Suppose that f(x, y) = 4x² + 4y¹ then the minimum is -2xy

Q: (a) The stable critical point and the unstable critical point of the + 4x = x² + 3 are,…

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Q: The auxiliary equation of y"" - 4y" - 4y' + 16y = 0 is r³-4r² - 4r + 16 = 0. The auxiliary equation…

A: The solution of an equation fr=0 is defined as the values of r which satisfies the differential…

Q: The auxiliary equation of y"-49"-49² +6 Y is f² ²3 ²³ 45²_-45+16=0. The auxiliary. equation hels a…

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Q: Monica needs to mix a 10% acid solution with a 40% acid solution to create 100 milliliters of a 22%…

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Q: (c) Use vector methods to find the point P on the circle (x - 5)² + (y-4)² = 4 which is closest to…

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Q: Find f ¹²(x + ln y) dydx 3 8 32 [in (12) 82

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Q: Use the Laplace Transform to solve the given initial value problem. y(4) - 4y=0; y(0) = 1, y'(0) =…

A: The given initial value problem is y4-4y=0; y0=1, y'0=0, y''0=-2, y'''0=0 We have to find the…

Q: 1 ~ P =| 2. P | Q = 3. PVQ = (

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Q: z¹-1 Find the following limit 1 = limi in z-i z-ez

A: We evaluate the following limit:                                            l=limz→eiπ2 z4-1z-i We…

Q: A drain, when accidentally left open can empty a big pool 1 hour SLOWER than a water inlet can fill…

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Q: 3. One of the ends of a line segment of length equal to 10 is point B (-3, 6); if the abscissa of…

A: Here we have to find the ordinates of other extreme of a line segment whose length is 10 and one end…

Q: Determine the inverse Z-transform of X(z) Select one: akt xk = = (-2j) sin( 2 (2a)k-1 sin (47) 2 xk…

A: Inverse Z transform of the function

Q: compute 13 inverse (mod 19) * also known as 13 to the power of -1 * by listing the multiples. Show…

A: Solution:-

Q: Excersik 2) For the Rieman tenser given by k ( 9 bd g - gad 9 bc)? ac Rabid Rab Rab - 3k gab R 37…

A: As given Rabcd=kgbdgac-gadgbc find (1) Rab (2) R (3) show that Rab=3kgab

Q: What is the inverse of the function? 2x-1 ƒ(x) = ² = = = =

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Q: 5. Show that {x² − 2x+3, 3x² − 2x + 5) is a subspace of P₂ (R). Define the subspace. -

A: We have to show that x2-2x+3 , 3x2-2x+5 is Subspace of P2R. Also define : Subspace .

Q: Use the definition of "f is O(g)" to show that (a) 4+25 is O(5"). (b) 5" not O(4")? EXPLAIN.

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Q: Let A be a nonnegative irreducible 3 × 3 matrix whose eigenvalues satisfy λ1 = 2 = |λ2| = |λ3|.…

A: It is given that, A be a non negative irreducible 3×3 matrix whose eigen values satisfy ;       λ1 =…

Q: g(x) = h * * A Xo elka

A: We know that: a·f'=a·f 'f·g'=f '·g+f·g'   Here, a is a constant.

Q: Use cylindrical coordinates. Evaluate JJJ x² + y2 dv, where E is the region that lies inside the…

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Q: Trapezoid - One of the legs: h = 2cm perpendicular to bases: b = 3cm and B where b is the shorter…

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Q: Let f: (0, ∞) → R be given by f(x) = 1, and let a € (0, ∞). Using only the definition of the…

A: It is known that f'(x)=limh→0f(x+h)-f(x)h, where f'(x) is the derivative of f(x).

Q: (a) Solve the linear, homogeneous, ODE: y′′′ + y′′ + 3y′ − 5y = 0.   (b) Prove that your answer…

A: Given ODE, y'''+y''+3y'-5y=0 Let ddy=D Now the homogeneous ODE become D3+D2+3D-5y=0…

Q: State the number of significant digits and the implied precision of the given number. 91.85 km/s.…

A: All the non zero digits are significant digits, hence the number 91.85 has 4 significant digits.

