5. Let r,ne N. Show that the product (n+1)(n+2)...(n+r) of r consecutive positive integers is divisible by r!.

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Q: Prove or disprove that Q(√3) and Q(√-3) are ring-isomorphic.

A: Here we have ℚ-3=a+b-3 / a, b∈ℚ Also ℚ3=a+b3 / a, b∈ℚ We know that, ring isomorphism is a bijective…

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Q: Similar matrices have the same eigenspaces. True False

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Q: If A=P-¹BP then B=Q-¹AQ for Q-¹-P where A.P.B and Q O True False are square matrices of the same…

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Q: 2. For tire size P225/45R17, give the following: Width (mm): Aspect Ratio (%): Height (in.):…

A: P= tire type 225 mm = tread width ( means that car of high performance use tires with higher section…

Q: Problems 5-6: Find the derivative of the function at the given point in the direction of A. ( 5)…

A: 5. Given,            f(x, y, z)=-2x-7y+8z, (-9, -8, 5), A=3i-6j-2k.

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A: Recall: a set is a basis for V if(1) it spans V, and(2) it is linearly independent.(1) holds for β…

Q: . Function: f(x): 2x-1 (0,1) -1<2x-1<1 f^{-1}(x) = (x+1)/2 (-1,1) x belongs to the set A A={1,2,3},…

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Q: Prove that the equation ax + b = c has a unique solution where a, b, c constants and a≠0.

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Q: Problems 1-4: Compute the gradient of the function at the given point. 1) f(x, y) - 4x2-2y. (-3,-4)…

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Q: An nxn matrix is diagonalizable if it has n distinct eigenvalues. O True O False

A: In this question, we have to determine whether the following statement is true or false : "An n×n…

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Q: Find an equation of the tangent plane to the parametric surface R(u, v) = 〈(u — sin u) cos v, (1 −…

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Q: Solve the initial value problem implicitly: (cos y) y' (t) = sin² tcost, y(0)= T ==

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Q: 14. Let (S, d) be a metric space, ACS, and c E S. Prove that c is a cluster point of A if and only…

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Q: Let a and b be vectors in R" such that |la||=|b||= 2 and (a,b>=. Then ab..

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Q: Translate each argument into symbolic form. Then determine whether the argument is valid or invalid.…

A: The given argument, If he likes to eat streak, he will not go out to eat He will go out to eat…

Q: 4. Let A € Rnxn, u, v € Rn. Compute the inverse of A = 1 + uv¹. Hint: try a matrix I-auvT with a R…

A: To Find: Inverse of A=I+uvT and constraint on u and v.

Q: Find k so that the vectors u= (1,2,k,3) and v= O Ak=3 OB. k=0 OC. 1 k=1- D. None in the given list O…

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Q: give me a chart showing notice that the high and low as shown to the right what is the difference…

A: Given, The chart is  Open = 65.61 High = 65.84 Low = 65.08 Volume = 6,649,212 Avg Vol = 8,263,000…

Q: dy y dx x xy' = y + xey/x tan y dx + (x + 1)dy = 0 = + tan:

A: An ordinary differential equation is an equation containing independent variables, dependent…

Q: Using the Method of Undetermined Coefficients, determine the form of a particular solution for the…

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Q: where is the answer for 4 to 7?

A: Since you have posted a multi subparts question according to guildlines the expert has solved only 3…

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Q: Solve the initial value problem. 1 dy y cos 0 3₁ = 0 de 2 2 y + 1 = 1 The solution is (Type an…

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Q: Let W be the subspace of R5 spanned by the vectors = (1,2,3,1,2) and v= (2,4,7,2, -1). A basis of…

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Q: Consider a game in which a fair die is rolled. If the die comes up 1, the player wins $4. If the die…

A: Expected amount is mean of the distribution  So we need to create a probability distribution table…

Q: Question 3 3-1 c Let B= 0 2 0 c -1 3 с OA. c = 1 OB.c=0 Oc= ±1 Find c so that the product of the…

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Q: ← The price of a condominium is $81,000. The bank requires a 5% down payment and one point at the…

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Q: Determine the W₂ fourth root of 81 +81i in polar form. COMPLETE THE MISSING THE BLANKS FOR THE FINAL…

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Q: red and a blue die are thrown. Both dice are fair. The events A and B are defined as follows: A:…

A: Probability of the dice

Q: Problem 6. Explain why the coefficient of x'y the same as the coefficient of x'y in the expansion of…

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Q: Given the data points 0 0.25 0.50 0.75 1.0 1.25 1.5 0 -1.2233 -2.2685 -2.8420 -2.2130 2.5478 55.507…

A: As per the question we are given the following ndata table : x 0 0.25 0.50 0.75 1.0 1.25 1.5 y…

Q: f(x) is apart of a quartic family of functions. f(x) ≥ 0, -1- √5 ≤ x ≤2-√√2,-1+√5 ≤ x ≤2+√√2 .…

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Q: ind the maximum rate of change of the function f = (a + 2)yb+³ ex+xza+2 at the point (0, b+2, 3) and…

A: We have to find the maximum rate of change of given function.

Q: Question 2 ||^L,= |ª²1 ∞ 1 Selected Answer: Answers: False True False

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Q: rties described. 7. (2)-1: f'(2) = 0; concave up for all .x. 3. (-1)-0; f'(x) 0

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: 3. Use Lagrange interpolating polynomial to approximate Answer up to 5 decimal places. f(¹) if…

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Q: yy" — (y')² = y'

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Q: 1. Determine whether or not the following relations are functions. If the given relation is a…

A: we solve these  problems by the help of graphs.

Q: ASSIGNMENT NO.2 = 1. If F = 3xyi - y²j, evaluate fF.dr, C is the curve in the xy-plane, y to (1,2)…

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Q: (Yi, X1i, X2i) satisfy the assumptions. You are interested in β1, the causal effect of X1 on Y .…

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Q: (a) Let T: P₂(F) → F be the linear map T(p) = p(1). = (You need not prove that T is linear.) Find…

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Q: Let a and b be vectors in R" such that ||a||=|| b||=2 and (a,b)= — . Then ||a - b||= ...

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Q: heastern Oklahoma State University's business program has the facilities and faculty to handle an…

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Q: Let Pn = {anxn + an-1xn-1 + . .  + a1x + a0 | each ai is a realnumber}. Is it possible to have a…

A: The polynomial space is defined as follows: Pn=anxn+an-1xn-1+⋯+a1x+a0  |ai∈ℝ Check whether is it…

Q: 07. Suppose that f, g : R → R, are convex functions of one variable things. Let's define a function…

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