Show the equivalent of (2x+3y) (4x² - 6xy +9y²) + (2x − 3y)(4x² + 6xy+9y²) 16x³ for x # 0.

Q: C. Write down a sequence for the number of shapes/dots in each pattern. Explain how to obtain the…

A: Sequence: A sequence is defined as the list of numbers that form a pattern.

Q: (d) Therefore n = s(0), because ... (e) Therefore n = 1, because ...

A: d) we know that s is injective function .therefore c implies d, Because if f is injective and f(a)…

Q: Question 4. A circle centered at (0,0) with radius one is revolved about the line x=3. The solid of…

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Q: Decide whether each of the following statements are true. (a) If a, b, m, n = N and a | m and b | n,…

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Q: what is 27=7+x

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Q: Evaluate the following integrals by first changing to spherical coordinates. 10. ₂²x²+² z dz dx dy

A: Given integral I=∫-22∫04-y2∫x2+y22z dz dx dy Evaluate the following integrals by first changing to…

Q: Let f(x) = 6x² + 2x³. Select all intervals where f(x) is INCREASING, (3) (0, ∞) (,0) (-∞, -3¹²¹)

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Q: 1. Let A = {0, 1,2,3,4,5). Write out the relation R that expresses > on A. Then illustrate it with a…

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Q: Indicate whether the statement is true always, sometimes, or never. Justify and provide example or…

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Q: QUESTION 4 ze² ¹ Joz dz, where the positively oriented C is given below. Write your answer 22² +8…

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Q: 3 show that if lin N-)P number . an = a, then lim 29 = 2a for all real 3-)

A: Given : limn→∞ an=a To prove : limn→∞  λan=λa.

Q: Determine whether the following statement is true or false: Given matrices A of the size 4 x 4 and B…

A: Determine whether the following statement is true or not : Given matrix A of size 4×4 and matrix B…

Q: Compute the following integral by hand, using an appropriately chosen contour integral in the…

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Q: Question 2. For what values of p is the integal 1 x(lnx)p convergent?

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Q: Q8. Suppose 8₁ = 4 and g₂ = 1. The rest of the terms in a recursive sequence are given by the…

A: Here given that g1=4 and g2=1  The rest of the terms in a recursive sequence are given by the…

Q: 16. An offshore well is located in the ocean at a point W which is six miles from the closest shore…

A: Answer :-

Q: What is a11  for the geometric sequence with a1 = 4 and r = 4? Suppose g1 = 4 and g2 = 1. The rest…

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Q: According to the definition of half-life, half of the original amount of the radioac- tive element…

A: The given rule is for carbon dating is N(t)=N0e-t ln2h. (a) To Verify: The rule for half life of the…

Q: REASONING 5. Determine if each of the following values of x is in the solution set to the compound…

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Q: Does the graph pictured below Have an Euler circuit? Answer YES or NO in the box below. Justify your…

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Q: Find a, the average f(x) value, of the following function f(x) = Ax²-2, -1<x<1; f(x) = f(x+2) Where…

A: Given f(x)=Ax^2 -2; We have to apply the Fourier series to find the required answer.

Q: The table shows relative frequencies for red-green color blindness in one doctor's practice. M…

A: Relative frequency of male persons, n(M) = 0.515 [from the table] Total number of persons, n = 1.000…

Q: Heller Manufacturing has two production facilities that manufacture baseball gloves. Production…

A: Answer :-

Q: Use Euclid's algorithm to find gcd(340, 144). Hence find Icm(340, 144). [Show your working.]

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Q: Give an example of a function from A to B that is one-to-one. e) Give an example of a function from…

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Q: Prove or disprove: If a relation is symmetric and transitive, then it is also reflexive. Define a…

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Q: (9.1) Show that 3 ∈ Z15 is a zero divisor. (9.2) Prove that in any ring R, if a ∈ R is a zero…

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Q: (1) Prove that a sequence (fn)n converges to f in measure if and only if for every k N, lim m ({\fn…

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Q: Find an explicit formula for kth term of the sequence with these initial terms. Assume k ≥ 1.…

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Q: Problem #5: Find the work done by the force F = -7yi 8xj along one loop of the curve r = sin 90 (in…

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Q: Let S = R-{-1}. Define an operation on S by a*b = a + b + ab, a, b € S. (6.1) Show that S is closed…

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Q: Set up (do not evaluate) the iterated triple integral in spherical coordinates that gives the mass…

A: Sketch the region. The objective is to set up an iterated triple integral to find the mass of the…

Q: Solution to Part ii) of the question above is missing: [ii] Let ABCD be a tetrahedron with…

A: (ii) Given that, ABCD is a tetrahedron with vertices A(−4,1,2), B(0,2,−2), C(1,−1,2) and D(1,0,2).…

Q: Given P(EorF) = 0.56 , P(F) = 0.43 and P(E and F)=0.09 what is P(E) ?

A: Any two events E , F  The event (E or F) is the occurrence of E or F or both. The event (E and F) is…

Q: Q17B. Define the sets A, B, C, and D as shown. Find A U (B n D). A W C S C Q 3 р a g D h f B…

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Q: The series sin²(n) 3 n=1 n is divergent by comparison test divergent by limit comparison test l…

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Q: 4. Let p be an odd prime. (a) For any integer 1 <k <p-2, show that (+1) = (#¹) where k denotes the…

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Q: Suppose n € N. Let S be the following statement: If n is prime, then 2n + 1 is prime. (a) Write down…

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Q: QUESTION 1 1 Consider the integral I = dz, where C' is the circle |z| = 3 taken in the…

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Q: Select 2 choices. The cost (in dollars) of a custom-made sweatshirt is represented by 3.5n+29.99,…

A: If a function y=f(x) is given then y is the value of the function and x is input for the function.…

Q: Consider the matrix A = 10332 -3 3 1 3 1 10 06-1 4 -2 1 0-4-2 Its rank is 634215 → and its nullity…

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Q: Find the inverse Laplace transform f(t) = L−¹ {F(s)} of the function F(s) You may use h(t) for the…

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Q: 8. Test the validity of the following arguments using: 8.1 Flow of the argument, 8.2 By using truth…

A: This is a question of logic.

Q: (1) (a) Find the equations of least four different level curves for the surface 2= = f(x,y), f(x, y)…

A: The given function is z=f(x,y), f(x,y)=xy. (a) To Find: four equation of level curves. To Draw: The…

Q: Two classes take the same examination and the grades are recorded in the table below. The table…

A: Number of students   Grade 9 AM class 10 AM class F 9 13 G 16 19 C 22 10 B 10 21 A 6…

Q: 6. You have a device that monitors the sound level of a conversation located 1 meter away. The…

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Q: Solve the differential equation y'= y + sint gro)=1

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Q: Find the Fourier series of f(x) = |sin x| on the interval [−π, π]. Draw a sketch of f(x).

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Q: Solve the linear ODE with initial values x'(t)+x(t)=f(t), x(0)=0, where f(t) = {1,² (1, in 0 ≤ t ≤ 1…

A: The given equation is  x' t+ xt = ft, x0=0 where ft=1, 0≤t≤10, 1&lt;t

Q: i. Using Arithmetic of Limits, find limn→∞ 2n / (3n + 5). ii. Working directly from the definition…

A: The given limit is limn→∞2n3n+5 We have to find the limit of the equation and prove this limit using…