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Graphs and Functions

Will Meteorites Travelling on a Parabolic Path Strike the Earth?

The earth with center at the origin has equation of xsquared + ysquared =65 where x and y are distances in thousands of kilometers. Will either of these two meteorites whose equations I will give you strike the earth? The first meteorite is a parabola whose equation is 18x-ysquared = -144. Please show all steps in sketching and

Draw the Graphs for Three Equations and Find a Common Point

Using first two equations determine 3 possible points that the 2 conic sections that you get from equations meet. Add a third equation figure to out the one point that all three conic sections meet. First equation is 9(x-squared)+25(y-squared)-72x=81 Second equation is 9(x-squared)-15(y-squared)=9 Graph these two conical

Choosing Between Point-Slope, Slope-Intercept and Standard Forms

Find an example, of the BMI between man/woman and estimate a best fit line graphically. Develop an approximate linear model using the point slope form, the slope-intercept form or the standard form line. You are not to graph the line here but help illustrate your point . You are only required to use the line of the forms to iden

Functions, Inverse Functions and Graphs

1. Let h(x) = (8x - 5)/(7-x). (a) Find the inverse of the function h. Show work. (b) What is the domain of h? What is the domain of the inverse of h? 2. Use a calculator (standard scientific calculator or the online graphing calculator) to find each of the following values. Write your answer rounded to 4 decimal places.

Polar Function : Graphing an Ellipse

Graph an ellipse as a polar function with a focus at the pole and parameterized by the eccentricity e and the distance d between the focus and a vertical directrix. ----------------------------------------------------- Please show me how step-by-step on how you would graph this. Thanks

Polar function

Graph an ellipse as a polar function with center at the pole and parameterized by the lengths of the semi-major and semi-minor axes. Can someone please show me step-by-step on how to do this?

Algebra : Graphing, Distance between Points and Equations of Lines

Please see the attached file for the fully formatted problems. Can you please help me with the following circled problems? Page 187 1. a) 12, b) 14, c) 16, d) 18 (Check for all four of our symmetries SY, SX, SO, SI; consult in WEEK7 NOTES, in COURSE CONTENT. Practice graphing these using the downloaded graphing utility Gr

Duality and Saddle Points

Please see the attached file for the fully formatted problem. I am working on a way to find the minimum of a function J(Y) with the constraint set C = {X E R^N such that gt(x) =<0 Vi E [1,n]} Let L(Y, mu) = J(Y) + SIGMA m --> i = 1 muigi(Y) be the lagrangean of the problem. I am having trouble proving the following

Lines through Non-Colinear Points

Given three points, there is one line that can be drawn through them if the points are colinear. If the three points are noncolinear,there are three lines that can be drawn through pairs of points. For three points, three is the greatest number of lines that can be drawn through pairs of points. Determine the greatest number of

Conic graph

Identify and sketch the graph of the conic described by the quadratic equation x^2 + 4xy + y^2 - 12 = 0. Do this by writing this equation in matrix form; then change the equation to a sum of squares of the form x'^T Dx' where D is a diagonal matrix.


If g(x)=x^2+1, find the formulas for g^3(x) and (gogog)(x).

Cubic Functions

Investigate the cubic functions of f(x) = ax^3 + bx^2 + cx + d which will pass through the points of A = (1,4) B = (2,2) C = (4, 1.5) Now explore the effect of 'd' on the behaviour of the cubic functions. Identify a value of 'd' that gives a cubic function which closely matches the quartic function that passes through these

Vectors : Force and Line Equations

(1) A force F of magnitude 6 in the direction i - 2j + 2k acts at the point P = (1,-1, 2). a. Find the vector moment M of F about the origin. b. Find the components of M in the direction of the (positive) x - axis, y -axis and z -axis. c. Find the component of M about an axis in the direction

Functions: Mapping

For the functions f defined below, determine which are 1:1, onto or both. 1) f: R onto R, f(x) = |x| 2) f: R onto R, f(x) = x^2 + 3 3) f: R onto R, f(x) = x^3 + 3 4) f: R onto R, f(x) = x(x^2-4) 5) f: R onto R, f(x) = |x| + x 6) f: N onto N, f(x) = x + 1 7) f: N onto NxN, f(x) = (x,x) 8) f: NxN onto N, f(

Two Segment Graph : Equation of Tangent and Calculation of Points

Please note: On the attached graph the scale is that each line represents one unit. Please show all work, thanks!! The graph of F consists of a semicircle and two line segments as shown (please see the attachment). Let g be the function given by: g(x)= def.integral from 0 to x f(t)dt. a Find g(3). b Find all value

Distribution graph

Look at the model you found for the data on the number of shopping centers and retail sales for the North Central states. a. Make a plot of the residuals versus the independent variable. b. From the plot, does it appear that a linear model is appropriate? c. Looking at the residual plot, do you think that the assumption

Planar graph

I need to show that if G is a planar graph, then G must have a vertex of degree at most 5.