Problem 4. Count the number of non-negative integer solutions to 3x₁ + 3x₂ + 3x3 +7x4 = 22. Justify your answer.

Q: Let U be the set of all circles in R2 having center at the origin with radius r where r ≥ 0. Define…

A: Let U=x,y: x2+y2=r2 : ∀ x, y∈R, r≥0 u1=x1,y1∈ℝ2:x12+y12=r12, r1≥0u2=x2,y2∈ℝ2:x22+y22=r22,…

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A: Let the weight of the person be x kg. According to the problem: 70% of x = 3 or, 70/100 * x = 3 or,…

Q: How to find the inverse of a matrix?

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Q: y+x=-3 y = x +4 ➜ 4 Ly My 0 x + 2 y = 4 || 4 ofk

A: We know that the slope-intercept form of a linear equation is given by y=mx+c, where m is called the…

Q: an Suppose {an} and {bn} are sequences such that a+b→0. Prove that 0 and bn →0. Does this conclusion…

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Q: Solve the following linear programming problem. z = 2x + 7y 5x + 4y ≤ 20 8x + y ≤ 20 x ≥ 0, y 20…

A: As per the question we are given the following linear programming problem : Maximize : z = 2x + 7y…

Q: 5. Find the orthogonal trajectory of the family of curves x² + y² = Cx.

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Q: A retail store stocks two types of shirts A and B. These are packed in attractive cardboard boxes.…

A: Let X1 be number of shirt A, X2 be number of shirt B. Max Z =   2 x1 + 5 x2 subject to…

Q: x²y" - 9y" + 6y' - 9 = x² + 6x y'(0) = 0

A: The given differential equation is ,     x2y''-9y''+6y'-9 = x2+6x   ;  y'(0)=0 (.)  The solution of…

Q: Consider the set U {a + bx a, b = 2 under the polynomial addition and scalar multiplication. Select…

A: Option: For every u1→, u2→∈U, u1→+ u2→∈U U=a+bx| a,b∈ℤ u1→=a1+xb1  and u2→=a2+xb2  where a1, b1, a2,…

Q: Consider the following assignment problem: An office has four workers, and four tasks have to be…

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Q: The member of staff lives in Bermondsey in London. She must speak at a conference in Birmingham at…

A: According to question, member of the staff who lives in Bermondsey must speak at a conference in…

Q: Let T : U → V be a linear transformation. 1. Let D ≤ V and consider the subset E = {u ∈ U | T(u) ∈…

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Q: Let f(x) be a function that satisfies 1 (x² − x + 1)² - for all x. Theorem. Which one is it? Only…

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Q: A software organisation employs 80,000 staff members. 16,000 employees are in the sales team, 24,000…

A: A software organization employs 80,000 staff members. 16,000 employees are in the sales team, 24,000…

Q: Solve the given differential equation. All solutions should be found. 2xy + y² +3 x² + 2xy dy d.x…

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Q: ۔ (6) گا X 21 if 04x42 if 24x<3 extension of f with its puried and sketch the gropl a) Find the even…

A: in this problem we use some formula for finding the coefficients of  Fourier series .

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Q: Determine the truth value of the following statements if A and B are known to be true, and X and Y…

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Q: 4. A tank initially holds 40 gallons of a brine solution containing lb of salt per gallon. At t = 0,…

A: Initial volume of the solution V0=40gal. Initial concentration of salt is 15lb /gal. Rate of brine…

Q: A ship has three cargo holds, forward, aft and center. The capacity limits are: • Forward 2000 tons,…

A: Given: The capacity limits are:   Amount in tons Volume/ton in cubic meters Forward 2000…

Q: Use the equation to answer these questions.  x + 2 = √ 3x+10 What is the solution to the equation?…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

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A: As per the question we are given the following trivatiate equation : w = x + z2 And we have to…

Q: Q5: Solve the following set of equations using Newton-Raphson with initial values x₁ = 0.5, x₂ =…

A: The solution is given by using the modified Newton Raphson Method with two decimal places as follows…

Q: 2. Which of the following series diverge by the BDT? (Σ(-2) k=0 ê (c) Σ Σ(1+1)" Σ(6) 13 (e) none of…

A: We have to check which series is divergent by basic divergent series test.

Q: 2. 1500-gallon tank initially contains 2271.2472 L of water with 2.267962 kg of salt dissolved in…

A: Note:-  1 Liter =  0.264172 gallon then 2271.2472 Liter =  600 gallon             1 kg = 2.20462 lbs…

Q: (b) Use an appropriate method of differentiation to determine the derivative of the following…

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Q: Question 3 Let B = {4, 8, 12, 16} Consider the universal statement, Vn € B, 4| n. (Wait - we need a…

A: (a) The given statement is          ∀ n ∈ B, 4 | n.       This can be equivalently expressed as per…

Q: Consider ∂/∂t f(tx, ty). Prove that if f is homogenous of degree n, then the attatched equation is…

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Q: Given r + x + x = 1, solve f(x)=a+2x+x3 - 20₁2-20₂03 = 3

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Q: If a matrix A is 9x3 and the product AB is 9x8, what is the size of B? The size of B isx0.

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Q: Question 2 Let E = {5, 6, 7, 8} and consider the sentence, 3 m Em² = m. a. Write one way to say this…

A: Given set E=5,6,7,8  and a sentence ∃ m∈E∋m2=m (a) given statement can be written as  There exist an…

Q: Problem 6. Let U = {(x, y, x+2y, 2x − y,x+y) | x, y € F}. Find a subspace V of F³ such that F5 = UV.

A: Recall direct sum is sum but intersection is trivial space {0}.

Q: Let ≤R. If s := sup № exists, then there is a sequence in ſ that converges to s. Hint: For each n EN…

A: I have given the answer in the next step. Hope you understand that

Q: R, and let V be the set of all functions f: (0,1)→ R such that Problem 3. Let b f f(x) dx = b. Prove…

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Q: Let f(x) = = 1 2022/1-x2022 . Evaluate f(f(f(...(f(2022))...))), where there are 2022 f's.

A: We will find a patter in composition to conclude about 2020 f s

Q: good day day can you help me with this question? i.  sketch the graph of y=3*2^x

A: sketch the graph of y=3*2^x

Q: Let U and W be subspaces of a vector space V such that V = U+W {0} if and only if every vector in V…

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Q: Translate each argument into symbolic form. Then determine whether the argument is valid or invalid.…

A: Given- The argument is as follows: If Amanda and Kelsey love soccer, then they will play.Amanda…

Q: يا أصدقائي، كل يوم ا يزيدنا إنجازاً. كلما زادت الضغوط والمسؤوليات ارتفعت وتيرة الطموحات والانتصارات.…

A: With my friends, every day I discover that the fight increases our love, and moving increases us in…

Q: Find an explicit description of Nul A by listing vectors that span the null space. A = 136 0 014-3

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Q: #5) Find the indefinite integral. (Use C for the constant of integration.) IVA x + 3 √4-(x - 2)² dx

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Q: 1. Given f(x)=(2x-5)(x²-1), find the following: Degree of the polynomial: Sign of the leading…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: True or False. If the statement is true, prove it. Otherwise, give a counterexample.  1. Let A, B ∈…

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Q: Eight hours of work time paid for approximately how many more dozen eggs in 1997 than it did in 1919…

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Q: De 5 gal = qt 72 fl oz =

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Q: Find an SVD of the matrix 70 000 A 0 3 00 0000

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: DIFFERENTIAL EQUATIONS Identify the particular solution of the problem using method of…

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