Express both 13 and 5 + i as products of irreducibles from Z[i].

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Q: You want to purchase a new car and you are willing to pay R400 000. If you can invest at 11% per…

A: Solution : Given that  The principal amount =R300000Total Amount A=R400000Interest rate…

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Q: 7. If I is a circle in the Euclidean plane with center O(12,-17) of radius 5, then compute the power…

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Q: TEST THE EXACTNESS OF THE ODE (2x +F) ckx + (x+2F) df = 0

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Q: A chemical manufacturing plant can produce z units of chemical Z given p units of chemical P and r…

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Q: (7) (2.3 problem 9) Show that Rel ΤΑ (H) YA R Rel(A) - Rel(y^), assuming Rel(yA) is small compared…

A: Given: In this problem, the given details are Here, we want to show that the expression,…

Q: Use the trapezoidal rule, the midpoint rule, and Simpson's rule to approximate the given integral…

A: Given : ∫47sinxdx   ,  n=6 To Find Integration By :  (a) The trapezoidal rule (b) The midpoint rule…

Q: Computee for the following matrices: a) A= 1 lo 20 1 -2 0 0 10 0 2 T 0

A: Since you have posted multiple questions, so we will solve only the first question for you. The…

Q: c) Consider the following knapsack problem: Maximize z = 10x₁ + 7x2 + 25x3 +24x4 subject to 2x₁ + x₂…

A: Max ZA=49 (x1=0,x2=7,x3=0,x4=0) and ZL=49 (x1=0,x2=7,x3=0,x4=0) obtainted by the rounded off…

Q: Solve ut = kuxx; u(x, 0) = e¯; u(0, t) = 0 on the half-line 0<x<∞.

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Q: Determine the following estimate without using a calculator. Then use a calculator to perform the…

A: Solution : Given that  A full time employee who works 40 hours per week  earns $25.50 per hour

Q: Derive the 4-point forward formula for f"(x) by using values f(x), f(x+h), f(x+2h), and f(x+3h).…

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Q: (a) Use properties of quadratic functions to prove that 6(x - 1)² ≥² for all real x > 2. (b) Use…

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Q: Pythagorus' Theorum Using conventional labelling practices, identify the three sides in this…

A: Pythagoras theorem: The Pythagoras theorem states that the square of the length of the hypotenuse…

Q: the left column enter the terms from the given algebraic expression, as they are written and without…

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Q: The bar graph on the right shows the average cost of room and board at four-year public and private…

A: For a function: y=f(x), the dependent variable is y and the independent variable is x. The value of…

Q: Q15. What is the first (rightmost) digit in the base 3 expansion of the base 10 number71?

A: Given: 15. A base 10 number 71. To find: The first(rightmost) digit in the base 3 expansion of given…

Q: (roots of unity) The extension of the real field to complex numbers ensures that any polynomial of…

A: The equation  xN - 1 =0 i.e. xN =1 has N- roots which are called Nth roots of unity, and are given…

Q: The initial value problem has a unique solution defined on the interval Type -inf for - and inf for…

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Q: A business ordered t-shirts for advertisement. They ordered red shirt and blue shirts. The order was…

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Q: Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the…

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Q: #4 Set an =!) * it n=3k 2K+1 2K+3 кк (-1)k if n=3K+1 it 11=3K+2 Find livizup an and limint an

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Q: 2.23 Find all four solutions to the equation x²10 (mod 35).

A: The given equation is: x2-1≡0 mod 35 We have to find all four solutions to the given equation.

