1. Vx(Gx→Px) F VxGx→VxPx
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- Eliminate the arbitrary constants of: x^2=Axy+ByIn a certain company, the income from the sale of x thousand pieces of products is given by I (x) = 9x, while the cost of making the same x products is given by C (x) = x ^ 3-6x ^ 2 + 15x + 1. Assuming that I and C are in thousands of dollars and everything produced is sold, what is the maximum profit the producer can make? Argues using first or second derivative criteria.John Swanson, president of Market Research Inc., has asked you to estimate the coefficients of the modelY = β0 + β1X1 + β2X21 + b3X2where Y is the expected sales of office supplies for a large retail distributor of office supplies, X1 is the total disposable income of residents within 5 miles of the store, and X2 is the total number of persons employed in information-based businesses within 5 miles of the store. Recent work by a national consulting firm has concluded that the coefficients in the model must have the following restriction:b1 + b2 = 2Describe how you would estimate the model coefficients using least squares.
- 1. calculate the following: a. (-3x2y2) X (-2x3y) X (-3y2) b. (-5x23) X (-2x3y2) X z4 c. 3y2z X (-4y2x) X (x2y)3 d. 4x2y3z2 X x3y2z3 X (-2xz3) e. (-3yz)2 X (2x2)3 X (x2y3)2 f. 3xyz2 X x3y2 X 2xy4 g. 6x2z2 X 2x3z X (x2y)3What are the critical points and inflection points of the equation 1/(x(x+1)^2)What is y' if xy^3 + yx^3 = x - 3y?
- If it is known that L {y'' (t)} = -15s+24 with y(0) = -3 and y'(0) = 6, then it can be ensured that:11.Show that if a11, a12, a21, and a22 are constants with a12 and a21 not both zero, and if the functions g1 and g2 are differentiable, then the initial value problem x′1=a11x1+a12x2+g1(t),x1(0)=x01x′2=a21x1+a22x2+g2(t),x2(0)=x02 can be transformed into an initial value problem for a single second-order equation. Can the same procedure be carried out if a11, …, a22 are functions of t?x^2=Axy+By