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Basic Algebra

Ratios, LCD and Simplification

1.)The ratio of strawberry ice cream lovers to vanilla is 9 to 5. If there are 144 more strawberry ice cream lovers than vanilla, how many of each are there? 2.) Find the LCD and convert each rational expression into an equivalent rational expression with the LCD as the denominator: 4/15xy^2, 3x/6y 3.) Simplify and writ

How to solve for the variable "X"

How to solve for the variable "X" The following problems have tripped me up. I can't seem to figure out how to solve them. I've tried, several times, and had my algebra teacher explain them, but I still can't get the answers. 3x - 11 = 6 2x - 7 = 3 + x 3 + 3x = 9 + 2x 3x - 3

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

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

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

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

Find an infinite set of numbers n for which some player

Players 1, 2, 3, ..., n are seated around a table and each has a single penny. Player 1 passes a penny to Player 2, who then passes two pennies to Player 3. Player 3 then passes one penny to Player 4, who passes two pennies to Player 5, and so on, players alternately passing one penny or two to the next player who still has some

Green's Theorem (Divergence)

? Let D a domain on the plane bounded by a curve C. by applying Green's theorem (in divergence form) to a conservative vector field with potential f, defined on d, show that before attempting this question, recall what is a conservative vector field, as well as the definition of the laplacian . ? Use the divergen

College Algebra I

1.)The following formula can be used to convert from degrees Fahrenheit, F, to degrees Celsius, C: C= 5/9*(F -32) Gold is liquid for Celsius temperatures C such that 1063 degrees <= C < 2660 degrees. Find a comparable inequality for Fahrenheit temperatures. 2.) The following mathematical model: w = 125 (6400/6400 + x)^2

Modern algebra

I am stuck with this question. If phi : F -> R is a nonzero homomorphism from a field F to a ring R, show that phi is one-to-one (Hint: recall that for a ring homomorphism, phi is one-to-one if and only if Ker(phi)={0}. ) Can you help with this? Many thanks in advance

Inequality Interval Functions

10 algebra problems - work must be shown so I can understand how to compute. Examples of questions: --> Solve: x2 - 8x + 20 = 5 --> Solve by quadratic formula: -3x2 - 2x + 5 = 0 --> The crop yield in bushels for a field of tomatoes is 10x2 - 80x + 200 where x is number of pound of fertilizer used. a) How many pounds

Financial Math

Please explain to me where the .5675 in the following formula came from: v_0 = .5675(110-E) This is from the solution to problem 6, lecture 6. I don't understand where .5675 came from, but I understand the solution. I'ved attached lectures 5, 6, and the solution to lecture 6. The formula for a state price vector i

Solving Rational Expressions

I'm having a difficult time figuring out some of these! For some reason the -1 in this problem is throwing me off - I think! Here's what I came up with last time, I keep getting a different answer each time I work it. 3/(y+5) -1 = (4-y)/(2y+10) 3/(y+5)-1 = (4-y)/2(y+5) y is not equal to -5 LCD is 2(y+5) 2(y+5)*3/(y+5) =

Cauchy-Riemann Equations in Polar Form

Please see the attached file for the fully formatted problems. 8. Let a function f (z) = u + i v be differentiable at a nonzero point z0 = r0 e(i&#952;0). Use the expressions for ux and vx found in Exercise 7, together with the polar form (6) of Cauchy-Riemann equations, to rewrite the expression f &#900;(z0) = ux + i vx

Exponential and Logarithmic Functions : Capacitance

If a capacitor with a capacitance of 0.000005 farads is wired in a circuit with a total resistance of 5000 ohms (the standard unit of electrical resistance), how long must the capacitor be wired to a source voltage to reach 50% of its maximum charge? (The Hint was: Begin by expressing q as 0.5Q)

Algebraic Properties 8b

Given the algebra <S;f,g,a>, where f and g are unary operations and a is a constant of S, suppose that f(f(x)) = g(x) and g(g(x)) = x for all x &#949; S. Show that f(f(f(f(x)))) = x for all x &#949; S.

Crytic math questions

Cryptic Math p Q R S T U V W X 1. Each letter stands for one of the numbers 1 - 9. 2. S + Q = V and S is smaller than Q. 3. P = R + U. 4. In one of the diagonals, all 3 numbers are perfect squares. 5. In one of the two diagonals, (P, T, X or R, T, V) the 3 numbers are in ascending orde