1) An open-top box is to be constructed from a 6 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. Answer b) Graph th
(See attached file for full problem description) --- We consider the special case when m=3 and n=4. (a) Write down the correspondence between numbers in and pairs of integers in given by the function f. In other words, write out the 12 values f(a) where . (b) Fore each value you computed above, circle the equations
(See attached file for full problem description) Conjecture: Suppose that m and n are positive integers. If gcd(m,n)=1, then . a. If m and n are positive integers and k is any integer, show that gcd(k,mn)=1 if and only if gcd(k,m)=1 and gcd(k,n)=1. b. Suppose gcd(m,n)=1. Prove that establishes a bijection between
Graph the functions y = x and y = -x on the same graph (by plotting points if necessary). Show the points of intersection of these two graphs.
Think of one real situation that involves exponential growth and that involves exponential decay. for each example, your project should include the following: * Paragraph - Briefly explain the situation. You may make up your own information, but make it realistic. Include the facts needed to write an equation. * Equation -
One of the civil engineers you interviewed for your article works for a company which specializes in bridge construction projects. In the process of designing suspension bridges, they must account for many variables in the modeling. Some of these variables include the bridge span; the force of the typical water currents wearing
When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. Create three unique equations where the discriminant is positive, zero, or negative. For each case, explain what this value means to the graph of y = ax2 + bx +
(See attached file for full problem description with equations) --- 1) Solve the following equations. a) Answer: Show work in this space. b) . Answer: Show work in this space. c) . Answer: Show work in this space. 2) Is an identity (true for all values of x)? Answer:
Assume that f and f ' are continuous on [a,b], and f ''(x) exists and f ''(x)>0 for each x 1) Prove that f ' is increasing on [a,b] Hint: the graph is concave up on this interval. 2) Prove that f(x) f(c) for each x if c and f '(c)=0.
Show that if gcd(a, b) = 1, then gcd(ac, b) =gcd(b, c).
An integer n is called k-perfect if σ(n) = kn (note that a perfect number is 2-perfect). (a) Show that 120 = 23? ? ? 3 ? ? ? 5 is 3-perfect. (b) Show that if n is 3-perfect and gcd(3, n) = 1, then 3n is 4-perfect.
Show that if and , then . (This shows that the function g is well-defined from to ) Note: g is defined as follows: g: Where is the multiplicative inverse of m1 modulo m2 and conversely. Please see the attached file for the fully formatted problems.
Assume that f is differentiable for each x and there exists M>0 such that for each x Prove that f is uniformly continuous on D. Hint: Can use the mean value theorem. keywords: differentiability, continuity
Suppose that X and Y are finite sets, with m and n elements respectively. Suppose further that the function f : X → Y is one-to-one and the function g : X →Y is onto. (i) Use the function f to show that m ≤ n. (ii) Use the function g to show that m ≥ n. (iii) Is f : X → Y onto? Justify your assertion. (iv) Is th
How many functions are there from S = {1,2,...,10} to T = {1,2,3,4,5}? How many of these functions are onto?
Decide whether the relation is a function. 1- (6,5), (4,3), (-2,3), (0,-1) , (-1,2), (-4,-5), (-3,4) 2- (4,4), (3,3), (-1,1), (6,6), (1,-2) make an input-output table for the function rule. Use a domain of -10,-5,0,5, and 10. Identify the range. y=8x+1 y=-6x y=x square 2+5 write a function that relates and x and
Given a 2 x 2 matrix sample = 2.0000 + 3.0000i 1.0000 + 2.0000i 4.0000 + 5.0000i 2.0000 + 1.0000i >> std(sample(:)) ans = 2.1213 >> According to matlab the answer is 2.1213. I'm not arriving at that answer. I need to see all work on how to achieve said result.
The following theorem could be used to write the proof. A theorem states that if d:D-->R is uniformly continuous on D iff the following condition is satisfied: If un and vn are both sequences in D, then lim as n-->infinity (f(un)-f(vn))=0 Show f is not uniformly continuous on D making use of the sequent
Identify the type of graph with the equation x- 4y^2 - 8y = 0.
Identify the type of graph with the equation x^2 = 4y - 8. See the attached file.
Y+7=4(x+3)^2
Identify the type of graph that each equation has without actually graphing. x=3y^2 + 5y - 6 Equations may need to be simplified first. See the attached file.
To identify if the graph is parabola, hyperbola or line. See attached file for full problem description.
A roof rises 7.25 ft over a horizontal distance of 13.71 ft. What is the slope of the roof to the nearest hundredth? A) 1.89 B) 0.53 C) 1.87 D) 0.77
Please review attachment for the problem.
A hyperbola is given the equation x^2/25 - y^2/9 = 1 A) Find the coordinates of the foci and the equations of the asymptotes. B) Find the point of intersection with the line y=4-x c) Graph the hyperbola, the line, and the point of intersection. Please explain how to graph this because I dont understand it and
Using the index of a series as the domain and the value of the series as the range, is a series a function? Include the following in your answer: Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series? Which one of the basic functions (linear, quadratic, ratio
Details: Using the index of a series as the domain and the value of the series as the range, is a series a function? Include the following in your answer: Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series? Which one of the basic functions (linear, quadrat
(See attached file for full problem description)
The volume of a cylinder (think about the volume of a can) is given by V = πr2h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 121 cubic centimeters. Write h as a function of r.