Find det(A) and determine if Ax=b has a solution? If yes, is it unique. You do not need to find X. B is any order-n vector.

A =

Row1 = (-4,9,-4,1)

Row2 = (2,3,0,-4)

Row3 = (-2,3,5,-6)

Row4 = (-3,2,0,1)

Sorry I don't know how to type matrices on here but thank you!

A.The surfaces intersect in a space curve C. Determine the projection of C onto the xy-plane.

x+4y+5z=5

x+y−4z=5

B.The surfaces intersect in a space curve C. Determine the projection of C onto the xy-plane.

2x^2+6y^2+(z−2)^2=2

2x^2+6y^2=z^2

C.

The surfaces intersect in a space curve C. Determine the projection of C onto the xy-plane.

x^2+y^2+z=2

2x^2+3y^2=z

Determine the quantity of grout needed for the wall in problem 6-1 if 18 cubic feet of grout is required per 100 square feet of block. (Problem 6-1) Determine the number of 7 5/8-inch-high by 5 5/8-inch-wide by 15 5/8-inch-long concrete blocks required to complete a wall 80 feet long by 12 feet high. Allow for a 3/8-inch mortar joint.

Problem 3 1. Choose either the Halton or the Sobol sequence of quasi-random numbers. Briefly describe how they are constructed.

2. Illustrate graphically the difference between pseudo-random numbers and quasi-random numbers.

3. Repeat step 2 of Problem 1 with quasi-random numbers. Comment.

2) Mark True or False for the following:

The representation of a point is space, “r”, is a scalar. True ___ False ___

Parameter “t” is a three-dimensional vector. True ___ False ___

When representing surfaces, the pair (t,s) points to a given point in space. True ___ False ___

In the following rotation matrix (about z), the rotation angle is -90°. True ___ False ___

0 1 0 0

-1 0 0 0

0 0 1 0

0 0 0 1

In the following rotation matrix (about z), the rotation angle is 90°. True ___ False ___

0 1 0 0

-1 0 0 0

0 0 1 0

0 0 0 1

An airline has 50 airplanes in Los Angeles, 16 airplanes in St. Louis, and 8 airplanes in Dallas. During an eight-hour period, 20% of the planes in Los Angeles fly to St. Louis and 10% fly to Dallas. Of the planes in St. Louis, 25% fly to Los Angeles and 50% fly to Dallas. Of the planes in Dallas, 12.5% fly to Los Angeles and 50% fly to St. Louis. How many planes are in each city after 8 hours?

Part A. If a function f has a derivative at x not. then f is continuous at x not. (How do you get the converse?)

Part B. 1) There exist an arbitrary x for all y (x+y=0). Is false but why?

2) For all x there exists a unique y (y=x^2) Is true but why?

3) For all x there exist a unique y (y^2=x) Is true but why?

Determine whether each statement is true or false. If it is true, prove it. If it is false, give a counterexample.

a) For every function f : X → Y and all A ⊆ X, we have f^−1 [f[A]] = A.

(b) For every function f : X → Y and all A ⊆ X, we have f[X \ A] = Y \ f[A].

(c) For every function f : X → Y and all A, B ⊆ Y , we have f^−1 [A ∪ B] = f^−1 [A] ∪ f^−1 [B].

(d) For every function f : X → Y and all A, B ⊆ X, we have f[A ∩ B] = f[A] ∩ f[B].

8. Show that the set of integer numbers is countable (hint: find a one to one mapping with the set of natural numbers which is countable by definition).

(1 point) A mass weighing 4 lb4 lb stretches a spring 6 in.6 in.
The mass is displaced 8 in8 in in the downward direction from its equilibrium position and released with no initial velocity.
Assuming that there is no damping, and that the mass is acted on by an external force of 5cos(7t)5cos⁡(7t) lb,
solve the initial value problem describing the motion of the mass.

For this problem, please remember to use English units: ft, lb, sec.ft, lb, sec.
Also remember to use g=32 ft/sec2.g=32 ft/sec2.

The solution to the initial value problem is:

u(t)=

At what frequency ωω will resonance occur?

Let R be a ring and f : M −→ N a morphism of left R-modules. Show that:

c) K := {m ∈ M | f(m) = 0} satisfies the Universal Property of Kernels.

d) N/f(M) satisfies the Universal Property of Cokernels.

Q2. Show that ZQ :
a) contains no minimal Z-submodule

1. Write the equation in general form.

8x² + 7 = x² − 8x + 8

2. Write the equation in general form.

(y + 1)(y + 3) = 8

3. Solve the equation by factoring. (Enter your answers as a comma-separated list.)

x² − 8x = 48

4.

Consider the quadratic equation

x = x².

Rewrite the equation in general form.

0 =

Factor the right side of the equation.

0 =

Solve the equation. (Enter your answers as a comma-separated list.)

x =

5.

Solve the equation by using the quadratic formula. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.)

3w² + w + 1 = 0

(a) Give real answers exactly.
w =

(b) Give real answers rounded to two decimal places.
w =

6.

Use any method to find the exact real solutions, if they exist. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.)

x² + 6x = 14 + x

x =

7.

Use any method to find the exact real solutions, if they exist. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.)

10y2 − y − 93 = 0

y =

3. Find the Fourier integral representation of each of the following functions.

f(x) = sin(x)/x

1. Performance metrics

   Buffalo BBQ Restaurant is trying to become more efficient in training its chefs. It is experimenting with two training programs aimed at this objective. Both programs have basic and advanced training modules. The restaurant has provided the following data regarding the two programs after two weeks of implementation:

   	Training Program A						Training Program B
   New chef #	1	2	3	4	5		6	7	8	9	10
   Hours of basic training	23	26	27	20	21		25	23	27	31	22
   Hours of advanced training	8	6	7	9	12		6	4	0	2	4
   Number of chef mistakes	11	13	17	15	15		8	6	7	7	7

   a. Compute the following performance metrics for each program:

   (1) Average hours of employee training per chef, rounded to one decimal place.

   Program A: hrs. per chef

   Program B: hrs. per chef

   (2) Average number of mistakes per chef, rounded to one decimal place.

   Program A: mistakes per chef

   Program B: mistakes per chef