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- With y=c1.x2+k curves and curves x2+2.y2-y= c2 intersect perpendicularly. Where C1 and C2 are arbitrary constants, So what is the value of k?determine the general solution of y''-y=0 given y1(x)=e-2x using reduction of ordersFind the values of constants a, b, and c so that the graph of y=ax^3+bx^2+cx has a local maximum at x=-2, a local minimum at x=-4 and inflection point at (-3,18)
- find the general solution given that y1(t)=t is a solution. use the method of reduction of order t^2y''+2ty'-2y=0Find the values of constants a, b, and c such that the graph of y = ax3 + bx2 + cx has a local maximum at x = 3, local minimum at x = -1, and inflection point at (1, 11).the relationship between aphids, A, ( prey) and ladybugs, L, (preditor) can be described as follows: dA/dt=2A=0.01AL dL/dt=-0.5L+0.0001AL a) find the two critical points of the predator-prey equations b) use the chain rule to write dL.dA in terms of L and A c) suppose that at time t=0, there are 1000 aphids and 200 ladybugs, use the Bluffton university slope field generator to graph the slope for the system and the solution curve. let 0 be less than or equal to A who is less than or equal to 15000 and 0 is less than or equal to L which is less than or equal to 400.
- Now lets use a graphing calculator to get a graph of C=59(F32). By letting F=x and C=y, we obtain Figure 7.15. Pay special attention to the boundaries on x. These values were chosen so that the fraction (Maximumvalueofx)minus(Minimumvalueofx)95 Would be equal to 1. The viewing window of the graphing calculator used to produce Figure 7.15 is 95 pixels dots wide. Therefore, we use 95 as the denominator of the fraction. We chose the boundaries for y to make sure that the cursor would be visible on the screen when we looked for certain values. This was accomplished by setting the aforementioned fraction equal to 1 By moving the cursor to each of the F values, we can complete the table as follows. F 5 5 9 11 12 20 30 45 60 C 21 15 13 12 11 7 1 7 16 The C values are expressed to the nearest degree. Use your calculator and check the values in the table by using the equation C=59(F32).For what value of k will x + k/x have a relative maximum at x = -2?1. For what value (s) of x is the function f(x) = 4/2x2 - 6x not continous? 2. If the demand of firm is QD (p) = 50 -3p and its supply function is Qs (p) = 14 + 6p. What is the equilibrium? 3. Find Lim x2 -4x + 3/5
- B) Use partial fractions to solve for y(t). (Do not use Heaviside coverup.)Your friend attempted to graph theequation f(x)=-2cos(1/3(x-60))+3. Based on their graph of the parentfunction (solid), and the transformed function (dashed) below, describewhich transformations have been applied correctly, and which have not.Justify your answer.7. Determine values of a, b, and c such that the graph of y = ax³ +bx² + c has a local extremum at (2, 11) and a point of inflection at (1, 5).