Suppose that U1, U2, ..., Un is a collection of n open sets. Prove that their intersection n(intersection)i=1 Ui is also open.

Q: Determine whether the statement below is true or false. Justify the answer. Asking whether the…

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Q: Prove the Triangle Inequality |v+w| <= |v| + |w|  (Hint: Use Cauchy Schwartz)

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Q: Provide a geometric description, including a sketch, of the image of the function f: RC, f(x) =…

A: The given function  is defined as .We know that .We know that  is a periodic function with period ,…

Q: if xzo The function f(x) = { 1 + x² if aso a) belongs to ('(R) b) has a cusp the origin at the c)…

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Q: dy Solve the differential equation (y¹ï)- da Express y¹5 in terms of ï. y15 = Check Answer 1 1+…

A: The given initial value problem is Lets use the method of separation of variables to solve it.

Q: Suppose 0 ≤ y ≤ x, and I have a bunch of x many identical grapes and a tin of y distinct chocolates.…

A: Out of n objects r objects can be chosen in ncr ways, where 0 ≤ r ≤ n.

Q: ax + by = c (Recall that solution refers to integer solutions, i.e., pairs of integers x = 0, y = yo…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Given two vectors x=[1 2 1] and y=[1 -1 0]+t[-2 1 4]. Find the value of t such that a) x and y are…

A: Given vectors are Now these two vectors will be parallel if in other words,  ,from last two ratio we…

Q: Find all of the units in Pn and verify where Pn is the power set of the set {1,2,...,n} with…

A: Find all of the units in  and verify where is the power set of the set  with addition defined as…

Q: • for any integers a, b, c, • n is not prime and p6 |n, where p; is the ith prime (i.e., p₁ = 2,p2 =…

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Q: 43. A fifth-degree polynomial function cannot have a single real zero.

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Q: Based on a grade 10 student, answer the following question: Consider the quadratic relation…

A: The objective of this question is to convert the given quadratic equation into vertex form by…

Q: Solve the system below. 2x + by + z +3y x -x 7w = 4w 3y + 2 + 5w T The particular solution is: y + -…

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Q: Let f and g be real-valued functions defined on (b, ∞). Suppose that limx->∞f(x)=L and…

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Q: Draw a sketch of the following subsets of R²:{(x, y) : x² + y² ≤ 1}

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Q: (d) AAT is 2 × 2, use the formula below for the inverse of a 2 x 2 matrix to find (AAT)-¹. (e) Use…

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Q: (3) Consider the derivative: 2xydx + (x² + 2y)dy. Evaluate whether this is a total derivative or an…

A: We will check whether the given function is total derivative or not. Consider dz = (2xy)dx + (x 2 +…

Q: 18.- Define the symmetric matrix corresponding to the following quadratic form: F(x, y, z)= x² + z²…

A: Given quadratic form isWe have to define the symmetric matrix corresponding to the above quadratic…

Q: The graph of f', the derivative of f, is shown below. Determine all possible inferences that can =…

A: From the derivative curve of the function we can say about the zeros, extreme point of f,whether the…

Q: y' = 4x - 2y + 2, y (1) = 6; y (1.5)

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Q: Let the following matrices be: [1 [3 A = 13² 2¹] A-G2)B-C-² ³- B= -1 3] - 13 10.- Obtain the…

A: To compute the expression  we need the following matrices.

Q: Express in polar form all z complexes that satisfy : 2 + 3iz = 4iz + 9

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Q: 4. Complete 3 iterations of the bisection method for x³ + 3x - 10 = 0 to find an interval of length…

A: Given function is Noted that Hence there must be a root between  .Now we calculate 3 iterations…

Q: 5. f(t)= (t -2)H(t-2), where H(-) is the unit step or Heaviside function

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Q: u: (vxw) FIND the triple scalar product and the triple vector product (xv)xw if ū = (-1,2,4), v =…

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Q: 1. Use set identities or different proof method to show that: a) (B–A)U(C – A) = (BUC)-A b) (A-C)n(C…

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Q: From the graphs given, select all graphs that represent power functions of the form yaz" (power…

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Q: Find the equation of the plane that passes through the point (1, 1, 1) and is perpendicular to the…

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Q: Use Gaussian elimination with scaled partial pivoting to solve the linear system represented by the…

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Q: Find all solutions of the system (E) of linear equations -98x + -24y + -9z = 13x + 3y + 1z = 7x + 2y…

A: The given system of linear equations are:We need to find the row reduced echelon form of the…

Q: then A(-2u - 20) = -2 ---B 5 and Au 3 Au = 2 4

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Q: If $15,000 is invested in an account for 15 years. Find the value of the investment at the end of 15…

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Q: For each problem below, set up an integral for computing the volume of the solid obtained by…

A: Consider the region in the first quadrant bounded by .To set up an integral for computing the volume…

Q: |Z| ≤ Rez+ Im z

A: We are to represent graphically the set if complex number z such that, |z|&lt; Re z+ Im z

Q: Let g:BX C- C(with BØ) be the function given by g (x, y) = y. (a) Prove that g is surjective. (b)…

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Q: 3 Sketch (by hand) the following function on the interval t € [−27,47] and find its Laplace trans-…

A: Sketch (by hand) the following function on the interval t ∈ [-2π, 4π] and find its Laplace trans-…

Q: A water storage tank has the shape of a cylinder with diameter 18 feet. It is mounted so that the…

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Q: Suppose k element R is a constant. Prove that. lim (x - - > a) k=k

A: Definition of a Limit: The limit of f(x) as x→a is denoted by limx→af(x)=L if, for every positive…

Q: Soluc the following initial veluc problems. Ef possible writo explicit solution. си sin x dx + ydy =…

A: A differential equation of the form  is a variable separable differential equation which can be…

Q: ((dvd) ← b) Ad₂

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Q: y = -1 [1]+[3 4]-K2x+y -²2] L4 0 <-y -1 -3 X -3

A: We need to find x and y.

Q: Solve: 18 || = -2 2 -3 4 -3 3 6 -3 -3 x = -19 28 12

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Q: km, k=1 m = 0, 1, 2 or 3 (these identities were discussed in class and also appear in the textbook),…

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Q: Consider the differential equation y'= y² where y is considered to be a function of x. In this…

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Q: c) Sketch w 7 using the Triangle Rule, then sketch the equivalent position vector. Make sure you…

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Q: Find the final amount of money in an account if $2,700 is deposited at 6.5% interest compounded…

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Q: Given that z²z+1=0, show that 2019 = -1.

A: Given that  z2 - z + 1 = 0 We are to show that z2019 = -1

Q: uestion 3 Let S be the solid obtained by rotating about the x-axis the region enclosed the curves y…

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Q: Ferry 7 13 16 11 62 Rental Car Train 8 45

A: A Venn diagram for  travelers are given.The aim is to find the probability that a selected traveler…

Q: Solve for x, given 2x3 + x² - 7x = 6

A: We have to find the value of x using long devision method .