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    Basic Algebra

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    Gaussian Quadrature

    1. Consider approximating integrals of the form I ( f ) = ∫ √x f(x)dx in which f(x) has several continuous derivatives on [0, 1] a. Find a formula ∫ √x f(x)dx ≈ w1 f(x1) ≡ I1( f ) which is exact if f(x) is any linear polynomial. b. To find a formula

    Variables in an equation were reversed

    If the variables in an equation were reversed, what would happen to the graph of the equation? For example, how would the graph of y = x² relate to the graph of x = y²? When might such a reversal of variables be useful in the real world? How does x=y relate to y=x? How about 2x = y and 2y=x? What about x^2 + y^2 = 49

    Parabola and Quadratic Equations: Maximum and Minimum Values

    From this we can see that we have function that whose graph is a parabola and we want the values of w that make the function positive. The parabola opens downward, the vertex is at Let me show you an actual example of inequalities. Several years ago I was the chairman of the banquet committee for our ski club. Since one of our m

    Physics and Algebra Traveling Speed

    1. Jeff rode his bike 45 miles to get to the park, and his co-worker Chris rode his bike 70 miles to meet Jeff at the park. Chris averaged 5 mph more than Jeff, and his trip took one-half hour longer than Jeff. How fast was each traveling? 2. Mike found a good deal on some golf clubs at an online auction site. The clubs were

    Solving Algebraic Equations for a Given Variable

    1. Solve the following formula for R: I = E / R + r 2. Sqrt of 5x - 9 = 4 3. One bag of grass seed will cover an area of 300 square feet. If the width of the area is 5 ft less than the length, determine the dimensions.

    Fourier Sine Series Solution - Wave Equation, Interval and Boundary Conditions

    Please see attachment for complete questions (for the below "..." indicates equation to be found in attachment). Thanks! (a) Write down the Fourier (sine) series solution u(x,t) of the wave equation ... on the interval ... satisfying the boundary conditions ... and the initial conditions ... (b) Use the identity ... to sh

    Comparing Rates: Scoring Rate

    Bob scored 68 runs from 102 balls and Brent scored 45 runs from 67 balls. Did Bob or Brent have a faster scoring rate?

    Solving a Ratio Problem

    On a farm the ratio of sheep to cattle to goats is 8:3:1. How many cattle does the farmer own if there are 720 head of livestock, sheep, cattle and goats, altogether?

    Area (Basic Algebraic Manipulation)

    The three remaining blocks of land in a new estate have a total area of 2029m2. The second block is 45m2 more than the first block and the third block is 65m2 less than the first block. What is the area of the first block?

    Independent and Dependent Variables

    In a typical algebraic expression, there are two variables: an independent variable and a dependent variable. The independent variable is the number or the value that can change. The dependent variable's value depends on the value of the independent variable. For example, in the following formula, X=Y*5 Y is the independent