Establish the formulas below by mathematical induction: 1^3 + 2^3 + 3^3 + .... + n^3 = [ (n(n+1))/2 ] ^ (2) for all n greater than or equal to 1

Q: 31 Given the sequence: at What is the fifth term? O 32 9 k +1 for k> 1:

A: Given that the sequence ak=9k+1 for k≥1  .

Q: The Mathematics Department is holding an election for department chair. Each member ranks the…

A:

Q: Write the scalar equation of the line given the normal vector point Po(-2,-4). n = and a

A: Scalar equation of a line is given by , Ax+By+C =0, where (A,B) are the cordinates of normal vector…

Q: Consider the equation f(x) = x² cos(x). Integrate f(x) from x = 5 to 3000 (inclusive) with 2211…

A: Given f(x)= x2cosx Simpson's 38rule points are 1,2,3,4 h=4-13=33=1 f(1)=12cos(1)=0.54…

Q: Given this matrix: A = 4 3 1 1 Which matrix is the inverse of A? 1 이러 [{ [1 3 [中] 1 == 14 3 4 3

A:

Q: Use the graph of the function to estimate the interval on which the function is decreasing. y Enter…

A: Here we have been given a graph which is increasing then decreasing then increasing again So the…

Q: Question 1. Let P(x) = ax²+bx+c with a 0. The polynomial P(x) is factorable in real numbers if we…

A: Introduction An algebraic that is able to split into two or maybe more parts is said to be by…

Q: 6) prove that cost '2 = log (2 + √2²-1).

A: To prove that cosh-1(z) = log(z + sqrt(z2 - 1)), we can start by defining the hyperbolic cosine…

Q: Compare the representative rectangles for the disk and shell methods.

A: The main difference between the washer and shell methods in calculus is the orientation to the axis…

Q: What is the value of the following expression? 10 n=1 3(-2)" O-1,023 2,046 O-3,069 6,150

A: Solution :-

Q: - Determine (with proof) if the following series is converging absolutely, onverging conditionally…

A: Consider the series ∑n=1∞1n2cot1n. To determine the series is converges absolutely, converges…

Q: Which compound proposition is logically equivalent to p V q? OP→q OP ¹9 OP →q 019-P

A: Answer:

Q: X y 0.4 0.6 0.8 0.423 0.684 1.030 1 1.557

A: Given

Q: a) Determine the solution(s) of each of the following equations, where 0≤x≤ 2n cos x = tan x = -√3…

A:

Q: Determine whether f is a function from Z to R if a) f(n) = tn. b) f(n)=√√n² + 1. c) f(n) = 1/(n² —…

A: Function: Let f:M→N be a function, then every element of set M has one and only one image in set N.

Q: Y=35x^(3)-257x^(2)+85x-7 list all denominadors for rational roots

A:

Q: Suppose R is the shaded region in the figure, and f(x, y) is a continuous function on R. Find the…

A:

Q: How would I put that into interval notation with any values to one decimal place?

A: Here we can see that the graph is first increasing to the certain points, then it starts decreasing…

Q: Find the function, f(k, p), such that Σε(k,p)=n" vp,n€ N k=1

A:

Q: 9. -6-5-4 -2 УА 10 in 3 6 5 -4- Ⓒ2- 1- 0 -1 -2- 3- 4- -5 -6- а 1 2 3 4 5 6 10. у -6 -5 -4 -3 -2 -1 6…

A:

Q: Find the values of a, b, ce R such that n k=1 ak² + bk+c= n³ \ne N

A:

Q: By changing to polar coordinates, evaluate the integral where D is the disk x² + y² ≤ 36. Answer =…

A:

Q: 7) The sequence an = 2ln (n+1). In (2n+1) a) Converges to 2 b) Converges to 1 c) Diverges d) None of…

A:

Q: circles with center on the line y = -x and passes through the origin. Create the DE

A:

Q: 1) State whether the following functions are odd, even or neither: a) t³ sin(wt) b) t cos(2t) c)…

A: Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Using direct comparison test, determine whether the series En n(n+1) =) Using Limit comparison test,…

A:

Q: Consider graph G: a b C What are the vertices of a cycle in graph G? O b, c, d, e, b O a, b, c, d, b…

A: Given a graph G with vertices a, b, c, d, and e. To Find: The vertices of a cycle in graph G.

