If a polynomial f(x) when divided by (x - a) gives a remainder r₁, and when divided by (x - b) gives a remainder 72, what is the remainder of dividing f(x) by g(x) = (x-a)(x-b)?

Q: ㅠ Use Green's theorem to find: where C is the circle x² + y² = 4 going counter-clockwise. -8T […

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Q: 2. p → (q^r) -q/:: -p

A: Given : Argument is           p=> (q Λ r).......(1)          ⌐q........(2)           ∴⌐p To find…

Q: Q1\ Choice the correct answer from the following: L[−t * e¯at * u(−t)] =

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Q: 5. Solve by using power series: y'=x'y. Find the recurrence relation and compute the first 33…

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Q: Evaluate the following integral using change of coordinates: SR S x³ + xy²dxdy where R is the region…

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Q: Solve using Gaussian Elimination, Given the equation, what is the next step to take? 2x+3y=6 x-y=1/2

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Q: Diagonalize the following matrix, if possible 0 9] 6 10-6 Select the correct choice below and, if…

A: We have A = 6010-6 A-λI = 6-λ010-6-λ We need o find the eigen values, A-λI = 6-λ-6-λ = -36-6λ+6λ+λ2…

Q: tudy showed the following migration Matrix, which describes the movement of the population of the…

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Q: Produce a rule for the function whose graph is shown. -5 -4 -3 f(x) = -2 -1 54 4 3- 2 1 1 -2 7 -3-…

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Q: If y₁ and y2 are linearly independent solutions of ty" + 2y' + te³¹ y = 0 and if W(y₁, y₂)(1) = 4,…

A: Here given the differential equation as ty''+2y'+te3ty=0 or y''+2ty'+e3ty=0  ........(1)

Q: 30. You work as a design engineer at a solid rocket manufacturer. You are analyzing a propellant…

A: Given: Height of propellant=168 cm, Outside radius=37.5 cm and radius of hole=15.5 cm. Formula used:…

Q: Find dy/dx by implicit differentiation. √xy = x³y + 20 dy/dx =

A: Given equation is  √(xy)=x5y+20. We find dy/dx by implicit differentiation.

Q: A certain experiment produces the data (1, 1.7), (2, 2.8), (3, 3.3), (4, 3.5), and (5, 3.9).…

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Q: conditional proof

A: The given argument is 1. p→q 2. q→r 3. ~r / ∴ ~p

Q: a. Using the General Binomial Theorem find the power representation of(1 + x)¾.

A: As you post multiple question according to guideline only solve the first one.

Q: If w = f(r, s,t), r = x - y, s = y - z, t = z -x then dw дх + aw Əw ду дz + ||

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Q: 450.41 0.24144

A: Angle=13.57°

Q: Using Bisection method, the root of the given equation x²-3-x with x₁ = 0 and ₂3 at the third…

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Q: Solve the following DE using TWO different methods (do not solve using the substitution y = ux. Use…

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Q: The value of limx→o ex-1-x x² by using series is

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

Q: b← d't <b -r/ :: -p

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Q: 1. Factor. a) x² + 7x + 10 b) x² + 9x + 20 c) x² + 8x + 16 d) x² + 10x + 25 e) x²-5x + 6 f) x² - 12x…

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Q: When interest is compounded continuously, the amount of money increases at a rate proportional to…

A: Given- When interest is compounded continuously, the amount of money increases at a rate…

Q: Find the Maclaurin series of Σ (x)³n n=0 3 1+x 3 Σ (1)"(x)" n=0 3 Σ (x) n n=0 .Write your answer in…

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Q: Sketch the following surface: (z+4)² + (y-1)² = 1 a.) Draw the projection on a xy plane Show…

A: given function z+42+y-12=1 (a) draw projection on xy plane put z=0 42+y-12=1⇒y-12=-15 projection is…

Q: J- d- / - ←b 1. p - q

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Q: y -2 (a) lim f(x) = + X-C (b) lim f(x) = X-C (c) lim f(x) = X-C 2 the function continuous at x = 4?…

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Q: Sketch the following surface: (2+4)² + (y − 1)² = 1 a.) Draw the projection on a xy plane Show…

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Q: a. Without doing any calculation, explain why one might conjecture that two vectors of the form (a,…

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Q: * 15% can be expressed as: O an insignificant minority O a significant majority O O a small minority…

A: We know that Greater than 50% is significant majority 75% is approximately three quarters Less than…

Q: noon, a large pool contains only 26 gallons of water. A hose is set up so that the pool is filled at…

A: Introduction: We use the term "Rate" to describe the comparison and ratio of two separate…

Q: Solve using Gaussian Elimination, Given the equation, what is the next step to take? x+y-z = -2 2x -…

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Q: A graph with an infinite vertex set or an infinite number of edges. * infinite graph finite graph…

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Q: Let f: R → R be a function that is differentiable on (a, ∞), where a is any real constant. Let g: R…

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Q: Two slabs, each 1 inch thick, each have one surface at 0◦ and the other surface at 100◦. At t = 0,…

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Q: Evaluate the following integral using change of coordinates: SRS2³ + xy² dady where R is the region…

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Q: Your company produces computers each month. In a given​ month, the company has fixed costs of…

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Q: The general trend sentence can be written as:

A: Have to write the conclusion of the diagram.

Q: 3. State and explain the Convolution Theorem for Laplace transform

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Q: Q2\ Choose true or false from the following sentences:- Matrix has only one row call Row Matrix.…

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Q: 2x + 4x + 3x 3y - 2 = 1 Зу - y - 3z 3z = 11 - - 2y + 5z = 2

A: 2x+3y-z=14x+y-3z=113x-2y+5z=21

Q: Evaluate the following integral using change of coordinates: SR S x³ + xy² dedy where R is the…

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Q: Using logarithmic differentiation, Show that y(x)=xa2xex2 has no stationary points other than x=0,…

A: Given function is yx=xa2xex2. We have to show that the given function yx has no stationary points…

Q: z(0) r(t) y(t) = Find the solution to the linear system of differential equations 8 and y(0) = 5.…

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Q: Find Maclaurin series of f(x) = x² + 5x ans: x4 + 5x = 0 + 5x + (0) Select one: O True O False x² 2!…

A: f(x)=x4+5x Maclaurin Series f(x)=∑k=0∞fk0k!xk

Q: مممممم م العمل لها -Pre-Hilbert space - Metric space and Complete - Normed space and complet

A: 1) the banach space is solution definition of Banach space A Banach space is a normed linear space…

Q: Find the volume of the solid generated when the region ? bounded by the given curves is revolved…

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Q: √1-y² If ²₁¹² x² + y² dxdy is changed to equivalent integral in polar coordinates, then the…

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Q: What is the height of the tree? * O 5 3 02 None from the choices 4 m What is the minimum height for…

A: Which of the following is correct :-

Q: Determine if the specified linear transform T(X₁ X2 X3 X4) = (x₁ + x₂,0₁X3 + X₁₁X_ a. Is the linear…

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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.