4) If X is a topological space and ffn X→ R are continuous. Show that both min fi and max1 fi, defined by the equalities (1), are continuous.

Q: The auxiliary equation of  of  y'''-4y''-4y'+16y=0  is r^(3)-4r^(2)-4r+16=0  . The auxiliary…

A: Given that fr=r3-4r2-4r+16, r∈3,6

Q: Given the parametric equations below, eliminate the parameter t to obtain a Cartesian equation. 0 <…

A:

Q: Let u = (4, 1, 5), v = (2, 1, 3) and w = (-a, 2, a). (a) Find a vector of length 6 in the opposite…

A:

Q: Calculate the flux of the vector field F (yz, ay, 3) through the elliptical cone S given by the…

A: Given : Vector Field F→=yz , xy , 3 and elliptical cone S are given by equation 25x2 +y2=z2 where…

Q: 2. Find the LU factorizations of and 20 5 2 -6 3 -13 -3 4 9 16 17 2 4 -6 2 13 9 دن و ان 5 4

A:

Q: (a) Which rules are broken if we keep only the positive numbers x &gt; 0 in R 1 ? Every c must be…

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

Q: Let S and T be sets of real numbers, and define S + T to be {x + y: x ∈ S and y ∈ T}. Show that if S…

A:

Q: p^2 = 26 has no rational solution

A:

Q: graph the function with a domain and viewpoint that reveal all the important aspects of the…

A: The given function is f(x,y)=x2+y2+4x-6y. to find: the domain of this function. To Sketch: The graph…

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT 4. One of the ends of a line segment of length equal to 4 is…

A: 4. Given :- One of the ends of a line segment of length equal to 4 is the point A(4,1); if the…

Q: For each of the following sequences, determine whether it is convergent or not. In case of…

A:

Q: What is the inverse of the function? 2x-1 ƒ(x) = ² = = = =

A:

Q: A tank holds 2000 liters of water in which 400 grams of salt have been dissolved. Saltwater with a…

A:

Q: Prove that the following statements are true (7) or false (F). (let log n = log₂ n). You must define…

A:

Q: balance method to calculate interest. The monthly interest rate is 2.5% of the average daily…

A: Note: as per the rules we can solve only 1 at a time

Q: S = 3 0.4 0.2 0 -0.2 Submit Answer to S 3s 5s 7s 9s Consider the function below when answering the…

A:

Q: Let u = (4, 1, 5), v = (2, 1, 3) and w = (-a, 2, a). (b) Find value(s) of a for which the angle…

A:

Q: Given the system of equations 5x+16y+10z = 45 3x-2y+7z=17 5x+y+3z=9 Find the fourth iteration value…

A: Given : System of equations  5x + 16y +10z=453x-2y+7z=175x +y+3z=9 To Find: The fourth iteration…

Q: Consider the DE dy/dt = ((y −3)^(2/3))/(t −2 ). At each initial condition, determine if the…

A:

Q: A fossilized bone is found to contain one-hundredth the original carbon ratio. Estimate the age of…

A:

Q: 1 Suppose that at t 4 the position of a particle is s(4)-8 m and its velocity is e(4) - 3 m/s. (a)…

A: As multiple questions are posted and it is not mentioned that which specific one to be solved, the…

Q: Hannah can paint a room in 15 hours. Destiny can paint the same room in 9 hours. How long does it…

A: Here we use the formulae, Time (taken for both) = Total work / capacity…

Q: What 3 by 3 matrix E21 subtracts 4 times row 1 from row 2? What matrix P32 exchanges row 2 and row…

A:

Q: Prove the following statements by contradiction. Theorem. (a) There do not exist integers x and y…

A: Here we have to prove the following statements by using contradiction. (a)  There do not exist…

Q: Find the products AB and BA to determine whether B is the multiplicative inverse of A. 12 [3²]. -[ 위…

A:

Q: Use the information given in the figure below to construct a mathematical model for the number of…

A:

Q: Use the extended euclidean algorithm to find a solution to the following modulo constraints. • x ≡…