Q: in a reaction time task, your reation time was 250ms when 2 choices were given in a task. when there…

A: The main objective is to find reaction time, if 8 choices were given in the same kind of task.

Q: L Question 3 The period of a clock pendulum T is given by the equation T = 2π₁ where the constant L…

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Q: Find the general solution of the given differential equation, and use it to determine how solutions…

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Q: Question 4 In this problem we consider f(x)=√ near r= 16. (a) Find L(x), the linear approximation of…

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Q: Use the Laplace Transform to solve the given initial value problem. y(4) - 4y = 0; y(0) = 1, y'(O) =…

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Q: Let m be an element of N, be a relatively prime to 5. Show that 5|(m^2 + 1)(m^2 + 4)

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Q: Determine the equation of the locus of a point that moves such that its distance from the line 4x +…

A: Here we have to find the locus of the point that moves such that its distance from the line 4x + 2y…

Q: Use the definition of divisibility to justify your answers to the following questions. a. Is 42…

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Q: Calculate ∪∞n=1 An and ∩∞n=1 Anwhere for each n ∈N the set An is defined as:…

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Q: Using Simple Fixed Point, determine x2if initial guesses x1=5 Mu = 0.9 x 0.85 x 24 x A x 299 x…

A: The function: f(x)=0 is rewritten in the form of x=g(x) in the fixed point iteration method.  It is…

Q: A fossilized bone is found to contain one-hundredth the original carbon ratio. Estimate the age of…

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Q: Compute by hand the natural cubic spline for the data points (2,0), (1, 1), (0, 0).

A: Given data points are: 2 , 0 , 1, 1, 0 , 0. To Find : Natural cubic spline.

Q: Find the successive difference constant for the table below. What type of function is described…

A: Given: x y 0 -10 1 -1 2 18 3 47 4 86 The successive differences are: x y First…

Q: a) Solve the recurrence relation an = 4an-1 for any integer n>0 with initial condition a0= 64. b)…

A: Let us consider the recursion relation an=c1an-1+c2an-2+.....+cn-kak. Then to solve the relation…

Q: (a) ( satisfies Find all possible bases B for R² such that the linear transformation or show that no…

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Q: The nature of the stationary point(s) of the function f = 11 x²2 -8 y² + 2x + 11 y + 3 is(are)…

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Q: Let Z distance 기 be d₂ Point on ellipse between z and I d₁ = and distance = a (Z-1) (2-1) between z…

A: We have to write the given data in digital format.

Q: :- 5) Find an example of a countable family of continuous functions f, [0, 1] → [0 + ∞[, i € N, such…

A: Answer follows

Q: A third order linear, homogeneous DE whose general solution is y(t) = C₁et + C₂e³t + Сzet is: [Hint:…

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Q: When is a set compact?

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Q: The price of a home is $227,000. The bank requires a 20% down payment and three points at the time…

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Q: graph the function with a domain and viewpoint that reveal all the important aspects of the…

A: The given function is f(x,y)=x2+y2+4x-6y. to find: the domain of this function. To Sketch: The graph…

Q: Let k be any integer and S= {a.a2.....am) be a CRS modulo m. Show that k+S;= {k+aj, k+ a₂,...,k+am}…

A: We use the definiton of CRS to show that k+S is also a CRS mod m

Q: For the weighted voting system, {160: 100, 90, 60, 50, 10), D is a critical voter for {ABCD}…

A: A weighted voting system contains three things, the players, weights and the quota. Players are the…

Q: DE dx dt = x² - 4x + 3. (a) Its stable critical point is X = unstable critical point is X =

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Q: Question 3 Use the definition of divisibility to justify your answers to the following questions. a.…

A: By using definition of divisibility, to answer the given questions