An open-top box is to be constructed from a 6 foot by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out. a) Find the function V that represents the volume of the box in terms of x. b) Graph this function an
1. Find the equation of a parabola whose vertex is (0,0) and directrix is the line y=3. 2. Find the vertex, focus, and directrix of (x-2)^2=12(y+1). Find the latus rectum and graph the parabola, making sure that all points and axis are labeled. 3. Find the equation of the ellipse whose center is the origin and has a
F(x,y) = x^2 + y^2 Are the xyz-intercepts all 0? The domain looks like it is all real #s. Is the range also all real #'s? I also see the graph is continuous on all points. Really I am just confused about the range.
F (x,y) = 4 What are the domain, range and intercepts of this one? I am totally confused about this graph. Are there even any x and y intercepts? I don't think so, since I am assuming z = 4 and that would be the z-intercept, right?
F(x,y) = sqrt (x^2 + y^2) I am not sure what the domain, range and intercepts are for this particular graph. Can you help me with this one?
F(x,y) = cos (y) What would the domain of this be? (-infinity, +infinity)??? Is the range between -1 and 1? Are the z and x-intercepts 1 and does a y-intercept exist?
I have graphed the following function: f(x,y) = 4-y^2 I am a little confused as to what the domain, range, and xyz-intercepts are. Can you help with that?
Algebra Questions. See attached file for full problem description.
1) Prove that in is a positive integer. ( : is the Mobius function) Hint: one of the four argument is divisible by 4. 2) If is a prime and . Show that ( : is the Euler function) 3) a. Prove that is an integer if n is a prime and that it is not an integer b. Prove that is not an integer if n is divisi
Gradient function. See attached file for full problem description. Let . Find a function so that , and .
Show that if an entire function f maps the real axis into itself and the imaginary axis into itself, then f is an odd function, i.e., f(−z) = −f(z) for any z. Give two proofs, which are really different.
Prove that if f(z) : H -> H is an analytic function from the upper-half plane to itself, then:|f(z) − f(z_0)|/|f(z) − (f(z_0))bar|<=|z − z_0|/|z − (z_0)bar| where z,z_0 are in H and |f'(z)|/Im(f(z))<=1/Im(z) where z is in H. When does equality hold?
3. Let D = {z : |z| < 1}. Suppose that f : D -> D is analytic, f(1/3) = 0 and f'(1/3) = 0. Show that |f(0)| <= 1/9.
1. Let f(z) be a holomorphic function in the disc |z| < R1 and set M(r) = sup|f(z)|(|z|=r), A(r) = supR(f(z)) (|z|<r) where 0<=r<R_1 (a) Show that M(r) is monotonic and, in fact, strictly increasing, unless f is a constant. (b) Show that A(r) is monotonic and, in fact, strictly increasing, unless f is constant.
For a parabola y^2 = 4ax: 1. Find the equation of the tangent at P ( at^2, 2at ) on the parabola. 2. Find the point Q on the parabola so that PQ passes through the focus F ( a, 0 ) of the parabola 3. Show that the tangents at P and Q intersect on the directrix of the parabola
Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (-4,2) and perpendicular to the line whose equation is y = 1/3X + 7
Selected amounts at December 31, 2003 from the Hay and Barnabas Company's information system appear as follows: Cash paid employees for salaries and wages 300,000 Cash collected from sales customers 1,850,000 Bonds payable 500,000 Cash 150,000 Common stock 60,000 Eq
1. Show that a = b mod m is an equivalence relation on Z. I used = to mean "equal by definition to" and Z as integers. 2. Find the inverse of each of the following integers. r 1 2 3 4 5 6 ----------------------------------- r^-1 mod 7 3. Sh
1. Let f : X -> Y and g : Y -> Z be mappings. (1) Show that if f and g are both injective, then so is g o f : X -> Z (2) Show that if f and g are both surjective, then so is g o f : X -> Z. 2. Let alpha = 1 2 3 4 5 and Beta = 1 2 3 4 5 3 5 1 2 4 3 2 4 5 1 .
Function Graph/Derivative Graph. See attached file for full problem description.
Consider the following graph of the function f(x) f(X) Positive and Negative. See attached file for full problem description.
Please see the attached file for the fully formatted problems. (Unit 3-IP3) Solve the following equations. a) √x - 1 = 3 Answer: Show work in this space. b) √x^3 = 8 . Answer: Show work in this space. c) . Answer: Show work in this space. 2) Is an identity (true for all va
Find the range of data: 87, 56, 93, 42, 78, 56, 48, 75
In most businesses, increasing prices of their product can have a negative effect on the number of customers of the business. A bus company in a small town has an average number of riders of 1,000 per day. The bus company charges $2.00 for a ride. They conducted a survey of their customers and found that they will lose approxima
Show that the Petersen graph is nonplanar by a) showing that it has k3,3 as a subcontraction, and b) using the problem 1 show above part a) You don't have to solve problem 1. Can you explain about contraction. problem 1.-Let k>=3 be an integer , and let G be a plane graph of order n(>=k) and size m. a) If the length
Require histograms of: 1 )Arrival Rate Number of Arrivals vs. Number of Occurrences This should be one consolidated histogram representing all of the observations from each data sheet. In plotting this data, the horizontal axis should be the number of arrivals during the 5-minute interval and the vertical axis should be th
A) Show that every bipartite graph G is a subgraph of a -regular bipartite graph. b) Show that every bipartite graph G is of class one , that is, What does -regular bipartite graph mean? Can you draw a graph for me please?
See the attached file. Let be pairwise disjoint graphs, and let . Prove that is called clique number of the graph G, is the maximum order among the complete subgraphs of G . Please see the attached file for the fully formatted problems.
Show that every nonempty regular graph of odd order is of class two. Please explain with details. Draw a graph.
(4) Explain why the function f (x) = =has a vertical asymptote but no vertical tangent. (5) Sketch the graph of the curve....for [0,2a). Show all special features such as vertical asymptotes, horizontal asymptotes, cusps, vertical tangents, and intercepts. See attached file for full problem description.