An automobile manufacturer can produce up to 300 cars per day. the profit made from the sale of these vehicles can be modeled by the function: p(x) = -10x2 + 3500x – 66,000, where p(x) is the profit in dollars and x is the number of automobiles made and sold. how many cars should be made and sold to maximize profit?

 175

Step-by-step explanation:

To find maximum, we need to find the vertex.  

The x-value of the vertex is the number of automobiles that should be made and sold.  The y-value is the maximum profit.

P(x) = -10x² + 3500x - 66,000

         a=-10, b = 3500, c=-66,000

BONUS:

The maximum profit is: P(x) = -10(175)² + 3500(175) - 66,000

                                              = -300,625 + 612,500 - 66,000

                                              = 245,875

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).