1.if (x, -4) is a solution to the equation 5x - 4y = 10, what is the value of x?
2. .if (7, y) is a solution to the equation 2x + 3y = 44, what is the value of x?
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11. [3pts] Find the values of h such that vector y will be in the subspace of R^3 spanned by {vector v1, vector v2, vector v3} where vector v1 = [1 2 -4] , vector v2 = [3 4 -8] , vector v3 = [-1 0 0] , vector y.
11. You and a friend walk in the hallway by the math offices and see on one of the boards Your friend says THIS IS WRONG even though neither one of you knows what A is. And he is correct. Explain why 9. Prove that if h E R^+ and.
11. Let S be the set of all nonzero real numbers. Define a function g from S to S by the formula g(x) = 1/x, for all nonzero real numbers x. (a) Show that g is a one-to-one correspondence from S to S. (b) Find g^-1..
1. Solve graphically the following optimization problems:
2. Consider problem (a) above.
a. Change the objective function (to be maximize) so that [4; 0]^T becomes the optimal solution of the problem;
b. Provide a justi cation of (i) why the point.
1. Suppose u is a unit vector and consider the orthogonal matrix Q=I-2u*u^T. Suppose x and y are two nonzero vectors such that (2-norms) ||x||2=||y||2. How do you define u to define Q such that Qx=y? Prove that with such a u then Qx=y is in fact the case..
1. What is a closure in a set?
2. Can you have two operations on a set with the following condations:
a) Under the first operation, the set has a closure.
b) Under the second operation, the set does.
10. Which of the following could be an example of a function with a domain ( -infinity, infinity ) and a range ( - infinity , 2)? Check all that apply. (Points : 2).
10. -13 points PooleLinAlg4 3.2.502.XP Write B as a linear combination of the other matrices, if possible. (If not, enter DNE in all blanks.) 10 0 1 1 1 A1 A2 A3 0 1 1 1 -3 1 1 0 0 1 1 -1 10 -3 1 0 1 1.
1. Suppose that fOx,y is a function with the property that vf (1,3) 4i -3j and f(1,3) 6. a. In which direction ii is Dif (1,3 the smallest? b. What is the smallest possible value of Duf(1,3)? c. Find the equation of the tangent line to f(x,y) 6 at the.
11 y = 1 (mod 17)
I know for linear congruence it can write as 17x + 11y = 1
then apply euclidean algorithm...(I don't know how to do it)
The answer for y is 14.
plz show.
10)Use any method to solve the following linear system. Please show your steps that lead to your solution.
Braket is in front of these to examples
2x+3y=-6
x+y=-1.
1. The area of a circle is related to the radius by the formula
Complete the following table for the given values of r and state the domain and range.
r
A
1
2
.
10. Describelillustrate the construction used by the ancient Indians to show that the difference between two squares can be converted into another square 11. Describe illustrate the const used by the ancient Indians to show that a rectangle can be truction transformed into a square, using the results from 10.
(10 pts) In exercise B3 from chapter 2, we are to consider the operation on R given by the
formula
a * b = la + bl:
Write out formal proofs that this operation has no identity element and that it.
1. The material properties of particulate composites are generally____
a.independent direction
b.independent temp.
c.based on the mass percentage of reinforcement
d.based on how the material is used
2.Which statement is true of dispersion strengthened composites?
.
1.A bowl contains 2 red and 2 white chips. Two chips are withdrawn from the bowl. Let X be the number of reds among them. (a) Give the pmf of X. (b) What is EX? 2. Two fair dice are tossed, a red one and a green one. Let X.
10.what is the sum of the solutions of 2| x - 1| - 4 = - 2 a. 1 1/2 b. -2 c. 2 d. 0
11. A furniture maker uses the specification 21.88 < w < 22.12 for the width w in inches a desk drawer..
1. State the formal dofinition of a group, a subgroup, and a group homomor phism. Give three examples of each definition. Show that the subset G of c CI defined by is a group. Can you think of any non-trivial subgroups of G. 3. Let G be the same group.
1. (TCO 5) Apply the power series method to obtain the solution of y'+x^2y=0. Compare this with the result obtained using MATLAB dsolve function. (Points : 10) PLEASE SHOW WORK!!
a.)y=a(base)0e^x^3/3
b.)y=a(base)0e^-x^3/3
c.)y=a(base)0e^-x^2
d.)y=a(base)0e^-x^2/2.
