There are 250 apartments in a complex. If they rent x apartments then their monthly profit, in dollars, is given by, P(x) = -8x^2 + 3200x - 80,000 How many apartments should they rent in order to maximize their profit?
First, we know the answer must be between 0 and 250 since there are only 250 apartments. Second, you must find the derivative of the profit formula to find the critical point(s). P'(x) = -16x + 3200 0 = 3200 - 16x x = 200, this is the critical point Now, plug in the minimum, maximum, and critical point into the profit formula to find which one yields the highest profit. P(0) = -8(0)^2 + 3200(0) - 80,000 = -80,000 P(200) = -8(200)^2 + 3200(200) - 80,000 = 240,000 P(250) = -8(250)^2 + 3200(250) - 80,000 = 220,000 The answer is 200 apartments!
You're planning a road trip from Denver to Los Angeles and you need to budget how much you're going to spend on gas. The shortest route is approximately 1,017 miles, your car gets approximately 25.3 miles per gallon, and the national average price of fuel is $2.38 per gallon. How much should you budget?
1,017 miles divided by 25.3 miles per gallon = 40.2 gallons needed 40.2 gallons multiplied by $2.38 per gallon = $95.68
You're driving an SUV when suddenly it's struck by lightning. You're not electrocuted. Why? What should you do next?
A hard-top vehicle acts as a Faraday cage, which means the electricity from the lightning bolt will flow through the metal frame of the car until it is grounded. When it's grounded the electricity will flow through the frame to travel into the ground or earth. Until it is grounded, you must be careful to avoid touching metal objects on the interior of the vehicle to avoid being shocked.