another algebra word problem?

Question

Rosie's Palm Pirates a manufacturer of electronic organizers,
estimates that when x hundred Palm Pirates are made, the average cost per unit is given by c(x)=0.3xexponent2 - 2.94x+ 8.183, where c is in hundreds of dollars. What is the minimum cost per unit?

Answer 1

There are several ways to go about finding the answer. You can make a table of number for X, for example: X= -10 to +10, and calculate Y. Plotting this out will show you that the minimum occurs at X=5.

There is another way if you have a little bit of a background in calculus. Write the equation out: (0.3 X^2) - (2.94X) + (8.183)

Take the first derivative of the above equation:
Y' = 2x(0.3X) - (2.94)
Set Y' = 0, and solve for X
0.6X - 2.94 = 0, 0.6X = 2.94, X= 2.94/0.6, X= 4.9

Now, we don't know if X= 4.9 is a Maximum or a Minimum.

To find out, we need to test the second derivative. If the second derivative is greater than zero, X is at a Minimum point. If the second derivative is less than zero, X is at a Maximum point. So, lets see:

Y' = 0.6 X - 2.94
Taking the second derivative,

Y" = 0.6, Thus, Y" > 0. X is at a Minimum which is what you want to know --- the minimum cost per unit.

Answer 2

nicely, all of us recognize that the hypotenuse is 10, so: 10^2 = a^2 + b^2 And if a is the gap from the floor to the main stunning of the ladder, then a - 2 is the gap from the backside of the ladder to the wall, so: one hundred = (a - 2)^2 + a^2 one hundred = a^2 - 4a + 4 + a^2 a^2 - 2a - 40 8 = 0 (a - 8)(a + 6) = 0 a = 8, which ability the gap from the floor to the main stunning of the ladder is 8 ft, and the gap from the backside of the ladder to the construction is six ft. stable success, insha'Allah. :)

Answer 3

The functions value continually increase from 1 unit to infinity. The minimum is at negative x so something isn't right.

Answer 4

the answer would be about 5, rounded