SET-UP the definite integral that will give the area of the region specified using (a) x as the variable of integration and (b) y as the variable of integration. y =1-2² y = x – 1

Q: 2. Determine a basis for and the dimension of the solution space of the homogeneous system X3 + X4 +…

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Q: 5. Chose the curl of f (x, Y, z) = x² i + xyzj-zk at the point (2, 1, -2). a) 2i + 2k b) – 2ê-23 c)…

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Q: S. y dk t x dly luhere L=

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Q: To accommodate more depositors, new investment products were made avanable to the small businesses…

A: We make an equation from given information and then solve that equation.

Q: Find a basis for the vector space of all 3 x 3 diagonal matrices. 0 0 1 0 1 0 1 0 0 0 1 0 0 1 0 0 1…

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Q: Problem 10.1.2. Let (xn), (yn) be sequences as in the NIP. Show that for all п, т € N, zn < Ут-

A: see attached image

Q: Let S = {a+ bi |a, b e Z , b is even}. Show that S is a subring of Z[i], but not an ideal of Z[i].…

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Q: Let f(x) = |x| where xeR. Discuss the continuity and differentiability of f(x) at x = 0

A: discuss the continuity and differentiability of f(x) at x = 0 f(x) = | x |

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A: Given:A taxi company has four available taxis (A, B, C, and D) and four calls for taxi service (W,…

Q: If F (2x + y)i + (3y 4x)j evaluate o. F.dr around a triangle ABC in the xy-plane with A(0. 0). B(2.…

A: Line integration of the function

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Q: A compact disk spins at a rate of 200 to 4000 revolutions per minute. What are the equivalent rates…

A: As per the company rule, we are supposed to solve one problem from multiple problems. Therefore…

Q: Solve this ODE using the Frobenius Method x*y"+x°y'_2y = 0

A: In the Frobenius method we will start by assume a solution of the form  y=xk∑n=0∞anxn

Q: Problem 3: Given the nth-term formula below, compute the first five terms of the sequence: an n=…

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Q: Suppose A and B are non-empty bounded subsets of positive real numbers. Define A·B = {r •y:x € A, y…

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Q: Since we have sin(r +y) sin(r) + sin(y), the function sin(r) is a linear transformation.

A: We know T: V---&gt;W  is said to be linear transformation if, T(x+y)= T(x)+T(y) for all x,y in V…

Q: Definition of Laplace Transformation. Definition Let f(t) be a function on [0, x). The Laplace…

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Q: Verify Green's theorem in plane for (x - 2xy)dx + (xy+ 3)dy where c is the boundary of the region…

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Q: REGIONS/SCOPE. Determine the regions occupied by the curve. y= x^2 / (x-1)

A: To determine the region occupied by the given curve: y=x2x-1

Q: Find all the pairs of integers (x, y) that satisfy 287x – 406y = 27.

A: This is a problem of Diophantine equation.

Q: Find all the solutions r E Ziz to the equation r³ – 5x² – 7x = 0 mod 13.

A: First, solve in real number then ring down to the finite field.

Q: B- [x+y A= 3 and C = y -2 x- y If AB = C, then what is A? equal to? 4 8 1. -16 2. [8 -16 -8] 3. 4 12…

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Q: f(t) = 2t² + 4t – 3 4+2s-3s? А. c 4+4s-3s? С. s3 2+2s-3s2 В. 2+4s-3s2 D. s3

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Q: Determine if the given set of vectors is linearly independent. B = {|1 2 }

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Q: SAP

A: Given, f has a derivative on an interval I, and f' has successive distinct zeros at x=1 and x=5. To…

Q: Let ø : Z25 → Ss be a homomorphism such that ø(1) = (12468). (a) Find o(22). (b) Determine kero. (c)…

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Q: Find the general solution of the differential equation y" +2y-35y = -113t + 70t. NOTE: Uset as the…

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Q: = The value X3 .3 -2 x1 + 6 x2 + X3 – X1 +x2 + 7 x3 = -6 4x1 – x2 – X3 = 3

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Q: f(x, 3) = In(x? + Y²òf function P(3,4) at the point of i = (9, 12) Directional derivative in the…

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Q: 3. Let å1, åz, åz be three nonzero vectors in R2 and let b1, b2, bz be three real numbers. Consider…

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Q: 3s - 2 Find the Inverse Laplace Transform of G (s) = 2s² – 6s – 2 A 8(1) = 3e 2 sinh cosh 13 B 8 (1)…

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Q: what IS the absolute value 7 -2 +i ? a. -J5 C. I b. J5

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Q: Cookie salon is celebrating their second anniversary. They are offering hair service for only ₱699…

A: Discount = 1699 - 699 = 1000.

Q: Find the solution. (D + 602 + 110 + 6)y = 0 A y = c,e-2«, +c,e y = c,e '+c,e -3x c) y = c ,xe" + c,e…

A: Consider y=emx be the solution of the given differential equation. Differentiate the equation y=emx…

Q: The value X1.1 -2 x1 + - X1 + x2 + 7 x3 = -6 4x1 — Х2 — Хз %3D 3 6 x2 + x3 = 9

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Q: Find the truth table for the given statements (a) (p ∨ r) ∧ (q ∨ r) (b) p ∨ (∼p → q) (c) (p →…

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Q: Express 7 (cos 300° – i sin 30°) in polar form.

A: convert in polar form

Q: Evaluate the following complex expressions. Present your answers in the trigonometric orm. Box your…

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Q: det (A) = 1. %3D

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Q: if f(z) = (ax – x³ + 3xy²)+ (by – 3x² y + y) is analytic, then the value of a and is

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Q: QUESTION 2 Let V be the set of all ordered pairs of real numbers with addition and scalar…

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Q: ty 100 (5, 96) 80 60 (4, 48) 40 20 (3, 24) (2, 12) 4 6 8 Which statement is true about the graph? a.…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: DIRECTIONS: The entire test has been answered for you. Your job is to check the answers for errors.…

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Q: Use Forward and Backward differentiation to f' (1) calculate as accurately as you can. Let h = 0.08…

A: To find the value of the derivative at a point x by forward and Backward differentiation with step…

Q: Tx/2+sin(ix) f(x) = V2r then = (x).

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Q: For integers æ, y, notation æ|y means that x is a divisor of y. (For example 5|30, but it is not…

A: After the assumption that 3| (22k - 1), we need to mathematically formulate this.  i.e., from the…

Q: w the depth first traversal of the following graph. Start at vertex 1. Ties are resolved in…

A: Here I run a python script and see the result.

Q: 3. In the following exercises, justify your answers using truth tables. (a) Are PV (Q A R) and (P V…

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Q: Q1:- Solve the following DEs:- xy2-cos x sin x y' = У(1-x?)

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Q: On a garage sale, a hoodie jacket costs ₱795 after a 75% discount. How much is the original price of…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.