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    Basic Algebra

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    Measurement

    Choose the most reasonable measurement. Tyrell read the nutrition label on the back of his frozen dinner. Choose the most reasonable estimate for the amount of sodium in the dinner. 480 t 480 kg 480 g 480 mg

    Gallon-liter relationship

    Provide an appropriate response. Which of the following statements is correct? A gallon is slightly less than four liters A liter is slightly more than four gallons A gallon is slightly more than four liters A liter is slightly less than four gallons

    Finding diameter of planets

    Solve: In a distant solar system the diameter of planet A is 8 times as great as the diameter of planet B. The diameter of planet B is 787 miles. Find the diameter of planet A.

    Using Order of Operations

    Simplify by using the order of operations. Round your answer to the nearest hundredth. 33.9 - 9.8 ∙ 2

    Parabola, Tangent to parabolas and Taylor Polynomial of sin

    This solution explains the concept of finding equation of tangent line to two given parabolas, polynomials, finding taylor of the function y = sin(x) and y=cos(x) at x = 0. Step by step detailed solutions are provided to explain the concept.

    Legendre Polynomials and Least-Square Approximation

    Using Legendre polynomials of degree 1, 2, and 3, find the least-squares approximation for the function e^(-x) on [2, 4]. I am confused as to how to do this on the interval [2,4] and not [-1,1] I have included the notes on this section, including an example (see the attached file).

    Quadratic Equation: Find the Length of the Original Garden

    Tashia Baker is planning an expansion of a square flower garden in a city park. If each side of the original square is increased by 7 meters and the new total area of the garden will be 144 square meters. Find the length of the original garden.

    Discrete Logarithm Problem via Shank's Algorithm

    Please see the attached file. 1. Solve the following Discrete Logarithm Problem via Shank's Algorithm: 12295 modulo 79839983 2. Solve the following Discrete Logarithm Problem via Pollard Rho Algorithm: 4341 modulo 39839983 3. Solve the following Discrete Logarithm Problem via Pohlig-Hellman Algorithm:

    Sigma algebras, measure spaces, rectangles, and cylinders

    Let (Omega_1, F_1, P_1) and (Omega_2, F_2, P_2) be the following measure spaces: Omega_1 = {a, b}, F_1 is the sigma algebra of all subsets of Omega_1, and P_1 is a measure on Omega_1. Omega_2 = {c, d}, F_2 is the sigma algebra of all subsets of Omega_2, and P_2 is a measure on Omega_2. Determine the makeup of the set C

    Prime and Maximum Ideals

    I am having difficulty formulating the proof for this problem. I understand the concepts but not sure how to go about the actual proof. Please help! In regards to J being an ideal I proved that no problem so I omitted those details from the problem. See the attached file.

    Simplify

    Simplify. Assume all variables represent positive numbers. √ (x4 y3)

    Inequality Numbers Determined

    Please see the attached file. Determine whether the given numbers are solutions of the inequality Hello I'm working on 250 questions and out of them I'm having a little problem with these problems and was wondering if any one could help put and walk me through them also Determine wheather the given numbers are solutions o

    Simplify

    Simplify ã (32x5y2) that is sqrt (32x5y2).