A:

Q: A store owner want to develop a new snack mix by mixing chocolate and trail mix. How many pounds of…

A: Let x pound of chocolate is mixed Given 21 pounds of trail mix costing $4.35 per pound is mixed. The…

Q: I. VECTORS A. Let A=(-2, 5), B=(3, -4) be vectors in R². 1. Find the magnitude and direction angle…

A:

Q: Let a1, a2, a3, · · · be a defined such that a1 = −2, a2 = −16 and an+2 = 8an+1 − 15an for n ∈ N.…

A: Given: a1=-2, a2=-16  and   an+2=8an+1-15an for n∈ℕ. By the use of strong induction we have to prove…

Q: (a) What 3 by 3 matrix E has the same effect as these three steps? Subtract row 1 from row 2,…

A: To find :  (a) What 3 by 3 matrix E has the same effect as these three steps? Subtract row 1 from…

Q: you make and explain how do you know tha is a

A:

Q: If x and y are integers such that x³ (y + 5) is odd, then x is odd and y is even.

A:

Q: Prove that for all x ∈ N, x is divisible by 4 if and only if the number given by the last 2 digits…

A: Soln) Let x be a natural number. Then we can write x as: x = x0+10x1+⋯+10nxn Since 102=4⋅25 ≡ 0 mod…

Q: 4 1 An object is traveling at a steady speed of 95 mi/h. How long will it take the object to travel…

A: speed=distance travelled Time taken 1 hour=60 minutes abc=ac+bc

Q: Find the convolutions of (²71) with (²1) assuming that the outsides are zeros.

A: Given: Two matrices 2111 and 2110To find: Convolution of given matrices.

Q: Find the particular solution of the differential equation satisfying the initial conditions y(1) =…

A: The given initial value problem x2y''-9xy'+24y=2x6, x&gt;0 with the initial conditions y1=2, y'1=1…

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT The extremes of the diameter of a circumference are the points…

A:

Q: Solve the given equation.. (x + 2)sinydx + xcosydy=0 a. b. C. d. x²exsiny = C e. x²excosy=C O O a b…

A: Given differential equation x+2sinydx+xcosydy=0

Q: Prove: If A is an m × n matrix and the column vectors of A span Rm, then A has a right inverse.…

A: let A be an m x n matrix and Column space of A is ℝm. To Prove: A has a right inverse.

Q: x² 3xy + y² = B Find the 3rd iteration value of y using the successive displacement method with an…

A:

Q: Questions: 3 -1 7 3 9) -2 2-2 75 -59 3 34 -2 6 6 3 7) [1] Find p and q such that Nul(A) is a…

A:

Q: Prove 2 {y } = 5 2 {y} -y (o) the U definition of Laplace integral definition using transform: 2 {F…

A:

Q: 6. The largest value obtained by 3 cos² x + 2 sin x + 1 equals A. B. C. D. 11 5 13 3 12 5 14 9

A:

Q: The graph shows a region of feasible solutions. Use this region to find maximum and minimum values…

A:

Q: The entries of A are aij. Assuming that zeros don't appear, what is(a) the first pivot?(b) the…

A: "Since you have posted a question with multisubparts, we will solve the first three subparts for…

Q: If you take powers of a permutation matrix, why is some pk eventually equal to I? Find a 5 by 5…

A: Permutation matrix: A square matrix which has exactly one entry equal to 1 in each row and each…

Q: Find the general solution of the given differential equation 2y" + 3y + y = t² + 3cost O y = C1e^-t…

A:

Q: Jsing only definition of divisibility, definition of modulo, substitution, and arithmetic, prove for…

A: a ≡ b (mod m), c ≡ d (mod m) ⇒ m | a – b and m | c – d ⇒ m | ((a – b) + (c – d)) ⇒ m | ((a + c) – (b…

Q: Let P(x) = x¹ + (2 − i)x³ + (1 − 2i)x² + (2 − i)x − 2i. Find all real values of a such that when the…

A: