n(n+1) 1. pdRecall the triangle numbers, 1, 3, 6, 10...where the nth triangle number tn Show that if you multiply any triangle number by 9 and then add 1, the result is another triangle number.

Q: Consider the function f : N x N → Z given by f(n, m) = 2n · m² – 1. What is the image of f? Prove yo...

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Q: Find the derivative by the definition of each of the following functions: - 1- y = 2x2-3x 2- yv1+2x

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Q: Is this pie chart a good way to represent this data? Why or why not?

A: The given pie chart is The given pie chart shows the distribution of redrawing the Starbucks logo. ...

Q: An open-top rectangular box is being constructed to hold a volume of 200 in³. The base of the box is...

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Q: Let f(u, v) be a differentiable function with f(0, 2) = 0, fu (0, 2) = 2 and f. (0, 2) = -3, g(z, y)...

A: Given fu,v is a differentiable function with f0,2=0, fu0,2=2 and fv0,2=−3. And given gx,y=fx2y+x,3x−...

Q: dy (MULTIPLE CHOICE) Consider the equation dt true in relation to the given differential equation? y...

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Q: Write a in the form a = a-T+ anN at the given value of t without finding T and N. r(t) = (5 e' cos t...

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Q: In Exercises 1-14, find the characteristic polynomial ar the eigenvalues for the given matrix. Also,...

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Q: Five paracetamol and a sodium ascorbate cost Php 87.00. A paracetamol and five sodium ascorbate cost...

A: Given Five paracetamol and a sodium ascorbate cost Php 87.00. A paracetamol and five sodium ascorbat...

Q: Perform the following as indicated. Show your complete solution to earn maximum marks If (x + yi) /i...

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Q: If e-x, xe-x are the solutions of y''+ay'+by=0 then, y=cx/ex is also a solution of y''+ay'+by=0. Ans...

A: Let us consider the given differential equation y''+py'+qy=0 To solve the differential equation  De...

Q: Find all the roots of z = 1

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Q: QUESTION 2 Over time, the number of Americans celebrating Halloween has increased. The bar graph bel...

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Q: Factor 42w+ 24. Write your answer as a product with a whole number greater than 1

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Q: (a) If a single infectious individual enters the city at t = 0, compute the progression of the epide...

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Q: 6. " If Alexander exists or x? – 2x + 1 = 0, where x = 1 then it is not true that 1+1 = 3 and mouse ...

A: This is a problem of propositional logic.

Q: y": 2. cy's (c² +1}y =0

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Q: Factor 50x + 90y. Write your answer as a product with a whole number greater than 1. Submit

A: To Factor 50x + 90y :-

Q: и" + 7u 3D 0

A: Given differential equation u''+7u=0we have to find general solution

Q: Jcos(2x)+ sin(0.5x) Using riemann compute for the integral of F(x) = tan(3x) sum over the interval [...

A: We can solve this using Riemann sum

Q: cos(2) dz c (z – n)(z – 27)3' 7. Evaluate where C : z– 27 = 27 described once in the clockwise direc...

A: Q7 asked and answered.

Q: If the resultant of the loads shown passes through point B, determine the equivalent force-couple sy...

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Q: True or False? The sample mean will always be an integer. A) True False

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Q: In a mathematics class of forty students, twenty- three are also taking chemistry, twenty are taking...

A: Given: Total students= 40 Students who have chosen chemistry = 23 Students in physics = 20 Students ...

Q: Find the third iteration value of an extremum (maximum/minimum value) of the picture if a = 4, b = ...

A: We can solve this using newton raphson method

Q: y Which of the following is the general solution to the differential equation 2 = 2 + ex? dy dx y e ...

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Q: Use the bar graph to determine each of the following. a. How many books are represented in this bar ...

A: Let us solve the statistic problem in the next steps.

Q: Obtain general solution of the D.E. y' + (1/3)y = e%y4

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Q: If f(z) = eV8 2' then the simplify form of f(z) is: %3D A) f(z) = i e-2VZ %3D B) f(z) = -i e²vZ C) f...

A: given fz=e8-π2i simplify form of fz is? solution it is known that  eiθ=cosθ+isinθ thus e-π2i=cos-π2+...

Q: 1. Let z and w be complex numbers. (a) Show that |1+ z w² + |z – w2 = (1+|z|?)(1+ |w/?). (b) Show th...

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Q: On the blueprint of a house, 35 millimeters represents 10 meters. The actual length of the living ro...

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Q: a. Plot these reaction functions in a graph with q, on the horizontal axis and q, on the vertical ax...

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Q: Consider the population of fish in a lake, and that people commonly fish in this lake. At a given le...

A: The differential equation given is as follows: dydt=r1-yKy-Ey..........................................

Q: Obtain general solution of the D.E. y + (1/3)y = e'y A) 1/x = e (c - 3x) B 1/y³ = e* (c - 3x) 1/y = ...

A: The given equation is Bernoulli equation we will solve this by substitution method

Q: Find the general solution of the given differential equation: 2x²y" – 5xy' + 5y = 0

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Q: Consider the following augmented matrix in which ∗denotes an arbitrary number and ■denotes a nonzero...

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Q: Prove that the sum of two symmetric positive definite matrices A and B is positive definite (A+B) me...

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Q: A company wants to plan production for the ensuing year so as to minimize the combined cost of prod...

A: We will solve this linear programming problem using excel solver. below excel screen print show the ...

Q: Given the vectors a=i + j + k,  b= i-j and c=i + 2j + k, determine the volume of tetrahedron

A: Given- Given the vectors a = i + j + k, b = i - j, and c = i + 2j + k.  To find- Determine the volum...

Q: Solve the following complex number: 1. 2+i/1-i = i(x+iy), x=? ; y=? 2. (2+i)(3-2i) = a+ib, a=?; b=...

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Q: 3y(x? - 1)dx + (x? - 8y - 3x)dy = 0 when x = 0 and y = 1 A xy (y - 3) = 4(1 - x²) B y (x² - 4) = 3(1...

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Q: Boris runs 3 miles in 28 minutes. At the same rate, how many miles would he run in 42 minutes?

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Q: If m1, m2 are the real and equal roots of the auxilary equation of second order linear differential ...

A: Let us consider the second order differential equation y''+py'+qy=0 To solve the differential equati...

Q: 5. Decide which of these integers is congruent to 13 modulo 17. a) 81 b) 18 c) -38 d) 83 e) -11

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Q: c. In what quadrant does 5.5 e3.5i rad lies?

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Q: What is the particular solution to the differential equation x(x³ – xy² + 2y³)dy – y(x³ + 2y³)dx = 0...

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Q: Jo (1+ For which valMcs af v does twe tamproper inbeg

A: Ghh

Q: Factor 12u - 20. Write your answer as a product with a whole number greater than 1. (0)

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Q: Suppose that f is a function whose domain is R and satisfies the following properties: • f(r) = -1 w...

A: Given: Let us consider the given function  fx=-1,x<-21,x=00,x>2 i) Let's define the function f...

Q: Find the order and the degree of the differential equation cos x COS X A 2,4 B) 5, 8 © 5,4 5,2

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