let x be 4-VV flom)- T0 e-w. Fined ECX) olEC)

Q: If Z=-+. Evawate (E)"

A:

Q: 6. Let A = {a, b, c, d, e} and B = {a, b, c, d, e, f, g, h}. Find a) AU B b) AN B c) A - B d) B- A.

A:

Q: Find that is cotefminalI with 0and aT 17TT 4. angle between

A: We can find the co-terminal angle as below.

Q: 3. What is another term for disjoint?

A: Sol:- Disjoint events are also known as mutually exclusive events.

Q: 5. AVWX = AXTU W T. V. ZWXV = ?

A:

Q: Let V = { a, e, i, o, u } andB = { a, i, k, u}. Find V – B and B – V

A: V-B= elements those lie in V but not in B  Hence, V-B={e,o}

Q: sinz = 0 iff %3D Select one: O z= kt. Oz=-+2kn. TO O z = + kt. 3T + kT. 2

A:

Q: Let U = { 20, 21, 22, 23, 24, 25, 26 }, A = { 23, 24, 25, 26 }. Use the roster method to write the…

A:

Q: Find the following

A: Integrate the function (v2-e3v) with respect to v to find the required one. Integration of the…

Q: QI Let x be anon- empty, Show that whetharn (Pcx), n) sa grouPor not ?

A: Explanation: Let X = 2, 3 Then PX = ∅, 2, 3, 2,3 For  A∈P(X) and B∈P(X),  A∩B ∈ P(X) That is, P(X)…

Q: 2.If alb and alc then al Cbx tcy) for all X>YEZ.

A:

Q: If a(3, 4) – b(2, 4) = (8, 10), determine a and b.

A:

Q: 4. Consider A={m,a,t,h}; C={x:x=3n,1šns4,neN}; B={s,t,e,m} ; D={x:x=2n,15n 56,nEN} What is CUD? *

A: Here given that                         A={m, a, t, h}                         C={x:x=3n, 1≤n≤4,…

Q: Prove: If = ¿ (where a, b, c, and d are nonzero), b then d*

A: Given:               ab=cd  (where a,b,c  and d are non zero.)

Q: show that (2n+1) Pr= PA+t=PAt Use tege ndre palgnanicds the

A:

Q: state the MUT two diferentways a in words

A: We have to state mean value theorem in two different ways.

Q: let frms D=. 4 (4切=rg。

A:

Q: al Evalute gred gg if Ø = ln Cx²+y*+z')

A: To solve this question first we solve for partial derivative with respect to x,y and z .Then we use…

Q: Let U= {q,r,s,t,v,w,x,y,z}  A={q,s,u,w,y}  B={q,s,y,z} c={v,w,x,y,z}  determine A n B'

A: Given that B={q,s,y,z} So, B'= U - B= {q,r,s,t,v,w,x,y,z}  - {q,s,y,z}= {r,t,v,w,x}

Q: 9f a,b,c,d EN & a = b frod n) C=d(modn) sherw that bd(radn)

A:

Q: . Let and B = Find AYB. h) AAB c) AOB.

A: The matrix are:A=11 01B=01 10

Q: Let xB(n, p) Find ECX3)

A: Given: X~B(n,p) Find: E(X3)=?

Q: Evaluate Cxp*q" -* for the values of n, x, and p given below. 1 n=7, x= 1, p=5

A:

Q: %3D If X-N(50,10), P(X < 60) = ? O 1) 0.841 O 2) 0.159 3) 0.341 O 4) 0.659

A:

Q: If X-N(50,10), P(X > 65) = ? O 1) 0.067 O 2) 0.033 3) 0.168 O 4) 0.832

A: The z-score can be calculated by subtracting the population mean from the raw score, or data point…

Q: let X be 4-VV flon)= To Finel ECX) oedECXY)

A: f(x) = x/10 where xx = 1,2,3,4

Q: Gu Sind values ofx in following fue 21 o Sgn Cx J =llo 22 3. sgn(x²x-2)= -\ 23 24

A:

Q: a) In1/e b) eIn5 c) In1/3 d) 2Ine e) 5In1 and F) Ine1/3

A:

Q: Nerifu verify the identity CoS x (secxt tanx)=1 + Sinx

A: Given query is to verify the identity.

Q: Suppose U = {a, b, c, d, e, f, g, h, i}, A = {a, e, i} B=(a, b, c, d, e} and C = {f, g, h}. What is…

A: The objective of the question is evaluate the operation on subsets.

Q: Let A %3D {1,2,3, 4}, В %3D {3,4, 5},С %3D {а, b, с}. Find A n B, A x С, В х С, (АnВ) х ( (Ах С)n (В…

A:

Q: 4) Find the measure of Z1 and 22. 117°

A: To find the measure of angles 1 and 2      Here, two parallel lines are intersected by a transversal…

Q: e 이므 + 약 ||

A:

Q: 1. xpI tçXA, ニ =xp( 6+ (xLつas

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Q: 5. Find the power set of each of these sets, where a and b are distinct elements. a. {a}

A:

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.