the total cost is then ...

  c = 162x + 128(14400/x)

We want the derivative with respect to x to be zero:

  dc/dx = 0 = 162 -128·14400/x^2

Solving for x gives ...

  x = √(14400·128/162) = 106 2/3 . . . . . compare to the solution above

  y = 14400/(106 2/3) = 135

the red lines denote the population of the bacteria after 35 hours. that would be 2,409.24. the y-intercept is the blue line which is 800 because that is the starting point. the equation used to make the graph is 800(1.032)^h, where h is the number of hours.

step-by-step explanation:

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.