Let f: S¹→ S¹ be a continuous function. Proof or disprove the following statements : a) f has a fixed point. b) Iff has one fixed point, then f has two fixed points.

Q: A 50 gallon tank initially contains 20 gallons of pure water. Salt solution, at 0.5 lb/gal, begins…

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Q: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

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Q: Solve the Neumann problem for the wave equation on the half-line 0 < x < x.

A: Consider the wave equation uxx-c2utt=0 for 0&lt;x&lt;∞ ux,0=ϕxut0,t=ψt , x&gt;0ux0,t=0, t&gt;0 Using…

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Q: a) What is the voter population in District 4 ? ________________ b) How many potential voters do…

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Q: Problem I Let f: R³ → R2 be the function given by the formule ([:]) (a) Find a formula for the…

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Q: Find a basis for the subspace (X1, X2, X3, X4) of V= R4: X1-2x2+3x3-4x4 and give its dimension.

A: Given , subspace x1, x2, x3, x4 of V=ℝ4: x1-2x2+3x3-4x4 Let ξ=a,b,c,d∈V Then a,b,c,d∈ℝ and…

Q: K / / / _|_—- ---ا_ ---ا_ ---ا۔ ---ا۔ --ا۔ -دار --/110 --/|\\ ///|\\ //||| |||||||||\\\\ \\\\||/| لد…

A: From the slope field, we can see that slope field is everywhere horizontal for k=1 and k=2. Hence…

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Q: 2) Let A be Compute: tr(AA) 51 4 1 T (iv) (A^¹)" (v) AA² (vi)

A: We have to solve given Questions.

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Q: If f(x) is a polynomial function satisfying sox-s()-500+ s() = f(x) + f(-) and ƒ(4) = 65, then find…

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Q: The triangular region shows the number of possible ounces of pepperoni slices, x, and the number of…

A: x---------&gt; the number of possible ounces of pepperoni slices y--------&gt; the number of…

Q: (a) Solve: 2611 = 605 (mod 2021)

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Q: Find the particular solution of the linear first order ODE: (4+ sine*)y' = e* (6 sec² e*- y cos e*);…

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Q: Show that day) = So, x** 0₁ X=Y. defines a metric on X₂

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Q: r(t) = 4 + sin(0.263t+4.7) + cos(0.526t+ 9.4) Here, t measures time in hours after midnight on a…

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Q: Find the coordinate vector of p relative to the basis S = {P₁, P₂, P3 } for P₂. p = 15 - 20x + 6x²:…

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Q: Problem 1. Suppose you are a two-dimensional being, living on a sphere of radius R. 1. Show that if…

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Q: The label on a bottle of medicine reads "Each 5 mL teaspoonful contains glucose, 1.87 g; levulose,…

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Q: Which is more economical: purchasing the economy size of a detergent at 4 kilograms for $4.15 or…

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Q: Determine whether (5,0) is a solution of the system: 2x-3y = -4 -x+ 5y = -8 Is (5,0) a solution of…

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Q: A custom guitar shop sells two types of guitars: electric and acoustic. The creation process of each…

A: Given: A custom guitar shop sells two types of guitars: electric and acoustic. The creation process…

Q: Problem II Find the inverse of the following matrix. 1 1 1 1 1 1 1 1 2 1 0-10 2 100 -1 20 21. 25.…

A: Note:-Our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: TEST THE EXACTNESS OF THE ODE (2x +F) ckx + (x+2F) df = 0

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Q: 2.5 (a) Prove that if x, y is a solution to ax+by = d, with d= gcd(a, b), then for all c Z, b x² = x…

A: (a) Let x,y is a solution of ax+by=d with d=gcd(a,b),  To prove: x'=x+c·bd , y'=y-c·ad is also a…

Q: A quadratic function f is given. f(x) = x² + 4x - 1 (a) Express fin standard form. f(x) = (b) Sketch…

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Q: A department store has a sale on snow blowers advertising 15% off all items in stock. You receive a…

A: The answer is NO. Because the second discount will be on the discounted price after first discount.

Q: 1. By minimizing the sum of the squares of the vertical distance between the line and the points,…

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Q: Let p be an odd prime d (p-1). Then in every reduced residue p there are exactly o(d) numbers a such…

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Q: Use Lagrange multipliers to find a vector in 3-space whose length is 5√3 and whose components have…

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Q: A first order linear equation in the form y + p(x)y = f(x) can be solved by finding an integrating…

A: It is known that:  ∫exdx=ex+C∫xndx=xn+1n+1+C

Q: Find an equation for the tangent plane and parametric equations for the normal line to the surface…

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Q: 2.15 For what values of n is (n) odd?

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Q: Show directly from definitions that if f(x) and g(x) are real func- tions, bounded on [0, 1], and so…

A: Given: limx→0+f(x)=2 and limx→0+g(x)=3 To show: limx→0+f(x)·g(x)=6

Q: Consider the the linear maps ƒ : R² → R² and g : R² → R² given by f((x, y)) = (x − y, 2 + y) and…

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Q: Q13. Convert the following hexadecimal number to its corresponding decimal representation: (2E4A2)…

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Q: Graph 2 + 4y = 8. +Move -8 -6 Line $ -2 0 4 -4 -6 -8 Undo Redo 4 6 x Reset

A: Sol:- x-intercept is a point on the graph where y=0Given :-x+4y = 8

Q: Suppose water is leaking from a tank through a circular hole of area A,, at its bottom. When water…

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Q: Semi transverse axis of hyperbola is 5. Tangent at point P and normal to this tangent meet conjugate…

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Q: 1. (x+y)dx + xex/ydy = 0

A: Given that           (x+y)dx+xexydy=0xexydy=(x+y)dxdydx=-(x+y)xexy Now put  y=vxdydx=v+xdvdx

Q: Prove that there is no 2 x 5 standard generator matrix G that willproduce a (5, 2) linear code over…

A: Let C be a 5,2 linear code over Z3 such that it can detect all possible triple errors. Then the…

Q: What is the surface area and volume of cylinder with a diameter of 24 in. and a height of 20 in.

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Q: N-1 Σe²rijk/N = 0 j=0 when 0 <k < N. 3 Exercise 7. (a) Equation (3) does not include the case k = 0.…

A: As per the question we are given a partial sum involving the exponential of complex number sequence.…

Q: Let o an be a series of complex numbers. Prove that if the series is abso- lutely convergent, then…

A: Let ∑n=0∞an  be a series of complex numbers. We have to prove that if the series is absolutely…

Q: Find the period of (i) f(x) = sin x + {x/3}, where {.} represents the fractional part. (ii) f(x) =…

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Q: Consider the initial value problem below to answer to following. a) Find the approximations to…

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Q: Graph the function ƒ(x) = sin 2x + cos 3x.

A: A function is said to be a real valued function if the function assigns the real numbers to each…

Q: 30.2 kg- 9

A: Since we know that when quantity is in kilogram then we can convert in grams and vice versa. Since…