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    Algebra

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    Solve show the equations and simplify

    The waste hauling company profits are stated as the difference between revenue and costs. That is P(x) = R(x) - C(x), where x is the number of tons processed. Find the maximum profit and the number of tonnage which must be processed in order to yield the maximum profit for each of the following: a) R(x) = 5x; C(x) = 0.0001x2

    Squared and cubed word problem

    I'm thinking of a 6-digit number. The sum of the digits is 43. And only two of the following three statements about the number are true: (1) it's a square number. (2) it's a cube number, and (3) the number is under 500000

    Home Mortgages Fixed and Variable Rates

    #4. Each of a sample of four home mortgages is classified as fixed rate (F) or variable rate (V). a. What are the 16 outcomes in the sample space? b. Which outcomes are in the event that exactly three of the selected mortgages are fixed rate? c. Which outcomes are in the event that all four mortgages are of the same type?

    1. Let N1(p) denote the number of pairs of integers in [1, p - 1] in which the first is a quadratic residue and the second is a quadratic nonresidue modulo p. Prove that N1(p) = (1/4) (p - ( - 1)^((p - 1)/2)) 2. Let N2(p) denote the number of pairs of integers in [1, p - 1] in which the first is a quadratic nonresidue and the second is a quadratic residue modulo p. Prove that N2(p) = (1/4) (p - 2 + ( - 1)^((p - 1)/2)) 3. Let N3(p) denote the number of pairs of integers in [1, p - 1] in which the first is a quadratic nonresidue and the second is a quadratic nonresidue modulo p. Prove that N3(p) = (1/4) (p - 2 + ( - 1)^((p - 1)/2)) 4. Use the results of theorem 10-4 and corollary 10-1 to construct solutions of x^2 + y^2 =29. 5. Prove ( without assuming corollary 10-1) that, if p is a prime &#8801; 1 (mod 4), then there exists positive integers m, x, and y such that x^2 + y^2 =mp, with p &#9532; x, p &#9532; y, 0 < m < p [ Hint: use the proof of Theorem 11-2]. Theorem 10-4: If p is an odd prime, then &#957;(p) = (1/8)p + Ep where | Ep| < (1/4)(p)^(1/2) +2. Corollary 10-1: Every prime p &#8801; 1(mod 4) is representable as a sum of two squares. Theorem 11-2: For each prime p there exist integers A,B and C, not all zero, such that A^2 + B^2 + C^2 &#8801; 0 (mod p).

    Theory of Numbers The Distribution of Quadratic Residues Sums of Squares Sums of Four S

    Solving an Equation by Substitution

    Please solve: v=ab/(c+d) where v = velocity where a = 6.67*10^-11 N m^2 kg^-2 where b = 5.97*10^24kg where c = 6.37*10^3km where d = 385km could you show all workings and all terms in the equation should be in SI units

    Solving an Equation by Substituting Values

    If air resistance is neglected, the number of feet "s" that an object falls during "t" seconds is given by the equation s = 16t^2. How long would it take for an engine of an airplane to reach the earth if it fell off the airplane at 32,000 feet?

    Solving for the Equation of a line

    Please address the following problem and include all of the required steps. Solve: Find the slope intercept form of the equation for the line parallel to y=4/3-1 that goes through points (6,-5).

    Solve: Slope-Intercept Form

    Question: Find the slope-intercept form of the equation for the line parallel to y=4/3x-1 that goes through the point (6,-5).

    Shapley-Shubik Distribution, Weighted Voting Systems and Combina

    1) Find the Shapley- Shubik distribution (in percent) for the system (7: 5,3,2,1,). 2) In a cafeteria every meal has a 5 choice main course, a 3 choice salad, and a 2 choice soup, and a 4 choice dessert. If some one ate a different complete meal every day, how many days could he eat before he would start to repeat a meal?

    Equation Intercept and Vertex

    I am trying to determine the vertex and intercepts for this quadratic function, and whether it opens up or down. y + x squared - 4

    Solve an Equation Word Problem

    The formula 1211.1L = CA squared S is used to determine the approach speed for landing an aircraft, where L is the gross weight of the aircraft in pounds, C is the coefficient of lift, S is the surface area of the wings in square feet (ft squared), and A is the approach speed in feet per second. I need help finding A for the Pi

    Rectangles : Solving for the Golden Ratio

    If the ancient Greeks thought that the most pleasing shape for a rectangle was one for which the ratio of the length to the width was 8 to 5, and the golden ratio. If the length of a rectangle painting is 2 feet longer than its width, then for what dimensions would the length and the width have the golden ratio?

    Simplify the Equation

    3X^2(X^2-4X+1)-2X(5X-6X^2). Simplify and please show all work to fully understand the question.

    Voltage and charge capacity

    If I have a capacitor with a capacitance of 0.000005 farads is wired in a circuit with a total resistance of 5000 ohms, how long must the capacitor be wired to a source voltage to reach 50% of its maximum charge? With q = Q [ 1 - e ( - t / RC ) ]. To help me understand this better, please show all work.

    Ratio

    The student-teacher ratio for Stratford High was reported to be 27.5 to 1. If there are 42 teachers, how many students are in the school?

    One to one and onto mapping

    Let G be the real numbers under addition G' the positive real numbers under multiplication. Show that the mapping... is one to one and onto. Please see attached for the full question.

    How do you solve an equation?

    In math class we have been assigned to answer the following question: How do you solve an equation? Please provide an example. I know how to solve an equation if it is given to me, but I do not know how to describe how to solve any equation. I hope you can help.