A die is rolled 15 times. Calculate the probability that 6 appears exactly three times. 0.236 O 0.254 O 0.654 0.354

Q: Use limits to determine all the linear asymptotes of 3r2 – 5 2r2 + x if r1. 1² + 2x – 3'

A: Given: f(x)=3x2-52x2+x,if x<1x3x2+2x-3,if x≥1 To determine: All the linear asymptotes.

Q: 1. Suppose x is an eigenvector of A corresponding to an eigenvalue 1. Show that x is an eigenvector…

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

Q: A parabola having a vertex located at (-4, -8) intercepted the x-axis at x = -2 and x = -6.…

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Q: An equation is given. (Enter your answers as a comma-separated list. Let k be any integer. Round…

A: Given:   sin(2θ) = 6cos(2θ)Part (a)sin(2θ) = 6cos(2θ)⇒ sin(2θ)cos(2θ) = 6⇒ tan(2θ) = 6So,…

Q: Σ nV n=3

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Q: Indepen-dent Variable Depen-dent Variable Equation Order Degree dy ²+2 = 0 d²y dy + dx e* dx2

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Q: 2. Finite Geometry: Draw one illustration each for the three-line and four-line geometries.

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Q: Certain automobile license plates consist of a sequence of three letters followed by four digits. If…

A: We have a license plate that consists of a sequence of three letters followed by four digits. The…

Q: Prove that the following sequence is cauchy sequence by definition (xn) = Vn +1– Vn Hint :…

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Q: A circle of radius 1 rolls around the circumference of a larger circle of radius 4. The epicycloid…

A: Given, x=5 cos t-cos 5ty=5 sin t-sin 5tTo find: Distance traveled by the point in one complete trip…

Q: What is the value of w if: w/x=2<180∘ w + y = -5 + 15i y is a conjugate of x

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Q: Determine the domain and range of the given functions. Then sketch the contour plot of function…

A: We have to determine the domain and the range of the function of two variables fx, y. We know that…

Q: 2. 2 PCn):芝(-リ 2h %3D j = 1

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Q: A "periodic function" is given by a function which O satisfies f(t+T) = -f(t) O satisfies f(t+T) =…

A: Definition of  Periodic function : A function y= f(t) is said to be a periodic function if there…

Q: 1. Suppose x is an eigenvector of A corresponding to an eigenvalue 1. Show that x is an eigenvector…

A: 1) Let , x be an eigen vector of A corresponding to eigenvalue λ. Thus , we will have ,  A - λIx =…

Q: for fa(a, y), let flg(2)) = (2² + y*)! %3D fa (2)%3D (2r)D %3D 2V + y2 3z (0) (i) (ii) 33z+y for…

A: We have to calculate the partial derivatives.

Q: 3. Show that if x is an eigenvector of the matrix product AB and Bx # 0, then Bx is an eigenvector…

A: 3) Let , A and B two matrices. Let , x  be an eigenvector of the matrix product  AB , and Bx ≠ 0. We…

Q: The function f.(z) = sin(2z) has one residue %3D 3) Find the absolute value of the residue of f. The…

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Q: Show that the following equation is homogeneous and then find the general solution. か_デー y -xy dx…

A: We have given differential equation ,  dydx = y2 - xyx2 - xy Here , fx , y = y2 - xyx2 - xy Now ,…

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 10 cos(t)i+11…

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Q: Find the tenth term in the sequence. an = n + 2

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Q: a) Write the following statement in symbolic forms (i) If either Pakistan government acts against…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: az (b) Determine the by using the Chain rule with the following information: ds z = cos (x"y) – sin…

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Q: ci When x9, y= 0. ii As the values of x increase, the corresponding values of y decrease. ii The…

A: Increasing function: The function said to be increasing, as the value of the x increasing, the value…

Q: -3 -2 -1 1. -8642 -2 3 * 6 4 2 0 2 46 8 10 2 2- -8-6 -4 -2 8 4 2 -2 4 -6 5 Determine whether these…

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Q: Find the solutions u(0.1) and u(0.2), of the initial value problem u' = x(1-2u ku(0) = 1 %3D Using…

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Q: 6. The value of L'{ 1/p*} a) t° /5! b) t /4! c) t³ /3! d) t6 /6!

A: We have given a function ,  fp = 1p4 We need to find Inverse Laplace Transform of fp. As we know…

Q: Q2: Find the interval convergence and radius of 00 xn F(x)= п! n=1

A: We have to find the interval convergence and radius of Fx=∑n=1∞xnn!

Q: The matrix -3 - A = has one eigenvalue of multiplicity 2. Find this eigenvalue and the dimension of…

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Q: Find the area of the surface given by z = f(x,y) over the region R.   R:  The triangle with…

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Q: 4. x"(t) – 2x'(t) + 2x(t) = 0, x(0) = 1, x'(0) = 1 5. y" +2y" + y = sin t, y(0) = y'(0) = y"(0) =…

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Q: Use the equation giving the flux of the vector field across the curve to calculate the flux of F(x,…

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Q: Find the minimum values for the set of equations; indicate if the solution has on converged. x² +…

A: We are given the set of equations, x2+2y3-5=02x4+y2-9=0 We need to find The minimum values for the…

Q: Let A be a 3 x 3 diagonalizable matrix whose eigenvalues are 11 = 2, 12 = -1, and 13 = -4. If V1 =…

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Q: Given: 4a - b + c = -1 -a + 3c = 6 a + 2c = 2 Instruction: a. Find the lower and upper triangular…

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Q: 4. a). Write the second-order-order Maclaurin series for the S(4) - fin (1 + x*r }t function

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

Q: -2 Find eigenvalues and eigenvectors for the matrix 3 -1 The smaller eigenvalue has an eigenvector…

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Q: To test this series for convergence n nº + 4 n=1 where p= пр n=1 You could use the Limit Comparison…

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Q: 4. Expand the following functions into Taylor series at the point indicated and find their radius of…

A: We have to find the Taylor series at the given point.

Q: Show that 1+3/ -5 is irreducible which is not prime in ZlV-5]

A: We know that ,  ℤ-5 = a + b-5 / a , b ∈ ℤ We need to show that , 1 + 3-5  is irreducible but not…

Q: 1.(a) Do there exist integers a, b, c such that gcd(a, b) = 30, gcd(b, c) = 24, gcd(a, c) = 54?…

A: (a) gcd(a, b) = 30       gcd(b, c) = 24       gcd(a, c) = 54      =&gt; 30 | a, 54 | a           24…

Q: In Exercises 17-22, write , fdA as an iterated integral the shaded region R. 17. y 18. 2 F 12 1. 3…

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

Q: How many positive integers greater than 5 and less than 2020 are divisible by 7? are divisible by…

A: 1) Here , 2020/7 = 288.57 So 288 multiples of 7 are there between 5 to 2020 So , 288 integers are…

Q: Question 3 1 Use the first derivative test to find the location of all local extrema in the interval…

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Q: a 6) Determine the value(s) of a such that is linearly independent.

A: Given the set 1a,aa+2 is linearly independent.

Q: y = Ce* + Cze3*

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Q: A farmer has 10 acres to plant in corn and peas. He has to plant at least 7 acres. However, he has…

A: Let x = The acres of corn planted      y = The acres of peas planted

Q: Find the exponential generating function F(x) for the numbers fn of forests on vertex set [n] having…

A: Given below clear explanation

Q: 1) (a) Convert the following equations from parametric to rectangular. State the domain and range of…

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Q: Consider A (0, 5, –1), B = (6, –1, 0) and C = (-4,0, 3). 1 A +B. 3 (i) Find the unit vector having…

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