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Lydia takes ten minutes more to complete an illustration than Tom. The total time taken by both of them is six hours.
Translate the following into algebraic expressions. Clearly identify the variables, coefficients, and constants:
The value of the second prize is five-sixths the value of the first prize, and the value of the third prize is fourth-fifths that of the second prize.
The space occupied by character 2 takes 5 units more than character 1, character 3 takes 7 units less than the character 2.
Lisa is coloring her creation. The blue color used is 50% of the green color used, yellow is 5% of the blue color used, and brown is 7% of the amount.
Use induction to show that the number of nodes in a binary tree is equal to one more than the sum of the degrees of the nodes in a binary tree.
The sum of 2 nonnegative numbers is 20. Find the numbers if the product of one number and the square root of the other is to be as large as possible.
Linear programming proof.One can convert the problem to an equivalent one with equality constraints
Linear Algebra : Modules, Linear Operators, Characteristic and Minimal Polynomials, Generators, Abelian Groups and Annihilators
Prove that for all odd integers n, (1^n)+(2^n)+(3^n)...+(n^n) is a proper multiple of 1+2+3+...n
If a,b,c are odd integers, show that all real roots of ax^2+bx+c=0 are irrational numbers.
If x were replaced with its opposite in each of the terms of the given polynomial, will it result in the opposite of the polynomial?
How many rectangles (of all sizes) are there in this grid? Can you generalize your results to an n by n grid? Can you generalize further?
The half-life of a certain radioactive element is 100days. That means that after 100 days ½ of the radioactive substance will have decayed.
Graph the following function when a=3 and b=2. Develop a generic expression (i.e., as a function of "a" and "b") to find the "x" and "y" intercepts.
Planetary orbit [2]. The expression z = ax2 + bxy + cy2 + dx + ey + f is known as a quadratic form. The set of points (x, y) where z = 0 is a conic section.
Walt made an extra $9000 last year from a part-time job. He invested part of the money at 9% and the rest at 8%.
Formulate two word problems from day-to-day life that can be translated to quadratic equations.
Maximum height. If a baseball is projected upward from ground level with an initial velocity of 64 fcct per second, then its height is a function of time.
Maya has deposited $600 in an account that pays 5.64% interest, compounded continuously. How long will it take for her money to double?
Banach space and closed subspace.Let I = [a,b] be a finite interval. Show that the space C(I,Rn) of continuous function
Explain the relevance and application of exponential functions in real-life situations. Explain the relevance and application of logarithmic functions.
Solve the following equation and check your answer. (1/2b)- (1/2)= 1/4b. Solve the following equation 19 - 3n = - 2n.
Solve the following problem by identifying a variable, writing an equation that describes the situation, and then solving the equation.
The total amount to be invested is $40000, and because "The Don" is concerned about risk, he only wishes to invest $13500 in stock funds