Prove: If a, b and c≠0 are integers, then a|b if and only if ac|bc.

Q: The average of two numbers is 42.25, and their product is 1647. What are the numbers? Enter them…

A: Given average of two numbers a and b is 42.25 Product of two numbers a and b is 1647 Average of a…

Q: Let F be a field of 4 elements and let f(X) e F[X] be an irreducible polynomial of degree 4. How…

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Q: A component has the following linear hazard rate, where t is in years a(t) = 0.4t, t2 0 a) Find R(t)…

A: Given: λ(t)=0.4 tt is in years

Q: 7. Given the following differential cquation: 2y" =y' -x, y(0) = 0, y'(0) =1. Find the value of y at…

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Q: 3. Prove the following using the epsilon-delta definition of a limit. 1 c. lim = 0 X→+o x-

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Q: Find the Lebesgue integral over R for the following function. 4-r, rE(-2, 1] 1+2, rE(2,4] 0,…

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Q: Find the solution to the initial value problem (1+ a®)y/ + 9®y = 9a? subject to the condition y(0) =…

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Q: Calculate the Taylor polynomials T and T3 centered at a = 3 for the function f(x) = x4 – 5x. (Use…

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Q: Use the substitution x = e' to transform the given Cauchy-Euler equation to a differential equation…

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Q: 4. Let X be the set {a, b, c, d, e} and Y be the set{g,h, i,j,k}. A description for the functio f:X…

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Q: 1. Draw a sketch of the cylinder z= ==V36 – 4y2.

A: Given: z=1336-4y2

Q: -3 -10 1.5 -2 18.5 ミ= ÿ = -5 -9 7 Use the Gram-Schmidt process to determine an orthonormal basis for…

A: Given vectors are x→=−3−1−40, y→=−10−2−51 and z→=1.518.5−97. We have to find an orthonormal basis…

Q: Suppose that liquid flows into a tank at a variable rate of q(1) litre per second. It can be shown…

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Q: Q3: Approximate the integral using the trapezoid rule with 5 partitions. cos x xp: Vx2 +1 Use n =…

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Q: Use the bisection method to approximate the root of f(x)=2x²-1 in the interval [0, 1]. Let E= 0.1 be…

A: To find the root of the given equation with the help of bisection method .

Q: 1. Using a Maclaurin series, evaluate the integral shown below to an accuracy of 0.0001: sin x – x…

A: To evaluate , I = ∫01sinx - xx2dx

Q: WHICH OF THE FOLLOWING ARE DISCRETE PROBABILITY DISTRIBUTION? IF IT IS NOT A DISCRETE PROBABILITY…

A: Solution: Probability function is a function which assigns probabilities to the values of a random…

Q: Find AB such that [3 1 21 T-1 A = 2 1 2 and B =|4 [1 2 2] -2 -5]

A: The solution is given as

Q: 1. Given the function f(x) = (=) %3D (a) Find a power-series representation for f(r). f(x) da = n(n…

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Q: Explain why S is not a basis for R². S= {(-4, 3), (0, 0)} O is linearly dependent. s does not span…

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Q: Q/Find half - range sine and cosine expansions of each of the following functions : 5 f(t) = t 0<t<p

A: We have a function , ft = t   , 0 ≤ t &lt; p We know that , half range cosine series for ft is given…

Q: for 0<t <2 Q8. Find the Laplace transform of the periodic function f(t)= 1 for 2<t <4|

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Q: 2. Use the Mean Value Theorem to show that f(r) = 2r sinh(r - 1) + 2" – r %3D has a critical number…

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

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Q: Calculate r'(t) and T(t) and evaluate T(1). r(t) = (6 + 7t,12,5 – 1²) (Give your answers using…

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Q: 7 3m converges or diverges. If it converges, find its sum. Determine whether the series m=2 Select…

A: The given series is ∑m=2∞73m.

Q: Show validity: Vxр (х, f (x)). Vx3yp(x, y)

A: Please check the answer in next step

Q: Draw the conclusion from the following premises using a formal proof (Rules of inference). • If the…

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Q: Consider the following. W = {(5t, t): t is a real number} (a) Give a geometric description of the…

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Q: dy - (x — у +1)dх 3D 0

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Q: Given we Kow Polo) = 1 ParE) = e df Pice) = cde'e-dt %3D what is the differential eguation to e…

A: We are given the following.               P0(0)=1P0(t)=e-λtP1(t)=λt1e-λt That is,…

Q: Find a formula in terms of k for the entries of Ak, where A is the diagonalizable matrix below. 17…

A: The solution is given as

Q: Make a comparison between Euclidean and Projective Geometry. Present your answer in a table.…

A: Given, Table to fill on the basis of "Quantities not preserved" and " Transformations" for Euclidean…

Q: f(x) = e2* if x> 0 Q5. The Fourier transform of the function: 0 if x<0]

A: We have given a function ,  fx = e-2x , x &gt; 00        ,x &lt; 0 We need to find Fourier transform…

Q: 3. Evalwate (5 B)" if : 3 4 -3 ; B= -5 5-1 4. Conmuk

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Find the distance from the point P(-3, 1,4) to the line through A(1, 1, 0) and B(-2, 3,-4).

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Given, A=( 1,1,0 ); B=( -2,3,-4 ); P=( -3,1,6 )To find: Distance from point P to the line through A…

Q: Answer the question below: Do not evaluate The student should setup the iterated double integral…

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Q: (-1)"x2" (2n)! +00 1. For all x ER, cos x = Σ n=0 a. Find a power series that is equal to x cos(x)…

A: We have to find power series.

Q: Consider the quotient ring Q[x]/ (a) Give an example of a zero divisor in this ring. Give the…

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Q: Find the domain of f and the intercepts of the graph of f.

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Q: Denote by C[0, 1] , the space of all continuous functions defined on the unit interval [0, 1]. Show…

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Q: Consider the functionf(x, y) = 7x? – 7y² subject to the condition x + y = 36. %3D Use Lagrange…

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Q: for 0 <x < 4, 4 - x Let f(x) = {0 for 4 < x < 5. Compute the Fourier cosine coefficients for f(x).…

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Q: I. Find the values of x1, x2, x3 in the system of Linear Equations 2.x, – 6x2 – x3 = -38 | -3x, – Xz…

A: The given system of Linear equations are  2x1-6x2-x3=-38-3x1-x2+7x3=-34-8x1+x2-2x3=-20 To solve…

Q: x + 2y + z – t = 5 3 ,* + y+ 2z + 2t = 8 2 4x + 4y + 3z + 4t = 22 1 x + 5+t= 3

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Q: Let 7,V be a projection af the Vect or space. Accordling to this: Show that every Xe Im (T) for…

A: The given problem is related with projection. Given that T is a projection of the vector space V .…

Q: What two months would the price land on the slanted midline?

A: Here is the actual graph of the price and the midline.

Q: An inverted pyramid is being filled with water at a constant rate of 25 cubic centimeters per…

A: Given: Height of the pyramid=9 cm Length=width=6 cm To find dhdt at h=5 volume=13lbhSince…

Q: Find the volume of the solid that results when the region enclosed by y = Vr, y = 0, and r = 81 is…

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