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Algebra

Relations between Non-Parallel Planes

Let P1 and P2 be two dimensional planes that are not parallel. If these planes are contained in R3 then they must intersect in a line. Prove that if they are contained in R4 instead then they can intersect either along a line, or at a single point. (HINT)- A two dimensional plane in R4 is determined by two equations in four unkn

Solving for n as a Factorial

Does there exist a natural number n such that [n!/(n-4)!] = 11,880 ? if so find n, if not explain why not (Hint: factor 11,880 into its prime factors)

Symmetric Functions

Please see the attached file for the fully formatted problems. Write the following functions in terms of the elementary symmetric functions: (u1 + u2)(u1 + u3)(u3 + u2) u31 + u32 + u33 + u34

Word Problems : Relative Speed of Swimmers

(#48) Two swimmers start at opposite ends of a pool 89 feet long. One person swims at the rate of 19 feet per minute and the other swims at a rate of 53 feet per minute. How many times will they meet in 33 minutes? (#33) Two swimmers start at opposite ends of a 90-foot pool. One swims 30 feet per minute and the other at 20

Solving functions

Given f(x)= 4x squared - 3x + 2 and g(x)= 3x - 2, find each of the following. simplify the expression if possible. a. f(-5) b. f(x+h) - f(x)/ h c. (f o g)(x)

Business Math : Revenue and Total Cost

The Revenue and Total Cost eqations for a glove company are R(x)=35x and C(x)=0.25x^2 + 30.5x + 10, where x is in hundreds of gloves and R(x) and C(x) are in thousands of dollars. What is the Revenue and production Cost for 700 gloves, the profit for this problem, the number of gloves that will produce the maximum profit, the

Solving Inequalities

Solve: -4 (x+6) < -4 -4x Is the answer, x< -10; x> -10; all real numbers or no solution? Please show step by step how to solve the inequality. Also, I came up with "x<0" but I do not know if this means "no solution" or "all real numbers" Can you please explain step by step h

Equation: GCD and Mod

Find the least number N such that 1024N-11529=15625x where N and x are non-negative integers

Algorithms : Finding integer values of x and y

A store offers 2 models of scooter, a $29 model and a $33 one. An order was placed with a warehouse which totalled $2490 but the details had been lost. Can you tell the order clerk howl many of each model to send to the store? I have been applying algorithm to equations and am trying to solve integer values for this problem.

Combinations : Problem Solving With Dice

Please see the attached file for the fully formatted problems. Question1: How many dots at the outer sides of the dice. Given view is from the top of these four dice? Question2: In the newly formed shaped below do you think answer is the same or different from above? What does your intuition say without investigating? Q

Central Extension Problem

Find a nontrivial central extension 1 --> Z_2 --> G --> A_4 --> 1 meaning determine a group G. Is it unique? (You may use the fact that A_4 has a normal series Z_2 x Z_2/Z3)

Discriminant and graphs

PART ONE: ATTACHED PART TWO: what type of graph is: x^2 + 3y^2 - 4x + 6y = -1 A) parabola B) circle C) ellipse D) hyperbola PART THREE: Find the value of the discriminant of the equation. Describe the roots completely. Do not solve. 3x^2 + 4x - 5 = 0 A) 31; 2 real, irrational root

Discriminant

Find the vaule of the discriminant of the equation. Describe the roots completely. Do not solve. A) 31; 2 real, irrational roots B) -44; 2 imaginary roots C) 76; 2 real, rational roots D) 76; 2 real., irrational roots

Finding the vertices of a hyperbola.

Find the vertices of the hyperbola with the following equation: (x-3)^2/25 - (y+4)^2/4 =1 EITHER: A) (8,-4) and (-2,-4) B) (5,-4) and (1,-4) C) (3,-2) and (3,-6) D) (3,1) and (3,-9)

Real-World Problem

In a real-world problem, what are some typical action items that you may need to do in order to get to the point having an equation to solve?

Choosing the correct statements about an equation.

This question concerns the equation 3x^2- 4x- 5=0 Choose the two correct statements about this equation Options. A. The equation has no real-number solutions. B. The equation has one real-number solution. C. The equation has two solutions x= - 0.7863 and x= 2.120 correct to 4 significant figures. D. The e

For the series 3+9+15..

Tn = a+(n -1)d sn = n/2(a + n) 4. For the series 3 + 9 + 15 + 21... Find: a) an expression for tn b) an expression for sn c) the answer if s = 20 d) the answer if t = 115 5. Find the # of terms in the sequencece 2,6,10... 626 I need a step by step procedure for solving these problems.

Proof of the Irrationality

2. Apply the proof of the irrationality of sqrt(2) to a) sqrt(3) and b) sqrt(4). If the proof breaks down, indicate precisely why. 3. Euler's phi-function is defined such that for n > 0, phi(n) = |{m < n: gcd(m,n)=1}|. So, e.g., phi(4) = |{1,3}| = 2; phi(5) = |{1,2,3,4}| = 4. a. Show that for prime p, phi(p) = p-1.

Word problem in regards to geometric sequences.

A college student humorously asks his parents to charge him room and board according to this geometric sequence: $0.01 for the first day of the month, $0.02 for the second day, $0.04 on the third day and so on. Find the total room and board he would pay for 30 days.