the profit made fram the sale of a dvd players from a company is found by subtracting the costs from the revenue. p=r+-c. Suppose that the companys revenue can be expressed with the function R(x)=x^2+59x and that the total costs for the company can be determined by the function, C(x)=5x+200.
Find the profit equation by substituting for R and C in the equation P=R-C
What is the profit made from selling 15 dvd players per month>
The break even values for a profit model are the values for which you earn $0 in profit. Use the equation you found in question one to solve where P=0, and find your break even values (factor the equation and solve for x)
The distance from the earth to the sun is 93 million miles. Express the distance in feet and in scientific notation (1 mile=5280 feet)
I will be happy to critique your thinking.
To find the profit equation, we substitute the given revenue function R(x) and cost function C(x) into the equation P = R - C:
P = (x^2 + 59x) - (5x + 200)
P = x^2 + 54x - 200
So, the profit equation is P(x) = x^2 + 54x - 200.
To find the profit made from selling 15 DVD players per month, we simply substitute x = 15 into the profit equation:
P(15) = 15^2 + 54(15) - 200
P(15) = 225 + 810 - 200
P(15) = 835
Therefore, the profit made from selling 15 DVD players per month is $835.
To find the break-even values, we set the profit equation P(x) = 0 and solve for x. So, we factor the equation:
x^2 + 54x - 200 = 0
To factor the quadratic equation, we can either use the quadratic formula or find the factors of the constant term (-200) that add up to the coefficient of the linear term (54).
The factors of -200 that add up to 54 are 100 and -2. So, we can rewrite the equation as:
(x + 100)(x - 2) = 0
Now we set each factor equal to zero and solve for x:
x + 100 = 0 -> x = -100
x - 2 = 0 -> x = 2
Therefore, the break-even values (where the profit is $0) are x = -100 and x = 2.
To express the distance from the Earth to the sun in feet, we multiply the given distance in miles (93 million miles) by the conversion factor of 5280 feet per mile:
93 million miles * 5280 feet/mile = 489,840,000,000 feet
So, the distance from the Earth to the sun is 489,840,000,000 feet.
To express this distance in scientific notation, we move the decimal point so that there is only one digit to the left of the decimal point, and record the number of zeros as an exponent of 10:
489,840,000,000 feet = 4.8984 x 10^11 feet