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Q: Before 1918, approximately 60% of the wolves in a region were male, and 40% were female. However,…
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Q: efore 1918, approximately 55% of the wolves in a region were male, and 45% were female. However,…
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- The work force of a certain factory is growing at rate of 2 per month while the average productivity of a worker is growing at a rate of 4 units per month. If the work force is currently 100 and the average productivity per month is 200 units, at what rate is the total productivity per month of the factory increasing?10.Anti-derivative of y(2y^2-3)^5Find the work done in emptying the tank in example 4. If the tank water is pumped to a level 1.00 meters above the top of the tank and the water is initially 4.00 meters deep.
- 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?If the average rate of change of q (x) in the period (5,7) is equal to 8 and y (5)*y (7) = 16 and f (x) = 1 / y (x), what is the average rate of change of the function f ( x) In the same period ?!The U.S. Bureau of the Census prediction for the percentage of the population 65 years and older can be modeled as p(x) = −0.00022x3 + 0.014x2 − 0.0033x + 12.236 percent where x is the number of years since 2000, data from 0 ≤ x ≤ 50. 1. Determine the value of x in the domain 0 ≤ x ≤ 50 for which the percentage is predicted to be increasing most rapidly (Round your answer to three decimal places). 2. Thus, in which year is the percentage is predicted to be increasing most rapidly? 3. Calculate the percentage at that time. (Round your answer to two decimal places.) 4. Calculate the rate of change of the percentage at that time. (Round your answer to three decimal places.)
- Find the first and second order derivative w=3z7-7z3+21z2A company needs to rent space for its office employees both in the suburbs and downtown. Space is available in suburbia at a rate of $120 per square metre (per annum), while downtown space rents for $250 per square metre (per annum). In suburbia, only 30% of the space is “executive” quality, while the rest is ordinary quality. At the downtown location, 70% of the space is executive quality, while the rest is ordinary quality. The company needs a total of at least 1000 square metres of space, of which at least 510 square metres must be executive quality. No more than three quarters of the entire space is to be at either location. They wish to know how much space they should rent in each place so as to minimize the total expenditure on rent. a) Show the decision variables b) Show the objective function c) Show the constraints in standard form (i.e. suitable for using Excel’s Solver) d) Solve the linear programming problem by graphingA critical communications relay has a constant failure rate of 0.1 per day. Once it has failed, themean time to repair is 2.5 days (the repair rate is constant). What is the point availability at the end of the 2 days?
- Estimate √3.9 using a linear approximation at a=4.Assume that the fire caused construction to slow down and caused a reduction in efficiency in completing the building. Estimate the number of labor hours needed to complete the building if there were no slow down related to the fire. Assume that the relationship that existed between HOURS and FLRCOM and FLRCOMSQ before the fire would have continued to exist to the completion of the building had the fire not occurred. Estimate the extra labor hours traceable to the fire.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.