Systems of Congruences
Find the necessary conditions on r1,r2 and n1,n2 that will guarantee a solution to the system: x ≡ r1 mod n1 x ≡ r2 mod n2. keywords: congruent, cogruency
Find the necessary conditions on r1,r2 and n1,n2 that will guarantee a solution to the system: x ≡ r1 mod n1 x ≡ r2 mod n2. keywords: congruent, cogruency
Among the professionals you have interviewed for your article, were several state and federal government spokespersons who use linear equations in a variety of ways. An employee of the National Parks Service told you about a location in Washington, DC. It is a large grassy area south of the White House known as the Ellipse.
Prove that y^2= x^3+23 has NO integer solutions.
Researchers at the National Interagency Fire Center in Boise, Idaho coordinate many of the firefighting efforts necessary to battle wildfires in the western United States. In an effort to dispatch firefighters for containment, scientists and meteorologists attempt to forecast the direction of the fires. Some of this data can be
Please see the attached files for the fully formatted problems. 1. Given the equation below, find f(x) where y = f(x). 8y(6x - 7) - 12x(4y + 3) + 265 - 5(3x - y + 2) = 0. 2. Solve these linear equations for x, y, and z. 3x + 5y - 2z = 20; 4x - 10y -z = -25; x + y -z = 5 3. The value of y in Question 2 lies in the ran
Please see the attached file for the fully formatted problems. 1. Write as a decimal. 2. Multiply. (-1)(5) 3. Give the coordinates of the point graphed below. 4. Solve. 8 - (4x - 3) = 19 5. A backyard has dimensions yards by yards. What is the area of the back yard in square yards (yd2)? 6. If a 4.4-pound bag of
There are 3 suspects, A, B, and C, for a robbery that presumably happened in a shop. We know that the following facts are true: (1) Each of A, B, C was in the shop on the day of the robbery, and no one else was there on that day. (2) If A was guilty, then he had exactly one accomplice. (3) If B is innocent, then so is
Row reduce matrix to reduced echelon from. Circle pivot positions in the final matrix and in the original matrix, and list the pivot columns. 1) Find the general solutions of the systems whose augmented matrices are given. 2) 3) Use the echelon form. Suppose each matrix represents the augmented mat
The augmented matrix of a linear system has been reduced by row operations to the form shown. In each case, continue the appropriate operations and describe the solution set of the original system. 1) 2) Solve the system. 3) 4) Determine if the system is consistent. Don not completely solve b
See attached file for full problem description. 1. Graph the inequality. 2x + 3y > 6 2. Given g(x) = -3x + 5, find g(2a) 3. Graph the inequality: x - y < = 2 4. Graph the inequality: y > =3x 5. Given f(x) = -x^3 - 3x^2 -3x +9, find f(-2), f(0), and f(3) 6. Given f(x) = -5x - 1, find f(-2) 7. Graph f(x) = 4x + 1 8. Grap
1. A coffee merchant has coffee beans that sell for $9 per pound and $12 per pound. The two types are to be mixed to create 100 lb of a mixture that will sell for $11.25 per pound. How much of each type of bean should be used in the mixture? 2. In a town election, the winning candidate had 220 more votes than the lose
Find values for M and B in the following system so that the solution is (-3,4) 5X + 7Y=B MX + Y=22
Prove the real numbers, R, contain a subring A with 1 ЄA and A maximal (under inclusion) with respect to the property that 1/2 not ЄA [Use Zorn's theorem]. See attached file for full problem description.
#14 Solve each system by the substitution method. Indicate whether each system is independent, inconsistent, or dependent. #24 Graph and solve the absolute value equality. #46 Graph each compound or absolute value inequality. |x-3y| ≥ 9 Please see the attached file for the fully formatted problems.
