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    Graphs and Functions

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    The Equation of a Line Given a Point and Slope

    Please answer the following two questions: 1. Find the equation of the line through the point (-1, 3), having a slope equal to 3/7. 2. Find the equation of the line that passes through the point (2, 3) and which is perpendicular to the line y = -4x + 5. Make sure to show all of your work.

    Problem on R-chart

    Attached is an R chart in Excel. Plastics food containers that can be baked in ovens must be able to withstand certain temperatures without melting. One such container, which is 4 inches deep, is designed for use at oven temperatures of 325°F. To monitor the quality of these containers, a subgroup of 5 finished containers i

    Graphing Surfaces

    Sketching Functions. Only circled questions. See attached file for full problem description.

    Comparing Equations of Lines

    1.For the pairs of lines defined by the following equations indicate with an "I" if they are identical, a "P" if they are distinct but parallel, an "N" (for "normal") if they are perpendicular, and a "G" (for "general") if they are neither parallel nor perpendicular. 3x + 4y + 5 = 0 and y = - 3 4 x - 54 . x = 2 and y = p

    Algebra Problems: Graphs and Functions

    1.) An edge of a graph "G" is a bridge of "G" If and only if there exist vertices "U" and "W" such that "e" is on every U - W path of "G". 2.) A graph "G" of order at least 3 is Non Separable if and only if there exist two internally disjoint U - V paths for every two distinct vertices "U" and "V" of "G".

    Vectors : Linear Combinations and Spans

    Please see the attached file for the fully formatted problems. 1) Determine if b is a linear combination of , . 2) List five vectors in span { }. For each vector, show the weights on used to generate the vector and list the three entries of the vector. Do not make a sketch. a) b) 3) Let For what

    Critical Points

    Let f(x,y)=((x^(2)y^(2))/(x^(2)+y^(2))), classify the behavior of f near the critical point (0,0).

    Graphs : Hyperbolas and Parabolas

    Given the graph, identify the graph of the function (line, parabola, hyperbola, or exponential), explain your choice, and give the domain and range as shown in the graph, and also the domain and range of the entire function. See attached file for full problem description.

    Vectors and Parametric Equations of Lines

    2. Find a vector equation and parametric equations for the line. 3. The line through the point (?2, 4, 10) and parallel to the vector (3, 1, ?8) Find parametric equations and symmetric equations for the line. 8. The line through the points (6, 1, ?3) and (2, 4, 5) 11. The line through (1, ?1, 1) and parallel to the line x +

    Crate's weight perpendicular and parallel to the incline

    The chemical retardants are freight shipped from a warehouse. A shipping crate that weights 450 kilograms is placed on a loading ramp that makes an angle of 30 degrees with the horizontal. Find the magnitude of the components of the crate's weight perpendicular and parallel to the incline.

    Expressing Volumes and Change of Volume as Functions

    A rectangular storage unit has dimensions 1m by 2m by 3m. If each linear dimension is increased by the same amount. a) What increase would result in a new storage unit with a volume 10 times the original? b) How many possible solutions are there to this problem? Explain the answer. c) Sketch the graph of the informatio

    Trivial, Irregular Graphs

    A non - trivial graph g is called irregular, if no two vertices of g have the same degrees. Prove that no graph is irregular.

    Equation of a Secant Line

    F(x)=x^2+2x-6 X(1)=2 and x(2)=-1 I have to find the secant line of this graph but can not remember how to find the points to graph the equation

    Does the parabola open upward or downward?

    Determine if the parabola for the equation, y = -2x^2 - 4x + 6, opens upward or downward. Find the vertex, x-intercepts, and y-intercept without graphing. keywords: concave, concae-up, concave-down

    Finding Areas Bounded by Functions

    Please see the attached file for the fully formatted problems. keywords : find, finding, calculating, calculate, determine, determining, verify, verifying, evaluate, evaluating, calculate, calculating, prove, proving keywords: integration, integrates, integrals, integrating, double, triple, multiple

    Sketch the region bounded by the graph of the function and find the area.

    Sketch the region bounded by the graphs of the functions and find the area of the region. f(x) = sin(x), g(x) = cos(2x), -pi/2 <= x <= pi/6 (a) Use a graphing utility to graph the region bounded by the graphs of the equations, (b) find the area of the region and (c) use the integration capabilities of the graphing utility

    Regions bounded by graphs of algebraic functions

    Sketch the region bounded by the graph of the algebraic function. 20. f(x) = -x^2 + 4x + 1, g(x) = x + 1 22. f(x) = -x^2 + 4x + 2, g(x) = x + 2 24. y = 1/(x^2), y = 0, x = 1, x = 5 26. f(x) = 1*sqrt(x - 1), g(x) = x - 1 28. f(x) = y(2 - y), g(y) = -y 30. f(y) = y/(sqrt(16 - y^2)), g(y) = 0, y = 3 32. g(x) = 4/(2 - x),