Min Median Max Mean SD IQR Range 103 109 112 109 3.4 6.5 12 Radio Station A 91 96.5 108 97.8 4.5 6 17 Radio Station B

Q: Sketch the graph of f(x) = -3x³-4x² + 6x-2 by following the steps in sketching the graph of a…

A: Given data :f(x) = -3x3-4x2+6x-2Critical points :put f'(x) = 0f'(x)  = -9x2-8x+6 = 0x1 = -1.374x2 =…

Q: 2. Consider the function f(r). 2r²-9r-18 r²-r-2 (a) Sketch the curve y = f(r). (b) Find the area of…

A: Given equation fx=2x2-9x-18x2-x-2 Apply division algorithm to the fx fx=2-7x+2x2-x-2…

Q: 8. Using the Mean Value Theorem and Rolle's Theorem, show that³+x-1=0 has exactly one real root. 9.…

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Q: 2. Use Method of Undetermined Coefficients: 5 y" - 2y + 5y = 4e*cos2x + x² 2

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Q: How to find the cofactor of a 4x3 matrix?

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Q: Question If f: (R, mL) → R and g: (R, mL) → R are measurable then:

A: Given statement:-  If  f  :  ℝ, mL  →ℝ  and   g  :  ℝ, mL  →ℝ  are measurable then:

Q: The following data gives an approximation to the integral M= f(x) dx N₁ (h) = 2.2341, N₁ () =…

A: Solution:-

Q: Question 1 Determine the inverse Laplace transforms of: 2s²-5s-1 (a) (s+3)(s²+9)

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Q: Test for exactness, and solve the Initial Value Problem for the following first-order ODE below: dy…

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Q: 4. Communication. Explain where the CAST Rule comes from by showing how we can determine that: A)…

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Q: Let Find an orthonormal basis of the column space of A. 2 5 3 -5 3 2 us

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Q: of K be a finite extension. Then |Emb_F(K, L)| ≤ dim_F(K), wher

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Q: Let B be the sphere x² + y² + z² = 1. The volume of the portion of B contained in the first octant…

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Q: 1) The polynomial P(x) = x²+4x³+x²-6x+2 has roots; a, 6, 7, 8. Given the condition that aß = -1: (i)…

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Q: The degree of precision of a quadrature formula whose error term is f() 2 4 This option This option…

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Q: List all the vertical asymptote(s) for the function y=tanx for 0≤x≤2л

A: Application of Calculus.

Q: (a) How many distinguishable ways can the letters of the word MILLIMICRON be arranged in order?…

A: The number of ways n items can be arranged, out of which, p items are of one kind and q items are of…

Q: The approximation of /= cos(x³ + 5) dx using composite Simpson's rule with n=3 is: 3.25498 0.01259 O…

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Q: dw dw as a function of t, both by using the chain rule and by expressing w in terms of t and…

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Q: (b) Find all solutions to the system of linear equations in x, y, z which has augmented matrix 1-2…

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Q: 2. Setup a double integral in Cartesian coordinates that will give the volume of the solid bounded…

A: This is a problem of multi-variable calculus.

Q: Angela currently owes $6,000 to a friend who is charging her interest of 2.80% p.m. She is required…

A: Given information Value of loan today=$6000. Rate r=2.80% p.m=0.028 p.m Let us assume the equal…

Q: syste 2x₁ + x₂ 3x3 = 4 + 2x3 = 10 4x1 -2x₁ + 3x₂ - 13x3 = -8 t is the characteristic of the given…

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Q: The value of the triple integral where E is the region inside both x² + y² + z² = 36 and -√√3x² 3x²…

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Q: 16 3. The value of 9 B) 4. The range of the function h(x)=0.5f(-x)+2 where f(x)=4* is: A) {y=R|y>2}…

A: 3. We want to find value of 169-0.5 As 169-0.5 = 9160.5 = 916 = 34 Hence Answer: A)   34

Q: 6. Find the units' digit of 202220212020

A: We will use the following points to figure out the units digit in this question: Let's assume a…

Q: Use a triple integral to determine the volume V of the region below z = 6 - x, above z = -2√√x² + y²…

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Q: If  d1−→+d2−→=5.0d3−→,   d1−→−d2−→=1.0d3−→ and  d→3=1.6î +5.4ĵ , then what are (a) the x component…

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Q: Find a solution to the system 3 1 [] D-640 = 1 by solving the IVP with initial condition = 3 -1 x(t)…

A: Solution

Q: 1 find a- w = +y b- w = tan-¹2 az w a²w ах дуа

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Q: The following is the data of inflation rates in th

A: Given,   Year Inflation  rate 2019       2.48% 2017      2.85% 2015     0.67% 2014…

Q: 5) Use Intermediate Value Theorem to explain why the function has a zero in the given interval.…

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Q: Use Method of Variation of Parameters: [D²-8D+ 16]y = e4x sec²x

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Q: 8. Find all values of (a) 212. (b) (-1). 6

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Q: Solve for the following ODE problem using Laplace transform y" + 2y' + 5y = 50t - 100 y (2) = -4 and…

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Q: Find a, b and c so that the quadrature formula has the highest degree of precision [ f(x)dx = af (1)…

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Q: 2. The height, h, in meters, of a car above the ground as a Ferris wheel turns can be modelled using…

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Q: Let C be the curve connecting (0,0,0) to (1,4,1) to (3,6,2) to (2,2,1) to (0,0,0) Evaluate •√(x² (x…

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Q: (ii) Prove the identity (2 – 2 cos 0) (sin 0 + sin 20 + sin 30) −(cos 40 — 1) sin 0 + sin 40 (cos 0…

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Q: Use Intermediate Value Theorem to explain why the function has a zero in the ga f(x)=x2 fo. 11 ace…

A: The given function f(x)=x3+2x-2 the given interval is 0,1 according to the intermediate value…

Q: Find the mean and variance of the continuous random variable X with probability density function…

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Q: 5. (a) 1 6. (a) The amplitude of the function y=4sin(x+ë)+1_is (b) 4 (c) 5 The horizontal…

A: The vertical shift in the graph of y=f(x) is represented by the transformation function: y=f(x)±n.…

Q: Find the Taylor series of f(x) at the given value of a a... £6x) ....... b. f(x) = cox az ·A=.-.1.…

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Q: 31 Let F be a field and let f(x) in F[x] be a nonconstant polynomial. Let K be the splitting field…

A: K is splitting feild. K=F(a1,a2,.......an) for ai roots for polynomial over F  we can prove it for…

Q: A B 3x-1 (1-x)(2-3x) in the form + - x 2-3x, where A and B are integers. (b) (i) Express 3x - 1 (ii)…

A: Binomial expansion

Q: 1 Consider The system

A: Introduction: In linear algebra, eigenvalues are related to eigenvectors. In the analysis of linear…

Q: Evaluate.. L Power series X->>> im sinx-tanx X M

A: Limit: A limit is defined as a real number that a real valued function approaches when the real…

Q: b) A= 43 34 4 23 3 4 12 23 32 21 3 32 43 3 4 b 1 1 -1

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Q: 8) An airplane is on a heading of 065° at 350 km/h and an 75 km/h wind is blowing from 310⁰.…

A: 0

Q: 3. y = (1 + tan² (12))'

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