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Evaluate the function at the indicated values.
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- orth0gonal trajectories y^2=4x^2(1-kx)The estimated Philippine population is 90 million in 2010 and the estimated growth rate was 2.4 % per year. That is n(2010) = 9 x107 and k= 0.024. So an equation for predicting the population with the stated initial condition and growth rate of 2010 isfind orthogonal trajectories of x2+(y-c)2=c2.
- 1. How do you find the linearization of f(x) at x = a? Illustrate with a concrete exampleApplication of Differential Calculus: Optimization Farmers use a certain plant food costing $4.00 per ounce to help them in growing oranges. It is estimated that when x ounces of the food are used on an ace of orange grove, the farmer is able to get Ln(4x+5) crates of oranges from that acre of land. If the farmer can sell the oranges at $20 per crate, how many ounces should be used per acre to maximize the orange crops net value.an epidemiological study of the spread of a certain influenza strain that hit a small school population found that the total number of students, p, who contracted the flu t days after it broke out is given by the model P+-t^2+13t+160, where 1 is less than or equal to t is less than or equal to 6. find the day that 200 students had the flu. recall that the restriction on t is at most 6.
- The function y = 2x2 - ln 4x (x 7 0) has one minimum point. Find its first coordinate.Application of derivative Optimization We are going to fence in a rectangular field that encloses 200 m2. If the cost of the material for of one pair of parallel sides is $3/m and cost of the material for the other pair of parallel sides is $8/m determine the dimensions of the field that will minimize the cost to build the fence around the field.Overtaking City A has a current population of 500,000 people and grows at a rate of 3%/yr. City B has a current population of 300,000 and grows at a rate of 5%/yr.a. When will the cities have the same population?b. Suppose City C has a current population of y0 < 500,000 and a growth rate of p > 3%/yr. What is the relationship between y0 and p such that Cities A and C have the same population in 10 years?
- a. What is the family of orthogonal trajectories for the family of parabolas with axis parallel to the y-axis and vertex at the point (−2, 4)? b. Give the family of orthogonal trajectories of the family of parabolas with vertical axis and vertex at the point ( -6 , -4 ).Using Reduction of Order: (D2-1)y = 2e2x