Given the vector function r(t)=〈√t , 1/(t-1) ,e^2t 〉 a) Find: ∫ r(t)dt b) Calculate the definite integral of r(t) for 2 ≤ t ≤ 3

can you please provide a Matlab code?

Determine whether it is true of false and justify your answer.

Every nonempty bounded set S of real numbers has a supremum and infimum, but those might not be elements of the set.

Topic: Differential Equations; reduction order.

The indicated fuction y₁(x) is a solution of the given differential equation. Use the reduction order technique to find a second solution y₂(x).

xy'' + y' = 0;    y₁= ln(x)

Please, explain deeply each part of the solution, and include complete algebraic explanation as well. Otherwise, the answer will be negatively replied.

Propose two of your own random number generation schemes. Please generate 100 random numbers ?? (? = 1,2, … ,100) for each scheme and show the results on the same plot for comparison (i.e., x-axis of the plot will show the index ? and y-axis will show the generated random numbers ??. You can use different colors and/or symbols to distinguish one sequence from the other). Discuss which scheme will be preferred.

MatLab code for Bisection and Newton Method to find root for f(k) = p(k)^3+2*(p(k)^2)-10 on interval [-1,2]. P(o)=1.5, P(1)=2.

Answer=
1.654249

Some species of rodents live on average 6 years. In the first two years of life they do not reproduce and only 20% of the females born alive reach 2 years of age. Between the third and fourth year females have 1 daughter on average and their survival is 50%, while in the las two years they have 2 daughters on average. If in an ecosystem there is initially a population of 10 females between 0 and 2 years old, 4 between 3 and 4 years and 3 with more than 4 years. After 3 years the estimated population of females will be:

Instructions: When calculating, round the result to the nearest whole number.

- females between 0 and 2 years:_____

- females between 2 and 4 years:_____

- females with more than 4 years: ____

Consider the formula

A : ∃x.[(∀y.P(x, y) → R(x)) → ¬∃z.Q(x, z)]

(a) Find a formula equivalent to A that only has negation symbols in front of basic formulas.

(b) Give an example of an interpretation where A is true. The domain should be the set N.

(c) Give an example of an interpretation where A is false. The domain should be the set N.

fx to fx-k define wrt graph shift and show it for 1/x to 1/x-1 along with domain and range

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Construct the truth-table for the following propositional formulas. In each case, explain whether the formula is a tautology, a contradiction, or neither. (Explain how you arrive at this conclusion.) (a) ¬((p → ¬p) → ¬p) (b) (p → (q ∧ r)) → (¬r → ¬p) (c) (p → ¬q) → ¬(¬p → q)

She uses e-commerce or she pays by credit card. She does not pay by credit card. Using a truth table we get result ending T T F F with the T matching with T's in premsis so it is valid,

but in this problem the only Ts from the premises match with the T in ending column of truth table MY QUESTION IS WHY IS THIS INVALID WHILE THE ABOVE IS VALID DOES IT HAVE TO BE A TATUOLOGY TO BE VALID OR MATCH WITH Ts FROM PREMESIS

If you use your seat belt, you will be safer. You don’t use your seat belt. Therefore you won’t be safer.

For the differential equation dy/dx=sqrt(y^2−36) does the existence/uniqueness theorem guarantee that there is a solution to this equation through the point

1. (1,6)

2. (4,42)

3. (−2,38)

4. (7,−6)

Use euler method to approiximate y(1)

y' is given , solve for y. approiximate y(1)

Create a table to show the approximate value of y(1) for each choice of h.

y’ = -15y y(0) = 1

h = .25

h = .125

h = .0625

h = .03125

Prove using induction:

If F is any field and f(x)=p1(x)p2(x)...pn(x) is a nonconstant polynomaial of the field, f an element of F, and p1,...,pn are irreducible factors of the field.

Then, there exists a field L such that f factors into linear factors over L.

Hint: start with p1(x) to prove that F is a subset of some K1=F[x]/((p1)) , then induct.

0.3 The Fibonacci numbers Fn are defined by F1 = 1, F2 = 1 and for n >2, Fn = F sub (n-1) + F sub (n-2). Find a formula for Fn by solving the difference equation.