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A dart board has regions worth a points and b points, where a and b are positive integers with no common factors.
Verify that the function f(x) = e^-2x satisfies the hypothesis of mean value theorem on the interval [0, 3].
What is the relationship between an exponential function, such as y = 2x, and a logarithmic function, such as the logarithm of x to the base of 2?
Let u be an algebraic element of K (field extension of F) whose minimal polynomial in F[x] has prime degree.
The owner hired three watchmen to guard his apple orchard, but a stranger got in and stole some apples.
The population of the United States is about 3.02 x 10 to the 8th power, and the average American uses about 1.5 x 10.
The fifth derivative of f(x) satisfies |f^(s)(x)| less than or equal to 25000 for all x in [0.8, 1.1].
Maximum Modulus Principle: Let U be a non-empty open subset of the complex numbers C, let D(z0,r)={z ? C: |z-z0| = r}
The electric power generated by a windmill varies jointly with the square of the diameter of the area swept out by the blades.
Sometimes you need to read a linear equation and determine the slope of a lone from the equation.
An initial investment of $1000 is appreciated for 8 years in an account that earns 9% interest, compounded annually.
A company makes three products X, Y and Z. Each product requires processing by three machines A, B and C. The time required to produce one unit of each product
Describe the mathematics used to solve each of these problems (you do not need to supply proofs).
A horseshoe is thrown upward from a initial height of 60 feet with a initial velocity of 40 feet per second. How long after the horseshoe is projected upward.
The formula A=P(1+r)2 gives the amount A in dollars that P dollars will grow to in 2 years at interest rate r (where r is given as a decimal).
Identify the degree of each term of the polynomial and the degree of the polynomial.
The height of a projectile fired vertically into the air (neglecting air resistance) at an initial velocity of 75 feet per second is a function of the time (t)
Solve the system of linear equations by substitution.Alice's Restaurant has a total of 205 seats. The number of seats in the non-smoking section
The volume (v) of a gas varies directly as the temperature (t) and inversely as the pressure (p). If v=56 when t=308 and p=22, find v when t = 270 and p=18.
The minimum value.Let I be an interval in R and assume f : I?R is twice differentiable at all points of I. Suppose that a?I, f'(a) = 0
Jack and Jill went up the hill and found that their grandmother had died. She left them in her will only one possession: an antique water pail.
What is factoring by grouping? When factoring a trinomial by grouping, why is it necessary to write the trinomial in four terms?
Antonio is a simple minded carpenter. He bought a shipment of external drywall panels (12 ft x 4 ft) that he wants to use for building new houses.
What constitutes a rational expression? Please give an example for reference. How would you explain this concept to someone unfamiliar with it?
Compute the discriminant of the quadratic equation 3x2+x+2=0. Briefly describe the number and type of solutions for this equation.