There are 345 students at a college who have taken a course in calculus, 214 who have taken a course in discrete mathematics, and 190 who have taken courses in both calculus and discrete mathematics. How many students have taken a course in either calculus or discrete mathematics?

Q: Use Stokes' theorem to calculate JJ (A) nds by A = 3yi-xzi+yz²k where S is the surface of the…

A: The given vector field is: A=3yi-xzj +yz2k The surface S is the paraboloid 2z=x2+y2 bounded by z=2.…

Q: An insulated heated rod with spatially heat source can be modeled with the Poisson equation. dr =…

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Q: y" - 10y' +9y = 5t, y(0) = -1 y' (0) = 2

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Q: If Col A has dimension 3, then the first three nonzero columns of A form a basis for Col A. True…

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Q: Determine h if V = 1.1535 m³ and r= 1m using Fixed point iteration on the given convergent equation.…

A: Given function is h=h3+3Vπ3r We have V=1.1535 m3, r=1 m. So we have h=h3+1.1023 For more convenient…

Q: Given the following recurrence relation, determine the first two terms of each of the two linearly…

A: Given is a recurrence relation as c2=-4c0     and     ck+2=2 ck k-4k+1 k+2 for k=1, 2, 3, ...   To…

Q: Use a degree 3 Taylor Polynomial to approximate square root of 16.2. Briefly explain your choice of…

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Q: Long-Answer Questions Important: In all proofs, for each step, you must clearly indicate whether you…

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Q: Draw the network using switches: C (AD + B).

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Q: 1. The paths of two dolphins playing in the ocean were recorded by some biologists. The first…

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Q: A furniture manufacturing company makes dining room tables and chairs. The relevant manufacturing…

A: Let x number of table and y number of chairs are made, then given LPP will be Max Z=90x+25ys.t.…

Q: Q3. Copy the graph drawn below. Sketch the graph of y = f' (x) accurately on the same page. M Part…

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Q: g (t) 3, 05. 10₁ 5 ≤ + √ 8 A 8 >

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Q: Use the method of variation of parameters to determine the general solution of the given…

A: Using the method of variation of parameters we have to determine the general solution of the given…

Q: Find the differential equation of the family of circles with centers on the line x – 2y = 3 and…

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Q: The estimated marginal profit associated with producing x widgets is given by P'(x) = -0.6x + 24…

A: The estimated marginal profit associated with producing x widgets is given by: P'(x)=-0.6x+24…

Q: Rewrite the set G by listing its elements. Make sure to use the appropriate set notation. G={x| X is…

A: Use the given information.

Q: Let Σ={a, b} 1- Find a CFG defining the language of all words that contain exactly two b's not more.…

A: Given: Let Σ=a,b.   To find / build: (1.) A CFG defining the language of all words that contain…

Q: Using the definition of convolution find the convolution of the following functions (f*g) OR f(t) =…

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Q: The definition of the Euclid Algorithm (EUCLID(a, b)) is given below. Calculate EUCLID(270,192) by…

A: calculate EUCLID270,192 by showing each step we can write 270=1·192+78192=2·78+3678=2·36+636=6·6+0

Q: Verify that the given functions y₁(t) = t and y2(t) = te³t satisfy the corresponding homogeneous…

A: Given solutions are y1t=ty2t=te3t Given differential equation is t2y''-t3t+2y'+3t+2y=7t3…

Q: ABCD is a parallelogram and M and N are the midpoints of BC and CD respectively. AM and BN intersect…

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Q: 2. Find a general solution valid near the origin: (x²+4)y" + 2xy' - 12y = 0

A: Hint: The point x=0 is a ordinary point so take the solution of the form y(x)=∑n=0∞anxn. The given…

Q: A survey of 400 small businesses indicates that 320 own photocopiers, 105 own fa machines, and 90…

A: There are total of 400 small business  320 owns photocopier 105 own fax machines  90 own…

