Consider the following problem. max ? 0.5?1 + 2.5?2 + ?3 subject to ?1 + 2?2 + 3?3 ≤ 8 ?1, ?2, ?3 ∈ ℤ + ∪ {0} Solve the problem by dynamic programming. Show each step clearly.

1.      Explain the importance of error analysis in numerical methods with suitable example.
2.      Out of Bisection method and secant method which one is better and why? Solve one application based problem using that method.
3.      Use Newton-Raphson Method to find the root of trigonometric function correct up to seven decimal places. (Trigonometric function should be complex)
4.      Solve one problem which is based on the application of Interpolation.
5.      Using numerical differentiation solve one application based problem. (Use central difference approximation and problem must include first order as well as second order derivatives)
6.     Out of Trapezoidal rule and Simpson’s 1/3^rd rule which one is better explain in detail. Also solve one application based problem using that rule. Compare the exact and approximate result to compute the relative errore

its solve once but I need different answer please

a quick please I'm in trouble

2) Let v, w, and x be vectors in Rn.
a) If v is the zero vector, what geometric object represents all linear
combinations of v?
b) Same question as a), except now for a nonzero v.
c) Same question as a) except now for nonzero vectors v and w (be care-
ful!).
d) Same question as a) except now for nonzero vectors v, w, and x (be
extra careful!).

i. Identify the conic whose equation is 11x2 + 24 xy + 4y2 − 15 = 0 by rotating the axes to place the conic in standard position.

ii. Find the angle θ through which you rotated the xy-axes in part (a).

Write a Matlab script-file probl1.m to execute the requested commands (as much as possible) in the exercises below. Increase N a number of times according to N = 4, 8, 16, 32, 64, 128, . . . (1) Determine for each N the (exact) error. (2) Determine for N ≥ 16 also the convergence ratio q(h/2).

This script should be based on a function-file trap.m (trapezoidal integration) as follows:

function [totarea] = trap(N)

format long;

a = 0; b = 1/2; h = (b-a)/N;

x = a:h:b; totarea = 0;

for i = 1:N

xl = x(i);

xr = x(i+1);

fxl = myfunct(xl);

fxr = myfunct(xr);

locarea = (h/2)*(fxl+fxr);

totarea = totarea + locarea;

end

end

You can refer to the integral as myfunct(). The interval is [0,1/2].

A field is a commutative ring with unity in which every nonzero element is a unit.

Question: Show that Z_5 under addition and multiplication mod 5 is a field. (state the operations, identities, inverses)

Obtain an estimate for the value of e by approximating the solution of the following initial value problem at t = 1

y'=y     y0=1    

Use a step size of 0.25. Apply Euler’s Method, the Midpoint Method, and the Improved Euler’s Method in order to approximate the solution to this problem. Calculate the absolute relative true percent error using seven significant figures. Calculate this error for each method and only for the last iteration.

Which of the following statements is/are true?

1) If a matrix has 0 as an eigenvalue, then it is not invertible.

2) A matrix with its entries as real numbers cannot have a non-real eigenvalue.

3) Any nonzero vector will serve as an eigenvector for the identity matrix.

1. Sketch a connected 2-dimensional complex with three 2-cells, 8 1- cells, and 5 0-cells.

2. Draw three examples of a connected 1-dimensional complex with 7 0-cells and 6 1-cells.

3. Sketch a connected 1-dimensional complex with 7 0-cells and 7 1-cells.

4. Sketch a connected 1-dimensional complex with 7 0-cells and 8 1-cells.

5. Is it possible to construct a connected 1-dimensional complex with 8 0-cells and 6 1-cells? Explain.

T:R ->R3 T(x, y, z) = (2x + 5y − 3z, 4x + y − 5z, x − 2y − z) (a) Find the matrix representing this transformation with respect to the standard basis. (b) Find the kernel of T, and a basis for it. (c) Find the range of T, and a basis for it.

Let X be the set of all subsets of R whose complement is a finite set in R:

X = {O ⊂ R | R − O is finite} ∪ {∅}

a) Show that T is a topological structure no R.

b) Prove that (R, X) is connected.

c) Prove that (R, X) is compact.

1. The equation of the line with an x-intercept of 33 and a y-intercept of 44 can be written in the form y=mx+b where
the number m is:    
the number b is:    

Enter each answer as a reduced fraction (like 5/3, not 10/6) or as an integer (like 4 or -2).

2. You have filled your car with a full tank of gas, and could travel 485 miles. For every 17 miles you drive, you use 1 gallon of gass (17 miles per gallon).

Please write an equation in slope-intercept form to model this situation. Please use m for the the miles you've traveled, and g for the gallons of gas you use.    

The displacement of an object in a spring-mass system in free damped oscillation is:

2y''+12y'+26y=0 and has solution: y1 =−5e^(−3t)*cos(2t−0.5π)

if the motion is under-damped.

If we apply an impulse of the form f(t) = αδ(t−τ) then the differential equation becomes :

2y''+12y'+26y=αδ(t−τ) and has solution y =−5e^(−3t)cos(2t−0.5π)+αu(t−τ)w(t−τ) where w(t) = L(^−1)*(1/(2s^2+12s+26))

a. When should the impulse be applied? In other words what is the value of τ so that y1(τ) =0 . Pick the positive time closest to t = 0

b. What intensity should the impulse be so that the object is in equilibrium for t > τ (i.e. what should the value of α be so that y(t)=0 for t>τ ).

c. Write up your work for this problem including the inverse transform needed to write out w(t) and the completed form of the impulse function f(t)