Answer:
Step-by-step explanation:
Given that,
...(1)
We need to find the value of .
Put n = 1 to find the first term.
Put n = 2 to find the second term.
Put n = 3 to find the third term.
Put n = 10 to find the tenth term.
It means we need to find the sum of 5,7,9,.....,23.
The formula for the sum of n terms is given by :
We have, n = 10, a = 5 and
So,
So, the value of is equal to 280.
Answer:
Profit function: P(x) = -0.5x^2 + 40x - 300
profit of $50: x = 10 and x = 70
NOT possible to make a profit of $2,500, because maximum profit is $500
Step-by-step explanation:
(Assuming the correct revenue function is 90x−0.5x^2)
The cost function is given by:
And the revenue function is given by:
The profit function is given by the revenue minus the cost, so we have:
To find the points where the profit is $50, we use P(x) = 50 and then find the values of x:
Using Bhaskara's formula, we have:
So the values of x that give a profit of $50 are x = 10 and x = 70
To find if it's possible to make a profit of $2,500, we need to find the maximum profit, that is, the maximum of the function P(x).
The maximum value of P(x) is in the vertex. The x-coordinate of the vertex is given by:
Using this value of x, we can find the maximum profit:
The maximum profit is $500, so it is NOT possible to make a profit of $2,500.