Acompany that manufactures racing boats estimates that the profit for selling its brand is given by the following equation. p(b) = -25b3 + 750b2 + 2,500b what is the least number of racing boats, b, that must be manufactured to make a profit of $75,000?

The smallest number of boats that must be produced to make a profit of $ 75,000 is 10 boats

Step-by-step explanation:

We have this equation

This equation shows the income obtained based on the number of boats sold. We want to know the minimum number of boats that must be sold to obtain $ 75 000.

Then we must equalize the equation to 75 000 and clear b.  

3 solutions will be obtained (because it is a polynomial of degree 3), and the lowest value will be taken.

Now we need to solve the equation, for that we seek to factor the polynomial

  We divide the equation by -25

  We take common factor b

  We take out common factor ()

Finally the solutions are:

and

We take the least positive solution (because you can not produce -10 boats)

Finally we have that

1,407.5 hours

step-by-step explanation:

we first convert all the time to hours and then sum them up.

there are 24 hours in 1 day, in 58 days, there are 24 x 58 = 1,392 hours.

there are 60 minutes in 1 hour, thus, 30 minutes will be equivalent to 30 / 60 = 0.5 hours.

therefore, the number of hours it will take mercury to complete a full rotation is 1,392 + 15 + 0.5 = 1,407.5 hours