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Please clear writing and explain step by step this should be a simple question. I will know if you understand this topic or not.

Consider the function f : [0,1]→R defined by (f(x) =0 if x = 0) and (f(x)=1 if 0 < x≤1)

(i)Compute L(f) andU(f).

(ii) Is f Riemann integrable on [0,1]?

“We must differentiate our mindset first and our lessons second.” (Dweck, 2012). What does this saying mean to you? In your own words, what is the difference between differentiation and tracking?

Use the Laplace transform to solve the following initial value problem:

?″+6?′+58?=?(?−4)

?(0)=0,?′(0)=0

(Notation: write u(t-c) for the Heaviside step function ??(?)uc(t) with step at ?=?t=c.)

1. A small furniture manufacture producer tables and chairs.  Each product must go through three stages of the manufacturing process:

Each table requires 4 hours of assembly, 3 hours of finishing and 1 hour of inspection

Each chair requires 3 hours of assembly, 2hours of finishing and 2 hours of inspection

The selling price per table is $140 while the selling price per chair is $90

Currently, each week there are 220 hours of assembly time available, 160 hours of finishing time, and 45 hours of inspection time.

Assume that one hour of assembly time costs $.00; one hour of finishing time costs $6.00; one hour of inspection time costs $4.50.

Linear programming is to be used to develop a production schedule.

Let:      T=number of tablets produced each week

            C=number of chairs produced each week

Which of the following expression would be the objective function of this LP problem?

1. Max 140T+90C
2. Max 97.5T+54C
3. Max T+C
4. Min 42.5T+36C

consider f(x) = ln(x) use polynomial degree of 5!!!

a) Approximate f(0.9) and f(1.1)

b) Use Taylor remainder to find an error formula for Taylor polynomial.

Give error bounds for each of the two approximations in (a).

Which of the two approximations in part (a) is closer to correct value?

c) Compare an actual error in each case with error bound in part (b).

Prove that the set of all subsets of {1, 4, 9, 16, 25, ...} is uncountable.

In a certain chemical reaction, substance A, initially weighing 12 lb, is converted into substance B. The rate at which B is formed is proportional to the amount of A remaining. At the end of 2.5 min, 4 lb of B have been formed.

(a) How much of the B substance will be present after 6 min?

(b) How much time will be required to convert 60 percent of A?

Work this problem in two ways:

1. Letting x represent amount of A remaining at time t.

2. Letting x represent amount of B formed at time t.

The answers are: (a) 7.47 lb. (b) 5.6 min.

I need someone to show me how this problem is worked out from start to finish. Thanks a bunch & take it easy!

Compact and analysis conception

1. Are all closed interval compact?

for example [0,1]. are they closed and bounded?

2. If i can find the Maximum and Minimum, does that mean the set is closed and bounded?

3. Before you sit three chests – one made of wood, one of stone, and one of steel. You know that one of the chests contains a great treasure, while the other two contain vicious, angry, man- eating, deadly poisonous scorpions (also known as scorpions). On each chest hangs a sign, giving you information about which chest contains the treasure. Problem is, you do not know which signs are true and which are false. The signs read: Wood chest: If the sign on the stone chest is true, then the treasure is not in the steel chest. Stone chest: Exactly two of these signs are false. Steel chest: The treasure is in a chest with a false sign. Which chest contains the treasure? Prove your answer is correct.

Use the method of undetermined coefficients to find one solution of

?″+?′−11?=9?4?.

y(t) = ?

The pottery shop opened a new branch this year. The following figures show the sales volume and advertising expenses.

Sales LY $900,000

Sales TY $1,050,000

Sales plan for next year $975,000

Advertising costs LY $28,500

Advertising costs TY $32,000

Advertising plan $27,500

a. What do the sales trends reflect?

b. What do the advertising costs reflect?

c. What is the percent of increase in sales from last year to next year's plan?

d. What is the percent of increase or decrease in advertising between last year and next year?

e. What is the percent of decrease in sales from this year to next year?

f. Why do you think these fluctuations of volume and expenses might be planned?

Jane wants to auction off an item, but does not know where to go to find bidders. David offers to find bidders for her, but will charge her $10 per bidder he gets to show up. Each bidder will uniformly value the item between [500. 1000). The highest bidder will win the item and pay the second-highest bidder's price (Vickrey auction). How many bidders should Jane pay David to find?

hey hey! mechanical engineering student who is VERY confused and has absolutely no idea what any of this means but really wants to know. could you please help me! this is the question. given M=4,5,7,10 and N=12.

Question 1: Explain how fundamental period of discrete-time sinusoidal signal can be calculated and calculate fundamental period for four cases in exercise

**100% RATING WILL BE GIVEN IF CLEAR, CORRECT ANSWERS FOR EACH FOUR CASES OF M ARE GIVEN

this is my matlab code for the M =5 value.

N=12;
n=0:1:N-1; %n is defined with step 1
M=5;
x=sin(2*pi*M.*n./N);%defines dependant variable x[n]
[~,T0]= rat(M/N) %using rational approximation the fundamental period is calculated.
%nosemicolon means matlab will display result.
stem(n,x) %using stem the discrete signal is drawn
xlabel ('n');
ylabel('y[n]');
title ('discrete sinusoidal signal example');

Suppose a is a positive integer and p is a prime/ Prove that p|a if and only if the prime factorization of a contains p.

Can someone please show a full proof to this, thank you.