Solving the following mathematical problems:

The profit of a company in Taka is given by P-3x² - 35x + 50, where x is the amount in Taka in lac spent on advertising. For what values of x does the company make a profit?

Solve the following mathematical problems:

Mr. Hossain invested m taka in a mutual fund which pays 10% interest and n taka in a privet company which pays 9% interest. He invested Tk. 18,000 and required that he receives tk 1,700 as interest. How much did he invest in each company?

Solve the following mathematical problems:

50 daily workers can complete a culvert in 40 days. If 30 of them work daily and the rest work in every alternative day, how many more days will be required to complete the project?

Solve the following mathematical problems:

A teacher has 6 hours to grade all the papers submitted by the 35 students in his class. He ge through the first 5 papers in 1 hour. How much faster should he work to grade the remaini papers in the allotted time?

Solve the following mathematical problems:

A two digit number is six times the sum of the two digits. If the digits are reversed, the number so obtained is 9 less than the original number. What is the original number?

Solve the following mathematical problems:

Factorize: $x^3-21x+20$