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Consider the intersection of level surfaces of F = x^3 + y^3 - u^3 - v^3 and G = xu + yv.
(a). Write down the linear equations in matrix form to decide on solving for solving for x and y as functions of u and v near (x0, y0, u0, v0).
(b). Write down the matrix equation for solving for dx/du and dy/du near (x0, y0, u0, v0).
(c). Describe the points (x0, y0, u0, v0) near which you may be unable to solve for x and y as functions of u and v near (x0, y0, u0, v0).
The difference exists between the mean number
Identify the critical points and find the maximum value and minimum value on the given interval g(x)=1/1+x^2 ; I=[-3,1]
which length measurement is most precise between 50 centimeters 24.36 centimeters 37 centimeters or 18.5 centimeters.
The sum of three numbers is 6. The third number is the sum of the first and second numbers. The first number is one more than the thrid number. Find the numbers.
Let A = Z + Z + Z, let x_1 = (1,2,1) and x_2 = (1,5,1), and consider the subgroup B = (x_1, x_2) is a member of G. For the quotient group G = A/B, and write (x,y,z) is a member of G for the coset determined by n element (x,y,z) is a member of A.
Let L:R^n -->R^n be a linear operator on R^n. suppose that L(x) = 0 for some x does not equal 0. Let A be the matrix representing L with respect to standard basis. Show that matrix A is singular.
a particle moves on the x- axis so that its accleration at any time t > 0 is given by a=(t/8)-(1/t^2). when t=1, v= 9/16 ft/sec, and s=25/49 ft.
In each case make a conjecture about a possible generalisation, and explore it (i.e. attempt to prove your conjectures true or false).
At a certain factory, approximately q(t) = t^2 + 50t units are manufactured during the first t hours of a production run, and the total cost of manufacturing q units is C(q) = 0.1q^2 + 10q + 400 dollars.
Explain in your own words how to use the zero-factor property when solving a quadratic equation. Post a problem for classmates to solve.
Set up a hypothesis test to try to prove that the mean number of hours studied at your school is different from the 14.6-hour-per-week benchmark reported by BusinessWeek.
a stockholder sold 150 shares of stock at 34 1/4 per share find the stockholders loss per share The stock had been purchased at 36 5/8 per share.
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