1. For the binomial case, we know that (2) n! k!(n-k)!* Find a closed form for the trinomial coefficients (2)3.

Q: BERNOULLI EQUATIONS. Find the general solution. If an initial condition is specified, find the…

A: Let us solve by  BERNOULLI method.

Q: By changing to polar coordinate, evaluate. c) ff xy da, where "R" is the upper half of the annulus…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Question 1 Given a linear homogeneous second order differential equation x²y²-(3x −5)y' + (4_15…

A: Given a linear homogeneous second-order differential equation                        To determine:…

Q: Show that T is a linear transformation by finding a matrix that implements the mapping. Note that…

A: We find the matrix representation of T with respect to the standard basis of R4.

Q: Convert the point or decimals to at least one decimal place, with positive val (+0,2)=

A: To convert the point (-5, 5, -3) to cylindrical coordinates, we need to determine the values of the…

Q: z=a(t-sint) y=a(1-cost) tE[0,pi/2] Find the area between the x-axis and the cycloid given by the…

A: The  given equation  is  We  have to  find area the area enclosed by the cycloid(1)  and X-axis.Now,…

Q: Consider F(t)= (-4+2t, 1-11t, 1+11t). Find (t) and T(t). > F'(t) T(t)=( >

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Q: Let u = 0 6 -1 and A = 48 4 103 12 1 Is u in the subset of R³ spanned by the columns of A? Why or…

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Q: Sketch several level curves of the function f(x, y) = xy. Use k = -4,-1, 0, 1, 4.

A: Function is .To Find:Plot the graph of the level curve of the given function for k=-4, -1, 0, 1, 4.

Q: Fast pls solve this question correctly in 5 min pls I will give u like for sure Sub Use the shell…

A: The region is bounded by:.To Find: The volume generated by revolving about the y-axis, using the…

Q: (1 point) Solve the following initial value problem: d 5 18e³t 12 1/² = (₁-3)* + (1960) 67²), 7(0) =…

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Q: Let a(x) = -=-31(x - ²) Σ where I is the unit step function. Evaluate and So da [xdxx ada

A: As per the question we are given the function α(x) including an infinite sum containing the unit…

Q: Let X be a normed linear space and let P, Q E B(X). Show that the transformation T: B(X) B(X)…

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Q: dy 2. Slove: a) Sinx ax + by зу COSX = CSCX b). y = tan ¹57, find day y dx

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Q: Find a basis for and the dimension of the solution space of the homogeneous system of linear…

A: Introduction: First convert the system of linear equations into the matrix equation. Then convert…

Q: 3. Is the factorization domain Z[i√6] a unique factorization domain? Explain it.

A: Let R=Now, any element  of R is given by where  To show  R= is  not a  Unique Factorization domain,…

Q: ther the space curve given by r(t) = (2t², t² + 2t - 8, t - 2) intersects the x-axis, and if it do…

A: Given space curve We have to determined whether it intersects x-axis or not?

Q: (5) Solve the initial value problem y”" + y = f(t); y(0) = 0, y′(0) = 1 where 1 if 0 π/2 f(t) =

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Q: The plane 12x+16y+50z=420 intersects the cone z2=x2+y2 in an ellipse. The sum of the z-coordinates…

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Q: Solve the quadratic congruence, 6x²-7x+2 ≡ 0 mod 31.

A: We have to solve the above quadratic congurence.

Q: 1.calculate ſ₁ (x² − y) dx + (y² − x)dy, where L is the left semicircle with (0, 2R) as the centre…

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Q: (b). Find a general solution to the given Cauchy-Euler equation for t > 0. t²y" - 3ty' + 3y =…

A: To Find: A general solution to the given Cauchy-Euler equation for…

Q: Solve following DE x^(2)y"-7xy'+16y=0

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Q: Find the largest and smallest values (absolute maximum and minimum) of In(4x+1 h(x) on the interval…

A: To Find:Absolute maximum and minimum in

Q: Find the roots of the equation 2 x³ - 16x² + 42x - 36 = 0 given that it has a root of multiplicity…

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Q: Theorem 2.1 For every graph G, o (G) ≤ x (G). Proof It suffices to assume that G is a nontrivial…

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Q: 3. Solve each initial value problem. (a) y" + 5y' + 3y = 0, y(0) = 1, y'(0) = 2 (b) y" + 2y' + 2y =…

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Q: Find the area of the region lying inside the circle r = √2 sin 0 and outside the lemniscate r² =…

A: The equation of the circle is               The equation of lemniscate is…

Q: For the curve given by F(t) = (2 sin t, -1t, -2 cos t), find the unit tangent vector, the unit…

A:

Q: Suppose the current cost of gasoline is $3.34 per gallon. Find the current price index number, using…

A: The current price index number of a commodity expresses the current price of the commodity relative…

Q: Verify Green's theorem for the disc D with center (0, 0) and radius R and the following functions. :…

A: Work in cylindrical coordinates system:Convert rectangular coordinates to cylindrical coordinates…

Q: i) lim f(x) X-2* a) -2 3 2 2 f(x) 4 ii) lim f(x) X→2 b) iii) limf (x) x -2

A: With the help of given graphs, we have to find given limits.Concept/formula required:1) is a number…

Q: A contour map for a function f is shown. If you start at the point (1,3) and move in the positive x…

A: A contour map for a function f(x)To Find:If we start at a point (1, 3)  and move in the positive x…

Q: excluding question 1 to 5

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Q: Question 3: Simplify the following expression: Re(-jes)

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Q: 7. A company uses a probability density function to estimate the duration of a call with a cus-…

A: Given probability density function for the random variable  is following :where,  represent duration…

Q: Series Find the exact value that the series diverges. n=1 2n 1 3n+2 converges to, or else conclude…

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Q: ASK YOUR TEACHER A student is given a reading list of nine books from which he must select three for…

A: We have to select the three books from nine books.So we apply the combination rule.

Q: Simplify the following expression: 9.com Re (-jet)

A:

Q: I1 = I2 || = Solve the following initial value problem: 20 ²-(-25) * + (2000) ¹) ² + (501), #(¹) =…

A: Let                            From given system ,…

Q: Find the curvature of the curve r(t) = (-5t, -5t5, 5t³) at the point t = 2. Give your answer to 2…

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Q: 2. Use spherical coordinates to find the volume of the solid that lies above the cone z = √√x² + y²…

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Q: 3. Solve of the Boundary-Value Problem (BVP) by the method of seperation of variables. du at a²u əx²…

A: The given problem is to find the solution for the given boundary value problem partial differential…

Q: Hi, I am looking for some help in understanding a differential equations problem to be solved by…

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Q: *************** Data released by the Department of Education regarding the rate (percentage) of…

A: Given thatData released by the Department of Education regarding the rate (percentage)of ninth-grade…

Q: Could you please explain the following example step by step with explanation, thank you in advance:…

A: The elements are {[1],[2],[4],[5],[7],[8]}.But elements of  are…

Q: To identify how much heat is required to bring a kettle of water to its boiling point, you are…

A: Here,

Q: what are the values of s1 and s2?

A: We have to

Q: 1.2. Decrypt each of the following Caesar encryptions by trying the various possible shifts until…

A:

Q: مدر prove by induction that 22-1 is divisible by 3 for every integer n>4.

A: Mathematical induction is a mathematical technique for proving that a statement, formula, or theorem…