Q: Are the ratios 1:5 and 14:15 equivalent? yes no Submit

A:

Q: I. Use Bisection and False Position Method to locate the root of x³ - 2x + 1 = 0 between X = -2.2…

A: The given function is fx=x3-2x+1. The given values of x are x=-2.2 and x=2.2 . The absolute error is…

Q: Find all the roots of the given equation. x4 -81 = 0 O-3j, 3j -3 - 3j, -3 + 3j, 3 - 3j, 3 + 3j -3,3…

A:

Q: What is the output of the composition of f and g when D is the input? OJ OK OL G

A:

Q: 19 For X = {1, 2, 3} and Y= {a, b, c), functions f. X - Y and g: Y-X are defined as follows: 1. NT 2…

A:

Q: Add: 2012, +1120, O 3132, O 10.202 O 10,200, O 11.200,

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: Problem Prove that increasing and bounded function f [a,b] - : limits at every z € (a,b). R has…

A:

Q: ind the equation of the plane tagent to the curves f (t) = [3t+4,4 tº, sin (πt) + 4] and g(s) = [8°…

A:

Q: Anabelle borrowed Php 12,000 that bears a simple interest. She has fully paid Php 12,750 after 3…

A:

Q: coefficients for n= es below.

A: ?1=2 ∗ − 111∗??=−2??= −0.6366

Q: 2. Describe the solution set in R³ of the linear system - 1, x1 + 3x2 + 5x3 = 2x1 + x₂ + 5x3 = 3,…

A: Linear equations are  x1 + 3x2 + 5x3 = -1 2x1 + x2 + 5x3 = 3

Q: 1. Determine whether or not each of the following syllogisms is valid. Support your conclusion with…

A: Hence the syllogisms are valid

Q: 4. Find the apportionment under the Jefferson method if there are 100 seats to be apportioned. Hint:…

A:

Q: Express the number in terms of j. √-15

A: Given expression is -n5 We know that j2=-1

Q: 3. 1) Given: g(x) = x-2 x+5x+6 2 a. Determine x and y intercepts. b. State the domain. c. State any…

A: The given problem is to determine the intercepts of the given function, domain of the function, and…

Q: Given the Fourier transform of signal z(t) = e-³t H(t) is 1 3 + jw Z(w) = F{z(t)} : = where H(t)…

A:

Q: I also asked for the b) part, which is missing . Please provide everything as requested

A: Let xn=n+(-1)n2n-3n3. Let an=n2n-3n3 and bn=(-1)n2n-3n3. Now an=n2n-3n3=12-3n52.Let cn=1n52.So…

Q: 16. Assume that a < 0 < b. Use a geometric argument to show that b - [²x dx = 5² = ² 2 a

A: Using geometric argument we have to show that ∫abx dx=b2-a22, where a&lt;0&lt;b.

Q: Solve the following system of equations by LU decomposition. Show all the steps of your calculation.…

A:

Q: 5. A moving particle has its velocity given by the quadratic function v pictured in and A₂ , as well…

A: The area are given by A1=76, A2=83. And the position function is s, s0=0.5. The velocity is given by…

Q: d If D= find a complete solution of: " di (D+5)x+ (D+3)y=e" (D+2)x+ (D+1)y=3 (1) (2) K

A:

Q: Give an example of an everywhere-defined real function that is continuous at exactly three points.

A: Introduction Theoretical frameworks for meter and conical fields both heavily rely on smooth true…

Q: Find the comples form of the Fourier series of: f(t) = et -1<t<1

A: Given: ft=et;   -1&lt;t&lt;1. We have to write the complex form of the Fourier series of the given…