Solve each system by the substitution method. Section 7.1 #54 X + 3y = 2 -x + y = 1 Section 7.2 #64 Book and magazines. At Gwen's garage sale, all books were one price, and all magazines another price. Harriet bought 4 books and three magazines for $1.45 and June bought two books and five magazines for $1.25. What was th
The solution of following system of linear equation is: 2x-2y+3z=1 5x-6y+10z=2 2x-4y+9z=1 x=2, y=3, z=1 And the solution of this system is: 2x-2y+3z=1 5x-6y+10.1z=2 2x-4y+9z=1 x=2.375 y= 3.75, z= 1.25 (You do not have to show this) Comparing the 2 solution can you determine whether the fist system of equat
The solution of following system of linear equation is: 2x-2y+3z=1 5x-6y+10z=2 2x-4y+9z=1 x=2, y=3, z=1 And the solution of this system is: 2x-2y+3z=1 5x-6y+10.1z=2 2x-4y+9z=1 x=2.375 y= 3.75, z= 1.25 (You do not have to show this) Comparing the 2 solution can you determine whether the fist system of equat
Consider the equation: y'' + k*y = 0 with BC: y(0) = 0 , y() = a 0 Answer the following: 1. What are the restrictions on k such that there is a nontrivial solution? 2. Find a solution using eigenfunction expansion on [0,] 3. Find a solution to the differential equation using any method 4. Co
Given the equation below find the eigenvalues and then the eigenfunctions. Compute the coefficients of the eigenfunction expansion. In each case determine what the eigenfunction expansion converges to on the interval and the sum of the first N terms on the same set of axes for the given interval. Please show the function (N=5
1. Sam needs to get carpet for two rooms of his house. Estimate the number of square feet (square footage) in the two rooms if one room measures 10 ½ feet by 9 ¾ feet; and the other room measures 19¼ feet by 18 ½ feet. 2. Sandra drove for 234.8 miles and used 12.6 gallons of gas. Estimate the number of miles Sandra's
Prove that there exist at most 2 non-isomorphic fields of order 4.
Analyze the stability of the fixed points of linear differential systems. Provide several explicit examples, with graphical illustrations
1. Consider the system of equations x + y + 2z = a x + z = b 2x + y + 3z = c Show that for this system to be consistent, the constants a, b, and c must satisfy c = a + b. 2. Show that the elementary row operations do not affect the solution set of a linear system. 3. Consider the system of equations ax + by =
Solve each linear equation. Show your work and check. 3(x-0.87)-2x=4.98 Solve each equation by first eliminating the decimal numbers. 0.08t+28.3=0.5t-9.5 Diameter of a Circle. If the circumference of a circle is 4pi meters, then what is the diameter?
Solve each equation and check your answer 2(a-4)+4=5(9-a) Solve each equation. Identify each equation as a conditional equation, an inconsistent equation or an identity. Solve each equation for y. Write the equation in the form of y=mx+b where m and b are real numbers Find the value of y in each formula if x=
Please explain how to prove the identity with the following example: sin x - sin 3x / cos x - cos 3x = -cot 2x
Find the expansion of f(x)=1-x on the interval [0,L], with respect to the eigenfunctions of the Sturm-Liouville problem: y''+λy=0 y(0)=y(L)=0
Prove that is p is prime, we have: n choose m is congruent to [floor(n/p) choose floor(m/p)]*[(n mod p) choose (m mod p)] (mod p) Hint: show that (1+x)^(pq+r) is congruent to (1+x)^r * (1+x^p)^q (mod p) If you can point me to a book or website explaining how to do this type of problem, and give a sketch of the proof,
The basal energy requirement B is the number of calories that a person needs to maintain the life process. For a 28-year old female with a height of 160 centimeters and a weight of 45 kilograms (kg), B is 1300 calories. If her weight increases to 50 kg, then B is 1365 calories. There is a linear equation that expresses B in term
Taylor series of e^A. See attached file for full problem description. 6. Use results from matrix algebra to show the following about the matrix exponential map (see attached file).