Q: Given: x³y"" - 3x2y" + 6xy' - 12y = 2x4 + Inx, write the complementary solution in x. A. Y c₂x³ + x²…

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Q: Given f(x,y)= x / x2 + y2 + 1. Determine critical points and classify whether its a minimum, maximum…

A: f(x, y)=xx2+y2+1 Critical points of the given function can be calculated by making fx=0, fy=0 and if…

Q: QUESTION 12. | Using a Proof by Induction, prove that (2n)! is a multiple of 2+1 for all integers n…

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Q: Solve the differential equation: 2y'''+3y''-3y'-2y=e^-t ; y(0)=0, y'(0)=0, y''(0)=1

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Q: Use the binomial series to expand the function as a power series. Find the radius of convergence. +…

A: We use binomial series to expand the function as power series.

Q: (a) Find the algebraic multiplicity of λ = -8 as an eigenvalue of A. (Enter the numerical value…

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Q: Let set W ⊆ R+ such that ∀w ∈ W, w < 1000 be our Universal set. Consider set X ⊆ W such that ∀x ∈ X,…

A: Given the set w⊆R+ such that∀ w∈W, w&lt;1000 be our universal set. Consider set X⊆W such that  ∀…

Q: Let Y = {−1, 1}. Then, (1) There is no continuous function f : X → Y , where Y is equipped with…

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Q: True or False: There are infinitely many numbers in the Fibonacci sequence that are divisible by 4.

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Q: x, 0 < x < 1 1. (a) Find the sine series for the function f(x) 2 x, 1 < x < 2 (b) Sketch the graph…

A: Extended f to an odd function to get sine series

Q: The exterior wall (the gabled end of the house shown) remains to be painted. -36 ft- IT: 10 ft 15 ft…

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Q: 2. Equip C[0, 1] with the inner product (f 19) = f(x) g(x) dr. Define the func- tions fi(x) = 1,…

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Q: Evaluate [¹ ` = s+1 S s² (s+2)³

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Q: Solve the initial value problem 25y" — 40y' + 16y = 0, y(0) = 2, y'(0) = 3. y(t) =

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Q: Let G be a graph with 20 vertices and 46 edges. Suppose the degree of each vertex in G is either 4…

A: We use Handshaking Lemma.

Q: ... 1 Suppose that for i = 1,2, m the function fi is real valued on the interval [a, b] of the form…

A: As per the question we have to prove that there exists a sequence of polynomials that converges…

Q: B/ Given a polynomial function with following data point Find 0 3.6 1.5 1.8 3 1.2 4.5 0.9 6 0.72…

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Q: Evaluate the integral of 0∫3 3x3+2x+10dx a. analytically b. using Simpson's 3/8 rule with 3…

A: ∫033x3+2x+10dxApply the Sum Rule:…

Q: Let u= (1,-1,0,4) and = (1,-1,2,0). Find a vector WE R4 that satisfies - 2 w). 4u wü.v(u =

A: The explanation is as follows

Q: Five stacks of cubes are given below. umbers of cubes in the stacks are 4, 2, 6, 10-nd 8 (a) Move…

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Q: Let W₁ = (6) 0 and W₂ = 00 (a) Find a basis for W₁ (b) Show that R³ = W₁ + W₂. (c) Find a subspace U…

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Q: The relation R₁ = {(a, b) = N²: alb} symmetric. O True False

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Q: 21: Find Maclaurim expression for the following functions 1. f(x)= sinh(x). 2. f(x)=sin(x). 3.…

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Q: -2 Gambar 7.3 X

A: Given the picture

Q: Given: [(4x + 3)²D² - 12(4x + 3)D +64]y = 16[(4x + 3)² sec² (In 4x +31)], what special case is this?…

A: Given 4x+32Dx2-124x+3Dx+64]y=164x+32 sec2ln4x+3 what special case is this? (A) Cauchy-Euler Equation…

Q: You are employed as a network engineer and have been asked to analyze a communication network to…

A: As ler the question we are given a network of five interconnected routers through which the data is…