d. The first five terms of 2n -1 are....and. (Simplify your answers. Use ascending​ order.)

Q: Determine whether the statement, 'If r > 1, nPr is less than nCr', is true or false. If the…

A: The formula of permutation and combination. Crn=n!r!n-r!Prn=n!n-r!

Q: 1-i Get the result of the expression (1 + i)2+i

A:

Q: a a. Write each of the following as a fraction in the form where a and b are integers and b#0. b i.…

A:

Q: Justify whether it is true to say that the following are the nth terms of an AP. (i) 2n-3 (ii) 3n² +…

A: Solution : We have given the nth terms of a series and we have to find out that they are nth terms…

Q: 1. Let, a, = 3, a2 = 4 and for n 2 3, a, = 2an-1+ an-2, express a, in terms of n.

A:

Q: 3. Let, a, = 3, a2 = 4 and for n2 3, a, = 2an-1+ an-2 + nº+ 1, express a, in terms of n.

A:

Q: 3 2 Let A = Write 2A. Is det(2A) equal to 2det(A)? 1 9 2A =

A:

Q: Let c, a, B be nonzero real numbers such that c + B. Find a given that 72n- 3 17 00 ac? с — в

A:

Q: Prove : (A-B)n C =(A n C) -B

A:

Q: Which x satisfies both Ix - 31 < 2 and Ix - 51 < 1?

A:

Q: 2. Let, a1 = 3 and for n 2 2, an = 2am-+1, express an in terms of n. 3. Let, a1 =3, a2 = 4 and for n…

A: Note:-Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: ro -1 + If A = : B = [ → 2A – 3B -3 -81 %3D l13 -3) true O False 2.

A: Matrix combination true or false

Q: -J: State whether each of the following statements is true or false. Then give an explanation, proof…

A: As per our guidelines we can answer only one question. please repost other seperately.  Use binomial…

Q: Considering only the values of B for which csc-Bcos (2B) is defined, which of the following…

A: We need to find the equivalent for the given expression.

Q: Which of the following is an example of the associative property? A 3(5 + 7) = (3x5) + (3x7) 34 + 3…

A:

Q: a. 14 + 15i has argument: 0 =|

A: By using argument = a+ib

Q: Find the explicit formula. 5) –33, –29, –25, -21, .. А) а %3D-37 + 4n B) а %3D-31 + 2n С) а %3-33 +…

A: nth  term of arithmetic progression is given by, an = a1 + (n - 1)d, where a1 is the first term and…

Q: If a1 = -5, and an -3. an-1, list the next five terms of an, starting with n = 2: %3D {a2, a3, a4,…

A: For this problem, we can easily find a2,a3,... By using formula an=-3an-1.

Q: 1. Let, a, = 3, a2 = 4 and for n 2 3, a,= 2an-1+ an-2, express a, in terms of n.

A:

Q: Using formal logic prove that for each integer a, if a -1 is even, then 4 divides a-1 by…

A: We have to prove that the proposition "If a2-1 is even, then 4 divides a2-1" using formal logic. We…

Q: 6. Determine the all values of the following. (1+ i)i а. b. (-1)i

A:

Q: II. Translate each of the following sentences into mathematical sentence using symbols or notations.…

A: we have given 5 statements we need to write them in mathematical terms

Q: -7.GIven: a,=2 findthe Qn term.

A: Given,    First term, a1= 2 Common ratio, r = 3   To find : a7

Q: a + b (2) (a) Prove by contrapositive : Va, b e R* : a <b → a < < b. (b) Prove by contradiction :…

A:

Q: Let S be the set of numbers of the form { ((-1)^(n)) (2n + 1)/(4n - 1) } where n is an element of…

A:

Q: Let A= and B= then AB equa 2 2

A: Given A=1100 and B=1122

Q: ne order of the element 16+ in Z24/ is None of the choices 8.

A:

Q: What is the fifty-fifth term of 1, -1, 1, -1, . A) o в) 1 (c) -1 D infinity

A: Given that: 1, -1, 1, -1, ....

Q: Given 0≤θ<2π , solve 2tan⁡ θ−6=0

A: 2tan(θ) - 6=0 2tan(θ)=6 tan(θ)=3 θ=arctan(3) + n*π  θ=1.10714+n*π  (in the interval [0,2π])…

Q: Prove: The difference of the reciprocals of two successive integers equals the product of their…

A: Given, 1n-1n+1    We have to prove the difference of the reciprocals of two successive integers…

Q: Find formulas for A(x) and B(x) valid on [4,7]. (Use symbolic notation and fractions where neec

A:

Q: [5 A = Let -3 -4 1 C = B = and 2] simplify AB+AC

A: Use the property of Matrix addition and multiplication to get this.

Q: Express the following statement using O-notation: 12.a5 (3x + 4) 2. x + 2

A: The given statement is 12x53x+4x+2≤36x5 for all real numbers x&gt;2. Express the above statement in…

Q: polyhomial iS equivalent t0 2n + 5)²? O 4n? + 25 O -4n? + 25 O 4n? - 20m + 25 O -4n? - 20n + 25

A: Given,  A polynomial  -2n+52  We have to find the polynomial equivalent to -2n+52

Q: Find AB and BA. 1 0 [0.73 -0.81 A = and B = 0 1 0.86 0.45 Part: 0/ 2

A:

Q: Find the first five terms of the following sequene starting withn = 1. An = 2n? – 6 - 6 Give Your…

A:

Q: (11) The adjugate of A= is: (») [ (b) (c) (d) (e) None

A:

Q: a + b (2) (a) Prove by contrapositive : Va, b e R* : a < b → a <• (b) Prove by contradiction : For…

A: Part(a) We need to prove by contrapositive. In proof by contrapositive, if we have a statement "if p…

Q: State the five key points to 2n. State the five key points to 2n.

A: As per guidelines, we are supposed to solve only first two questions. Please repost other question…

Q: Find adj (A). -1 -2 -3 -41 1 Let A = 3 6 1

A: Given the matrix

Q: Let, {an} = -5, 10, -20, 40, . . . , {bn} = 10, -5, -20, -35, . . . , and {cn} = -2, 1, - 1/2, 1/4 ,…

A: the given sequence are  {an} = -5, 10, -20, 40, . . .  {bn} = 10, -5, -20, -35, . . . , we have to…

Q: 0. Prove that (i) |4' ||, =||4||,, and (ii) ||4' A|| -||4|-

A:

Q: Prove the statement 12 + 22 + 32 + 42 +. .+ n² n(n- ...

A: To prove:

Q: What are the first three non-zero terms in the Mac a. O b. z+ ++….. o d. z+++

A: We can solve this as follows:

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.