If the length of a certain object is increasing, then the rate of change would be positive. If it is decreasing, then negative. If it is constant, then the rate of change would be infinity. True O False
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- If two companies have the same marginal cost, is their total cost always/sometimes/never the same? Why or why not? Use Calculus to explain.A small business invests $25,000 in a new prod- uct. In addition, the product will cost $0.75 per unit to produce. Find the cost function and the average cost function. What is the limit of the average cost function as production increases?The price P of gasoline increases to a maximum and then stays at a fixed price. What is the rate of change dp/dt and how is it changing at the time when the price reaches a maximum?a. dp/dt is negative at the maximum and is decreasing.b. dp/dt is equal to zero at the maximum and remains the same.c. dp/dt is positive at the maximum and is decreasing.d. dp/dt is negative at the maximum and is increasing.
- Suppose that a company's average cost is A(x)=1.7x+7. Step 2 of 2: Determine the marginal cost.Life Expectancy at 65 Using data for selectedyears from 1950 and projected to 2050, the functiony = 0.077x + 13.827 gives the life expectancy atage 65, with y equal to the number of additional yearsof expected life at age 65 and x equal to the numberof years after 1950.a. Why is this a linear function?b. Find and interpret the slope of the graph of thisfunction.(Source: Social Security Administration)As with discrete-time dynamical systems, equilibria can act strange when the slope of the rate-of-change function is exactly equal to the critical value of zero. Graph a rate-of-change function that has a slope of 0 at the equilibrium but the equilibrium is stable. What is the sign of the second derivative at the equilibrium? What is the sign of the third derivative at the equilibrium?
- A visitor is staying in a tent that is 7 kilometers east of the closest point on a shoreline to an island. The island is 3 kilometers due south of the shoreline. The visitor plans to travel from the tent to the island by running and swimming. If the visitor runs at a rate of 6 kmph and swims at a rate of 5 kmph, how far should the visitor run to minimize the time it takes to reach the island?A problem that occurs with certain types of mining is that some byproducts tend to be mildlyradioactive, and these products sometimes get into our freshwater supply. The EPA has issuedregulations concerning a limit on the amount of radioactivity in supplies of drinking water.Particularly, the maximum level for naturally occurring radiation is 5 picocuries per liter ofwater (on average). A random sample of 24 water specimens from a city’s water supply gave ̄x= 4.61 and s = 0.87. Do these data provide sufficient evidence to indicate that the meanlevel of radiation is safe (below the maximum level set by the EPA)? Test usingα= 0.05.The success of a project depends on the effort level of a worker. In case of successthe revenues will be 400,000 TL whereas in case of no-success the revenues will be 0. The workercan provide a low effort level or a high effort level. The effort level cannot be observed by theprincipal. The worker requires an expected salary of 60,000 TL to provide the low effort leveland an expected salary of 80,000 TL to provide the high effort level. The success probabilitiesfor the project are 40% in case of low effort level and 80% in case of high effort level. Whatshould be the minimum bonus (that is awarded in addition to the base salary in case of success)and the base salary for the worker so that the worker has the incentives to provide the higheffort level?
- Suppose stock A is priced at $30/share and the company will pay a dividend of $0.30/share after two months. An investor purchases 100 shares of A and invests all dividends received at a continuosuly compunded risk-free rate of 5%. After 3 months the stock is sold when the price is $35.40/share. Calculate the 3-month profit.A rock formation is 3 miles due north of its closest point along a straight shoreline. A visitor is staying in a tent that is 4 miles west of that point. The visitor is planning to go from the tent to the rock formation. Suppose the visitor runs at a rate of 6 mph and swims at a rate of 3 mph. How far should the visitor run to minimize the time it takes to reach the rock formation?homogenous linear de with constant coeffiecients