A manufacturer believes that the cost function C(x)=52x2+85x+560 approximates the dollar cost of producing x units of a product. The manufacturer believes it cannot make a profit when the marginal cost goes beyond $270. What is the most units the manufacturer can produce and still make a profit? What is the total cost at this level of production?

$697

Step-by-step explanation:

Marginal cost is the additional cost incurred as a result of increasing the number of items produced. Marginal cost is used to optimize production.

The marginal cost is gotten by differentiating the cost function, it is given by:

Marginal cost = C'(x)

The cost is given as  C(x)=52x²+85x+560.

Given that the marginal cost should be less than $270, hence:

C'(x) < 270

104x + 85 < 270

104x < 270 - 85

104x < 185

x < 185/104

x < 1.77

Therefore x ≈ 1

C(1) = 52(1²) + 85(1) + 560 =

C(1) = $697

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

13cm

step-by-step explanation:

(apex)