The demand function for a certain commodity is given by p = 100e^-q/2. (p is the price per unit and q is the number of units.)
(a) at what price per unit will the quantity demanded equal 6 units? (round your answer to the nearest cent.)
(b) if the price is $2.99 per unit, how many units will be demanded, to the nearest unit?

(a) the price per units is $5.0

(b)the number of units demanded = 7

Step-by-step explanation:

The demand function is given by

(a) Now, we have to find the value of p when q = 6

Substitute q = 6 in the above equation

On simplifying, we get

Rounding to nearest cents, we have

Therefore, the price per units is $5.0

(b)

Now, we have to find q for p = $2.99

Divide both sides by 100

Take natural log both sides

On simplifying, we get

Therefore, the number of units demanded = 7

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: