If I have a function that is one-to-one but not onto (e.g., f(x) = e^x) why does this not contradict the Rank-Nullity Theorem?

Q: The radius of a circle is 16 in. Find the circumference to the nearest tenth.

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Q: 1.1. s. Find the general solution to each of the following differential equations. Write the…

A: Partb Consider: y'+y2sint=0⇒dydt+y2sint=0⇒dydt=-y2sint⇒dyy2=-sint dt

Q: 3. Show that [(pv q) ^ (p →r) ^ (q→r)] →r is a tautology using logical equivalences.

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Q: Suppose denotes an equivalence relation on a set A and a, b E A. Then a b if and only if anb=0.

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Q: Hello, can you make the solution handwritten? I dont understand the text you type, its complicated.…

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Q: 2. Express each statement as PAQ, PVQ, or P. Write what P and Q are. (a) The number 8 is both even…

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Q: j. 2xcos2x - (x - 2)² = 0, [3,4]

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Q: 6. Sketch a possible graph of a quadratic function, whose discriminant is 0 and its graph opens…

A: The given problem is to sketch the possible graph of a quadratic equation, whose discriminate is 0…

Q: Problem 2: a. Find the differential equation by eliminating the arbitrary constants of the family of…

A: a)

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Q: Solve the linear programming problem. Maximize P=10x+65y Subject to x+3y ≤ 18 xy 20 What is the…

A: The Given problem, P=10x+65y subject to x+3y≤18x,y≥0

Q: Define the sets A, B, C, and D as follows: A = {-3, 1, 6, 7, 10} B = {-10, -5, 1, 4, 6} C = {x ∈ Z:…

A: Given: The sets are: A=-3,1,6,7,10B=-10,-5,1,4,6C=x∈Z: x is oddD=x∈Z: x is positive To find: The set…

Q: 2. (x-yesc²2-x cot)dx + (xcsc²2) dy=0; y(1)= =1/44

A: Given: The equation is x-ycsc2yx-xcotyxdx+xcsc2yxdy=0. The given condition is y1=π4. To find: The…

Q: Interpolating the function f(x) = 1+25 across the interval [-1, 1].

A: Introduction:             By using related known variables to predict an unknown price or possible…

Q: Let v and w be nonzero vectors in R³ such that the equation XXV = W is satisfied by at least seven…

A: Given v and w are nonzero vectors in ℝ3 such that x×v=w is satisfied by at least seven distinct…

Q: Find the centroidal coordinates of an area bounded by the following curves: y = 4 X = 20 y² = 4x

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Q: Question 1 Outpatient clinics are hospital clinics that have appointments for patients who visit the…

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Q: 1. xtan’ydx+(1+Và d =0

A: Given , xtan2y dx+1+xdy=0    …………………1

Q: Using differentials, approximate the change in length of the space diagonal of a parallelepiped of…

A: Here we will use total derivative for approximate change  in a function  Approximate change in a…

Q: Solve the 1. following differential equation. (x + sin y) dx + (x cosy-2y) dy=0

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Q: Identify whether the limits of the following does exist or not. If yes, find the limit and if not,…

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Q: Let N, H, S, D, R, J, and B be the propositions: N: Mr. Smith is the brakeman's next-door neighbor…

A: Given: N, H, S, D, R, J, and B are the propositions: N:  Mr. Smith is the brakeman's next-door…

Q: ..] Find the general solution of each of the following differential equations. t2 y + 3ty (sin t)/t,…

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Q: What is the advantage of a Vernier Caliper over a meter stick in measuring the diameters of…

A: Introduction:           A calliper having a vernier scale is known as a vernier calliper. Vernier…

Q: 2 1.60 A function f(x)=3* + 3 ..3x + 4 9 8 3x + · 3* + ..., defined in the set R, is given, and the…

A: To solve this problem we use a geometric series formula.

Q: Find the centroidal coordinates of an area bounded by the following curves: y = 4 x = 20 y² = 4x

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Q: 8 225x3 49x

A: find I=225×x349×x solution I=225×x249  =25×25×x27×7

Q: Find an explicit solution of the given initial-value problem. 8(x²+1), x(1) x() = 1 4 X = dx dt =

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Q: 1. x tan’ ydr+(1+Vx)dy=0

A: Given differential equation  x tan2y dx +1+xdy=0

Q: True or False: Let A = {a,b,c} and B = {d,e,f}. Then the following set is the rule for a function…

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Q: Let AEM (3, R) be invertible. Consider the system of linear equations (x y z) A = (7 10 14). If it…

A: Properties of matrix  AA-1=A-1A=IAI=A=IA

Q: Use De Morgan's laws to express a negation for the following statement. Assume x is a particular…

A: De Morgan law     (A U B)' = A' ∩ B'

Q: MODULE 2. ASSESSMENT I. Express each of the given sentences using set notations or functions. 1. Set…

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Q: 2. Determine one real root of h (a) = ln(²_) = -2.5 between -0.8 and -0.3 accurate to 2 significant…

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Q: Plz solve exactly i need exact soloution correct answer plz

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Q: Suppose that fex, & C² [0, 1], fixo Lo at f fox dx fill L 0 Prove that

A: What is Antiderivative: In calculus, a differentiable function F whose derivative is identical to…

Q: 14,6-6324

A: 146 - 624=146 - 64×6=146 - 64×6=146 - 6×26=146 - 126 =(14-12)6 (by distribution property of real…

Q: Using the indicial notation, show that: a. (āx b) a = 0 b. c. div(curl v) = 0 curl Vu = 0 for any…

A: To prove: (a) (a¯×b¯)·a¯=0. (b) div (curl v¯)=0. (c) curl (∇u)=0. As per policy, only the first…

Q: Problem 1: Using differentials, approximate the change, in terms of , in the total surface area of a…

A: Given that r=3,h=5 changes with respect to time t , in radius is drdt=0.2  and changes with respect…

Q: Express 4 as a linear combination of 72 and 104. Find x and y such that 4=72x+104y

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Q: In Exercises 11-14, find the value(s) of h for which the vectors are linearly dependent. Justify…

A: What is Linear Independence: A set of vectors is said to be linearly dependent in the theory of…

Q: Solve the following LP by using Excel. State the Optimal Solution and the Objective Function Value.…

A: Given: The given details are The minimize cost, ⇒6X+5Y And the subject, 5X+3Y≥40 4X+5Y≥36 X-Y≤0 2X≤6…

Q: 2. Consider a rule r that takes as input any integer z and outputs . Is r a function? Why?

A: What is Function: Function is a mathematical term for an expression, rule, or law that establishes…

Q: 1) Chela wants to determine which electrical company would be better for her household. The first…

A: The main objective is to compare the two companies charges.

Q: In the xy-plane, the line tangent to the graph of 2 x² + xy + y² = 3 at the point (1, 1) has a slope…

A: Given equation is  x2+xy+y2=3  we need to find slope of the graph at (1,1)

Q: Fill in the missing element of B such that A = B. A = {7, 19, g, #, 2, 4, &, f, 17, 1, k} B = {#,…

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Q: (3) The distance of a particle from a point O at time t seconds is given by s = 2t³ - 27t² + 108t -…

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Q: 19. 1(s²+1²) ds-s(s² - 1²) dt = 0.

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Q: Consider the ellipsoid +²+3. (a) Carefully graph the ellipsoid. (b) The point (-2, 1, -3) is on this…

A: The equation of a plane passing through the point: x0, y0, z0 is ax-x0+by-y0+cz-z0=0. Here, a, b, c…