1. Suppose that j(x) = h^-1(x) and that both j and h are defined for all values of x. Let h(4) = 2 and j(5) = -3. Evaluate if possible:
(a) j(h(4))
(b) j(4)
(c) h(j(4))
(d) h^-1(-3)
.
11. In 2011, a total of 171.1 billion items were sent through the U.S. mail. Of these, 78.8 billion items were first class mail. What percent of the items, to the nearest tenth, were pieces of first class mail?.
1. Write the negation of the statement: I study or I do not pass.
2. Determine the value of the statement: ~p <--> (~q^r) when p is true, q is false, and r is false.
^= and symbol.
.
1. What is a polynomial and what is the "order" of a polynomial. What is meant by the roots of a polynomial. 2. How many minimum and maximum roots can a polynomial have. 3. What is Routh Hurwitz criterion and why is it useful.
.
1. This problem has two (related) parts. a) Consider a set of five numbers zi z2 z3 zu ars, with the property that there are only seven distinct values among the ten sums zi r, with i j. Prove that zi,r2,23.24, r5 form an arithmetic progression. b) Consider a set.
1. Use long division to rewrite the fraction in q(x)+ r(x)/d(x) form
\(\frac{2x^{5}-3x^{2}+1}{x^{2}+1}\)
2. Use the rational Zero Theorem, Descartes' Rule of Signs, upper and lower bounds, synthetic division, and the quadratic formula to find all the zeros of the following polynomial.
.
1. write the positive exponents as one rational expression: 4-5x^(-1/2)
2. simplify and write as one expression:
x(1/2)(x^2-1)^(-1/2)(2x)+(x^2-1)^(1/2)
3. write as a quotient and a remainder: (3x^2-3x+1)/(x-5) - show work
4. evaluate:
a. f(3+h) if.
(10 points) The tower of Hanoi is a puzele invented by E. Lucas in 1883. Given a stack of n disks arranged from larger t on the bottom to smallest on top placed on a rod, together with two empty rods (Fig. 20. the towers of Hanoi puuele asks for.
1.) Solve the following recurrence relation:
P(1)=2
P(n)=2P(n-1)+n2n for n>=2
2. A sequence is recursively defined by:
T(0)=1
T(1)=2
T(n)=2T(n-1)+T(n-2) for n>=2
Prove that T(n)<=(5/2)n for n>=0.
1.Given the polynomial, list each zero and the corresponding multiplicity.
f(x) = 2x(x + 4)2
2. Given the polynomial, determine the end behavior by stating the power function that the graph of f(x) resembles.
f(x) = 2x(x + 4)2
.
11+ 16x^4 -19x - 16x^3 - 13x^2
Find the leading term and the leading coefficient.
A. the leading term is -16x^3 and the leading coeffienct is -16.
b. the leading term is 11 and the leading coefficient is 11
.
1. Solve the following system using matrix equations. PLEASE SHOW WORK
{x-y=5
{2x+y=1
2. In the 2006 Winter Olympics in Turino, Italy, the top medal-winning countries were Germany, the United States, and Canada, with a combined total of 78 medals. German.
10. If A = {w, x, y, z}, determine the number of relations on A that are
(a) Reflexive;
(b) Symmetric;
(c) Reflexive and symmetric;
(d) Reflexive and contain (x, y);
(e) Symmetric and contain.
1. Which of the following is a eighth-degree polynomia ion? select all that a point) apply. f(x) f(x) 10x f(x) 2. Which describes the end behavior of the graph of the function f(x) 8x4 2 x? (1 point) f(x) co as x -co and f(x) oo as x co f(x).
1. Suppose you're relaxing one evening with a copy of Twelth Night, and the reading light is placed 5 ft. from the surface of the book. At what distance would the intensity of the light be twice as great?
2. Tamino's Aria is playing in the background,.
10.1. Very Garlic Inc. produces garlic powders in three Asian countries: China, India, and South Korea. The company ships garlic powders from its production facilities to four US warehouses (Seattle, New York, Phoenix, and Miami). The shipping costs per ton from each production facility to each warehouse are listed below..
11. For any relation R, sR and tR denote the symmetric and transitive closures of R respectively, and |R| denotes the number of ordered pairs in R. When R = {(a,b), (a,c)} the value of |s(tR)| + |t(sR)| is (a) 8. (b) 10. (c)13. (d) 18..
