Let x be the set of integers recursively defined by belong to x and if a belongs to

t divisible by 4. Then the sum of x, y, and z cannot be divisible by 4.

mand is 18,200 rolls. When the demand increases to 26,200 rolls, the supply is 20,000 and the price is $1.24 per roll. Let x be the quantity in thousands of rolls. The table below gives the price-supply and price-demand equations. Price Equations for Toilet Paper Type Equation Price-Supply P = -0.04x + 2.04 Price-Demand P = 0.025x + 1.495 QUESTION 1 Find the supply at a price of $2 per roll. 1000 rolls 10,000 rolls 1 roll 5000 rolls QUESTION 2 Find the demand at a price of $2 per roll. 20.2 rolls 202 rolls 20,200 rolls 500 rolls QUESTION 3 Use the substitution method to find the equilibrium quantity. Round x to the nearest tenth first and then convert to thousands. Include the units in your answer. QUESTION 4 What is the equilibrium price? Write the answer in dollars and cents, rounding to the nearest cent.

countered (unidirectional flow or parallel flow). The planer walls and the fluids are initially at rest. Lower plate moves to left and upper plate to right. Let the fluids be an oil, where kinematic viscosity (ν) = 2.17 x 10-4m2/s and the distance between both plate (h) is 10 mm. U0 = 0.4 m/s I need to find the governing equation, boundary conditions, initial conditions and to derive velocity distribution in steady state. Also, Use FTCS explicit method to calculate the velocity distribution as a function of time by implementing these governing equation in Matlab

So far I just tried to do the obvious and substitute -a for - sin b. Like so; sin 2x = - sin b which then becomes; sin 2x = sin -b and then I can remove the sines and rearrange for x, which gives me this. 2x = -b x = -b/2 However, if I were to look at the domain of b. Any value within the domain will give a value that doesn't fit the domain of x. Any suggestions would be great. Thank you!

Use your result in (a) to solve the system: ■(x&+2y&+z&=1@x&y&+2z&=2@x&+y&+2z&=3) Question#2 (5) (modified from #13 p. 102 in your book) Solve the matrix equation for X X[■(1&1&1@1&2&0)]=[■(1&1&1@3&4&2)] Question#3 (5) (modified from #9 p. 102 in your book) Let [■(a&0&b&2@0&a&3&6@0&a&b&c+2)] be the augmented matrix of a linear system. Find for what values of a,b,c the system has: (i) a unique solution (ii) a one-parameter solution (iii) a two-parameter solution iv) no solution Question#4 (7) Write the matrix A=[■(-1&1&-1@1&1&-1@1&-1&2)] as a product of elementary matrices Question#5 (3) Find the determinant by any method: |■(0&-1&0&0&1@1&1&1&3&1@1&2&3&1&2@1&-1&0&3&1@1&-1&1&0&1)| Question#6 (3-2)Given thissystem: ■(x_1&+2x_2&+x_3&=1@x_1&-〖3x〗_2&+0x_3&=2@x_1&+0x_2&+2x_3&=3) a) Use Cramer’s method to solve for x_1 only b) Solve for the other variables by any method.

uminum and steel. The company has available 38 comma 160 units of steel and 48 comma 380 units of aluminum. The​ 1-, 3-, and​ 10-speed models​ need, respectively, 8​, 12 and 16 units of steel and 15​, 10​, and 20 units of aluminum. The company makes ​$4 per​ 1-speed bike, ​$6 per​ 3-speed, and ​$16 per​ 10-speed. Use the simplex method to complete parts​ (a) and​ (b). ​(a) How many of each type of bicycle should be made in order to maximize​ profit? What is the maximum​ profit? Set up the linear programming problem. Let x 1​, x 2​, and x 3 represent the numbers of​ 1-, 3-, and​ 10-speed bicycles,​ respectively, and let z be the total profit. ▼ Minimize Maximize zequals nothing subject to 8 x 1 plus 12 x 2 plus 16 x 3 ▼ greater than less than or equals greater than or equals less than nothing 15 x 1 plus 10 x 2 plus 20 x 3 ▼ greater than less than or equals less than greater than or equals nothing x 1greater than or equals​0, x 2greater than or equals​0, x 3greater than or equals0. ​(Do not factor. Do not include the​ $ symbol in your​ answers.) Set up the initial simplex tableau and use the Simplex Method to solve. The maximum profit is ​$ nothing. To get that​ profit, the company should make nothing ​1-speed bicycle(s), nothing ​3-speed bicycle(s), and nothing ​10-speed bicycle(s). ​(Type whole​ numbers.) ​(b) Explain what the values of the slack variables in the optimal solution mean in the context of the problem. Select the correct choice below​ and, if​ necessary, fill in the answer​ box(es) to complete your choice. A. When the profit is​ maximized, all of the steel is used but nothing units of aluminum remain unused. ​(Type a whole​ number.) B. When the profit is​ maximized, some of each material remains unused.​ Specifically, nothing units of aluminum and nothing units of steel remain unused. ​(Type whole​ numbers.) C. When the profit is​ maximized, all of the available aluminum and steel is used. D. When the profit is​ maximized, all of the aluminum is used but nothing units of steel remain unused. ​(Type a whole​ number.)

lve an equation, find the derivative of a function at a point, or calculate the value of a definite integral. However, you must clearly indicate the setup of your question, namely the equation, function, or integral you are using. If you use other built-in features or programs, you must show the mathematical steps necessary to produce your results. Your work must be expressed in standard mathematical notation rather than calculator syntax. Show all of your work, even though the question may not explicitly remind you to do so. Clearly label any functions, graphs, tables, or other objects that you use. Justifications require that you give mathematical reasons, and that you verify the needed conditions under which relevant theorems, properties, definitions, or tests are applied. Your work will be scored on the correctness and completeness of your methods as well as your answers. Answers without supporting work will usually not receive credit. Unless otherwise specified, answers (numeric or algebraic) need not be simplified. If your answer is given as a decimal approximation, it should be correct to three places after the decimal point. Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f(x) is a real number. Let f be a twice-differentiable function such that f′(2)=0 . The second derivative of f is given by f′′(x)=x2e2−x−1 for 0≤x≤6 . (a) On what open intervals contained in 0 View More

AP Math