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Solving Equations

Solve the following equation for X. Write your answer as a fraction in simplest form. 7(x-3)=-3x+2-3(-2x+7)

Slopes of Perpendicular and Parallel Lines

13. The slope of the line perpendicular to the line passing through (0, 0) and (-5,-5) is a) 0 b) inf c) 1 d) -1 16. The line y = x+4 is parallel to 4x + 4y = 15 a) True b) False 17. The above two lines (question 16) intersect at a) (-3.875, 0.125) b) (0.125,3.875) c) (-0.125, 3.875) d) (3.875, 0.125)

Line Intersection Problem

Let L whose be a straight line in the xy-plane whose equation is of the form y - 8 = m(x - 2). (a) Determine all the points in the xy-plane where the line L intersects the curve y = 2x^2 . (b) Using the results of Part (a), determine whether there are any values of m such that L intersects the curve y = 2x^2 in exactly

Uniform Convergence of a Sequence

Let (f_n) be a sequence of continuous functions on R--->R^q which converges at each point of the set Q of rational numbers. If the set {f_n} is uniformly equicontinuous on R, show that the sequence converges at every point of R and that the convergence is uniform on every compact set of R. keywords: equi-continuous

Solve: The Slope of a Perpendicular Line

Consider the line x+5y = 5. Please address the following questions: What is the slope of a line perpendicular to this line? What is the slope of a line parallel to this line?

Solve the recurrence

Solve the recurrence T(n) = 2T(sqrt(n)) + 1 by making change of variables. The solution should be asymptotically tight. 2. Use a recursive tree to give an asymptotically tight solution to the recurrence T(n) = T(n-a) + T(a) + cn, where n > = 1 and c > 0 are constants.

Recursive Definitions

I want to get a better understanding of how these problems are done. For Exercises #1-3, decide whether the sequences described are subsequences of the Fibonacci sequence, that is, their members are some or all of the members, in the right order, of the Fibonacci sequence. 1. The sequence A(n), where A(n) = (n-1)2^n-2 +

Power Series

Expand (1-z)^-m in powers of z for m in N. Let (1-z)^-m=sum from n=0 to infinity of (a_nz^n) then a_n ~n^m-1/(m-1)! as n-> oo where ~ means that the quotient of the expressions to the left and the right of it tends to 1.

Solving Inequalities

Solve the inequality for W. Simplify your answer as much as possible. -(2/7)w + 9 ≥ 4w + 4

Algebra Questions

For 3y - 5x > 15 a) Find its slope. b) Find its y-intercept c) Is the line dashed or solid? d) Is the shaded area above or below the line? e) Write in slope-intercept form and standard form. (using only integers for standard forms). f) Does the point (1, -3) satisfy the inequality?