For a certain product, cost C and revenue R are given as follows, where x is the number of units sold in hundreds. Cost: C² = x² +92√x+56 Revenue: 898(x-6)² + 24R² = 16,224 dC a. Find the marginal cost at x = 6. dx The marginal cost is estimated to be $ ☐ . (Do not round until the final answer. Then round to the nearest hundredth as needed.)

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The half-life of caffeine is about 5.7 hours. This means that half of the caffeine intake will still be in your system after 5.7 hours. The general formula (using rational exponents) is:    A=C(0.5)t/k where:  t = the hours since drinking the caffeine k = the half-life of caffeine (about 5.7 hours) C = the milligrams of caffeine ingested A = the milligrams of caffeine left in your body after t hours New Thread Post 1: Find the amount of caffeine in your favorite caffeinated beverage by checking the nutrition label or doing research on the internet. Be sure to find the amount of caffeine in the entire container, not just in one serving. This will be C in the equation. Assume you drink the entire beverage in one sitting. Share the name of your favorite caffeinated beverage and the amount of caffeine in that beverage. Calculate the amount of caffeine (mg) still in your body after t = 2 hours after you drank the beverage. Show all steps in your calculations and round your answer to the…

Solve for x

Charles is cutting and re-sewing a plain rectangular tablecloth to fit a square table. The cloth can be turned into a square by increasing the width by 3 ft and reducing the length by 5 ft. There is no waste and the area of the rectangular blanket and the square blanket are the same.Find the length and the width of the original cloth. Round your answer to 2 decimal places.

The total number t of items that a manufacturing company can produce is directly proportional to the number n of employees.

a whole Each freind get 1/18 Of Wh 5. Oscar's aunt lives 50 miles away. This is 6 times as far as Oscar's grandfather lives. How far away does Oscar's grandfather live? so SO 5. OScars Abuelo lives8113 miles awaye A banner has a length of 10 feet and an area of 7 square fe What is the width of the banner? Brady has three goldfish. This is times as many as Sam has. How many goldfish does Sam have? Lucy has hour to decorate a dozen cupcakes for a bake

Solve for x

An electronics company analyst has determined that the rate per month at which revenue comes in from the portable GPS division is given by the following formula where x is the number of months the division has been in operation.   R ( x ) = 109 e 0.09√x +29   Use a calculator with a program for​ Simpson's rule with n = 20 to find the total revenue between the 12th and 33rd months. Do not round until the final answer. Then round to the nearest dollar.

The number of Rednwood pine trees per acre N(d) in a test plot can be approximated by the following model N(d)=68(-0.04d); 5 less than or equal to d less than or equal to 40 where d is the average diameter (in feet) of the trees when they are measured 3 feet off the ground. To the nearest hundredth of a foot, find the average diameter of the trees in a 1-acre test plot containing 21 trees. Explain how you got your answer.