Q: The percentage of U.S. college freshmen claiming no religious affiliation has risen in recent…

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Q: Do the following with the given information. ['s cos(x²) dx (a) Find the approximations Tg and M for…

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Q: Use the big-θ theorems to find good reference functions for the following: f(n)=(n2 +5·2^n)lg(n^7…

A: Solution:     We know, n2 ≤ 2n , for n ≥ 4.     =&gt; n2 + 5.2n ≤ 6.2n     lg(n7.2n) = lg(n7) +…

Q: 3 4x³-6x²-x+2=0; (between 1 and 2

A: to find the root of equation we use newton raphson method  the process given below

Q: 2.21. Consider the sentence "For every integer n > 0 there is some real number x > 0 such that x 0…

A: The given sentence is " It is false that for every integer n&gt;0 there is some real number x&gt;0…

Q: 2 2) A factory makes three types of granola cereal: Plain, Nutty, and Chewy. Each batch of Plain…

A: Let us consider the system of equation AX=b Now, the solution of the system using the cramer's rule…

Q: Suppose that a and b belong to an integral domain and b ≠ 0. Showthat &lt;ab&gt; is a proper subset…

A: Let R be an integral domain. A commutative ring R is said to be an integral domain if non zero…

Q: The region between the curve y = 1/x² and the x-axis from x = ½ to x = 2 is revolved about the…

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Q: E. Find the Fourier Transform in both f format and omega format. 1, 0₂ = -1≤t≤1 otherwise

A: Fourier Transform:         A signal x(t) and its frequency domain, Fourier transform Xω is  defined…

Q: Find S1 through S5 and then use the pattern to make a conjecture about Sn. Prove the conjectured…

A: Given that, Sn: 14+112+124+.....+12nn+1 We have to find the values of S1,S2,S3,S4,S5 and the value…

Q: (a) State the definition of a compact subset of C. (b) Show that if K is a compact subset of C, and…

A: a) We have to write a definition of compact subset of ℂ b) If K is a compact subset of ℂ and A is a…

Q: Given the graph of a transformed rational function (you may include your own example create an…

A: Given graph is

Q: (i) f(x) = sin x + {x/3}, where {.} represents the fractional part. (ii) f(x) = sin 7x-cos 4 3x - 4…

A: We have to solve given problem;

Q: Given f(x)=x²+1 and g(x)=3-4, find 9.(g-f)(x) b. (fg)(x) C-(fog)(x) d. (gof)(x)

A: As per Bartleby rules we have to answer only first three questions.

Q: (1) The set Ro of rational numbers is done in R.

A:

Q: 9. Conversion key: 1 gallon = 4 quarts; 1 quart = 2 pints; 1 pint = 16 ounces a) If your car's gas…

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Q: -. Let f(x):= and let F(x) be the odd periodic extension of f(x). (a) Plot F(x) on [-6, 6] (b) Find…

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Q: The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors V₁, V₂, and v₂…

A: Linear Combination:       A vector V is called a linear combination of vectors   v1, v2, . . ., vn…

Q: In this problem you will solve the homogeneous system C. Multiply by g→ and integrate (Do not…

A: A. The  fundamental matrix is: ψ=et(-cos3t+sin3t)et(-cos3t-sin3t)3etcos3t3etsin3t. B. The inverse…

Q: n=0 Let An be a sequence so that lim an/√n = 0. Show that the series neoo converges.

A: Given: Let an is convergent and limn→∞ an/n=0 . To Show :∑n=0n=∞ann2 is convergent .

Q: A. Suppose that the economy is characterized by the following behavioral equations: C = 160+ 0.6 Yd…

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Q: The initial tableau of a linear programming problem is given. Use the simplex method to solve the…

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Q: ving problems w olume of a rectangu Osoid 9x² + 36y² +

A: we solve this sums by lagrange  method  for this we have two function  then we do partially…

Q: 2. Your friend has also has no money, and he owes your aunt $9 to tip the taxi driver. If they…

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Q: 4. dy dx (sin x) cos y (a) y(0) = 1 (c) y(3) = 3 (b) y(1) = 0 (d) y(0) = - 512

A: From the given differential equation we have to find the linear equation of x and y. We use the…

Q: (a) Solve: 2611 = 605 (mod 2021)

A: We have to find the value of X from the given information. According to guidelines we can solve only…