A A If the incident ray on a surface is along the unit vector v, the reflected ray is along the unit vector w and A the normal is along the unit vector a outwards, express w in terms of a and v. â ŵ

Q: Assume that Achilles' speed as 100 times as fast as the tortoise's and that this animal has been…

A: Achilles' speed = 100 times of tortoise's Achilles' speed = 200 m/min So, tortoise's speed = 2 m/min…

Q: (a) Find the reduced row echelon form of the given matrix. Record the row operations you perform,…

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Q: Determine this function from R to R is a bijection. f(x)=2x+4

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Q: Evaluate the value (a) sin(2) (b) tan (5) (c) sin-¹(√3/2) (d) sin-¹(sin(¹1))

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Q: 1. Writing 5 first terms of the sequence with general term as: n² 5n' Un = sin nл + n ≥ 1

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

Q: re this sum

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Q: 4. SI. 1 2 3 4 X 0 1 2 Y 2.2 10.6 17.0 22.4 a. Use the nodes given above to set up a lagrange…

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Q: Explain what geometric problem As there local ०४ is solved here and global constraint- d

A: Please find the attached solution

Q: Use row operations to solve the system. X+ y-z=-3 2x = y + z = 3 x - 4y + 3z = -7 .... Select the…

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Q: Need d,c

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Q: Multiple Choice о O The probability of a 1 bit is 0.6; hence, the required probability is (6)¹0.06.…

A: Solution:- Option third is correct.

Q: Consider the system described by ÿ ₂ 3 7 + 2 j + 47 au + = Derive a state-space representation of…

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Q: M 1 {[1 '* . _ (w/wn)²]² + [2¢w/wn] 1/2 2 1²}' ||

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Q: An aunt wants to make a gift of $90,000.00 to their niece's for her college education on her 21st…

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Q: find x, y € Z such that 2261x + 1275y = gcd(2261,1275).

A: we want to find the greatest common factor  we will use Euclid's algorithm 2261=1275×1+986 -----1)…

Q: 3. (a) (b) Compute the upper bound of the error using Cauchy's Theorem for f(x) = sin² (r/2) with…

A: please find the attached answer

Q: particular shipment of thousands of aspirin tablets actually has a 4% rate of defects, what is the…

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Q: AN Solve the following to find one real non zero root: non-linear algebraic equation f(x) = sin…

A: The given functon is,fx = sinsecx +x3 e5xtanx -e-x To find: One non-zero real root of the  above…

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A: The number of ways r items can be selected from n different items is equal to C(n,r). The formula…

Q: the equation to the plane in the new position is ax + by ±z √√a²+ b² tan α = 0.

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Q: State A: - 6x + y = 11,600 State B: 141x+y=7,000 where x = 0 corresponds to the year 2000 and y is…

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Q: 1. Find (-1 - i)5 and express the result in rectangular form. 2. Find the square roots of 1 + (√3)i…

A: The given problem is to evaluate and simplify and express the following complex expressions.

Q: Use substitution to solve the system. 7x+9y = -24 4x - y = 17 ... Select the correct choice below…

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Q: What is the transformation given by the following matrix 1000 0 1 0 0 0 0 -1 0 0001 Reflection about…

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Q: Question 3 Assume that a sequence of integrable functions (fn)n converges pointwise to an integrable…

A: Please find the attached solution

Q: Audrey has graduated from college. She wants to rent an apartment for $400 per month. She already…

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Q: a) Three seats on the county council are to be filled, each with someone from a different party.…

A: The solution follows by using basics of combinatorial theorem. Principle of addition and the…

Q: For each of the following two LP models, respond to the following questions using graphic tools and…

A: (1) The constrain which are binding the solution is  3x+4y≤242x+y≤10x≥1y≤5y≥0 (2) The redundant…

Q: The U-Drive Rent-A-Truck company plans to spend $8 million on 280 new vehicles. Each commercial van…

A: First we find the corresponding system of linear equations and then we solve them to get the…

Q: Let a plane ax + by + cz + 1 = 0, where a, b and c are parameters, make an angle 60° with the line…

A: ax+by+cz+1=0 →1It makes an angle 60° with the line x=y=z. So we get sin 60° = a+b+c3Σ a2 or…

Q: ydx - xdy + 3x²y²e*' dx = 0

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Q: 2) Find what conditions must be placed on b, b, and b¸ in order for the 1' 2' following linear…

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Q: 2. Complete each of the following. a) Let [x] € Z/nZ. What is the additive inverse of [x]? b) Show…

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Q: Determine whether or not the following set of vectors span R³, (i) {(1, 1, 2), (1, -1, 2), (1, 0,…

A: Span of R3 .

Q: Let a, b, c E Z and n E N. Assume a = b (mod n) and b = c (mod n). Prove that a = c (mod n).

A: Suppose a,b,c∈ℤ and n∈ℕ and assume that a≡bmod n and b≡cmod nTo Prove: a≡cmod n

Q: 34 5 10 From the 5 points A, B, C, D, and E on the number line above, 3 different points are to be…

A: The answers for each of the questions are given in the next steps.

Q: Let f(x) = 424-82² + 12 Input the interval(s) on which f is increasing. Input the interval(s) on…

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Q: Cet R3 be the set of all row vectors [x, y, z]. Which of the following sets constitute a subspace of…

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Q: For any integer z, if 3 divides z2, then 3 also divides z.

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Q: Solve the solution 1. (x - y) y' - for the ff. differential y² 2y + 3x + = 0 Xx ; equations: y (1)=5

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

Q: prove that A Sub. treelong powevr 21 L droeb to H dreelans бога b of G if and is a only ; f every…

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Q: Show that the straight lines whose direction cosines are given by the equations al + bm + cn = 0 and…

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Q: c. 6-3

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Q: Task 1 using the definitions of limit and/or infinite limit show that if  limn→∞ sn = ∞,  then also…

A: If (s_n) is a sequence, then we write lim_n→∞ s_n = ∞ if ∀M >0, ∃N s.t. s_n > M ∀n ≥ N. Such…

Q: Let X = C[0,4], with the usual notation and suppose X is endowed with the norm, ||f||2 Consider the…

A: Let X=C0, 4, with the usual notation and suppose X is endowed with the norm,…

Q: 2. sin x 3. dy dt dy dx + y cos x + 2xey + y² cos (2t) = 0 4. t²y' + 2ty - y³ = 0 - (1-x²ey) dy dx…

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

Q: 5) Write the following matrix, A, as the sum of a symmetric matrix and a skew-symmetric one. 13 2 -3…

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Q: Solve 3- (1 + x)y' – xy = 1 - x x .. 2 د. علشان مایه رندار

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Q: 2. Given g(x, y) all of them. - xy x-y 1 compute all 2nd-order partial derivatives and use Leibniz…

A: Here we use the properties of partial derivatives of function to find the all second order partial…

Q: Solve the matrix equation AX = B for X. A = X= 1-2-3 3 6, B= 6 7 - 1 4 1 -1 -2

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