PLEASE HELP ASAP !! A car company’s profit can be modeled by the equation P = –2x^2 + 44x – 42, where P is the profit in millions of dollars and x is the number of cars sold in thousands.
(a.) How many cars are sold when the company breaks even?
(b.) What is the company’s maximum profit? How many cars sold gives the maximum profit?

Step-by-step explanation:

In order for a company to break even, it earns no profit but it also incurs no loss. In other words, set the quadratic equal to 0 and factor to find x.

If you factor this using the quadratic formula you will get that the number of cars sold for the company to neither earn nor lose money is 1 or 21. Right in the middle is where we will find the maximum value (the vertex). This max value will give us the number of cars sold, h, and its corresponding value, k.

To solve for h easily, use the formula

where a and b are the coefficients found in the standard form of a polynomial :

and for k, use:

:

This means our vertex is (11, 200) and in the context of our problem, we know that when the company sells 11,000 cars it makes a max profit of 200 million dollars.

The king left his castle with 44 silver coins.

Step-by-step explanation:

A king left his castle with a bag of silver coins and he gave his coins to 3 peasants in an order. Finally he went home with two coins left.

To solve this question we calculate it in reverse order.

Finally the king has in his bag = 2 coins

Before it he met third peasant king had =

= (2+2) × 2

= 4×2 = 8

Before the king met third peasant, he had 8 coins.

Before he met Second peasant king had :

= (8+2) × 2

= 10 × 2 = 20

Before he met second peasant king had 20 coins.

Before he met first peasant he had :

= (20+ 2) × 2

= 22 × 2 = 44

Before King met first peasant he had 44 silver coins.