4. In the diagram below, Ĝl is parallel to NT, and IN intersects GT at A. Prove: AGIA~ATNA

Q: Prove that  that the y=0 is the horiz.asymp.  and x=-1 and x=1 are vert.asymp, of y=coth-1x through…

A: As given that for the function y=coth-1x has verical asymptotes at x=-1 and x=1 and has horizontal…

Q: 26. Given: B is the midpoint of DC. ABL DC 1. B is the midpt of DC, AB 1 DC 2. 3. 4. Prove: AABD =…

A: Consider the triangle

Q: Given: AB // DC, Eis the midpoint of BC Prove: AABE=ADCE

A: Given that      AB // DC     E is the midpoint of BC .

Q: 9. Find the point C such that AC = ² AB. 4

A:

Q: Q=- Find the Zero and its oider for the function fiz) = 1- Ki+Z+ ¢ ?

A:

Q: In the given figure, ABCD is a parallelogram in which E is mid-point of AD and AM//EC. AM and DC and…

A: Given- In the figure ABCD is a aprallelogram in which E is mid point of AD and AM/EC. AM and DC are…

Q: Leb Fur =ue Show thab f6/0 )c

A:

Q: G 5. GIVEN: FH bisects GHJ, GH = JH. PROVE: X1 = X2. F HE

A:

Q: 1). Let, 2=x+iy *,y€R. In this case, (a). Prove the equations 2-2+2 and a = i.2 %3D %3D

A:

Q: ABCD is a parallelogram. From Da perpendicular DR is drawn to AC. BN is drawn || to AC to meet DR…

A:

Q: 4) Find intlection points ot the dollowing tunetions. X-1 X-2 X+1 .

A:

Q: AD perpendicular to OF is not given , please prove also this

A: I am going to solve the problem by using some simple geometry to get the required result of the…

Q: 7. Given RS and TV bisect each other at point x. TR and SV are drawn Prove: TR = SV

A:

Q: In AABC andAXYZ, AB = AC = XY, BC =Y Z and mZZ = 90. Prove: mZX > mZA %3D

A: We have given two triangles , ∆ABC,∆XYZ and AB=AC=XY and ∠Z=90∘ . and BC=YZ We have to prove that…

Q: prove that n E vol(B6)) > II(b: – a;) vol( B jEJ i=1

A:

Q: Let A be a 7*4 matrie. What must a and b in or der to TO= Ax?

A: For it to be possible that two matrices A,B  can be multiplied as AB then we must have number of…

Q: Let x, y ∈ R. Suppose x2 + y2 = 0. Prove that x = 0 and y = 0.

A:

Q: Prove that (AUB)UC = AU(BŪC).

A: To prove that any two sets are equal, we need to prove that the first is a subset of second and the…

Q: Please answer the quesiton in the image (d), thank you.

A:

Q: Compute Cixj)xk and un h Find patro of he pMane gog ingi (-i, novmetit tj 4K

A: The equation of the plane passing through the given point and perpendicular(normal) to the given…

Q: . Given: GK bisects ZJGI; m ZH = m ZI Prove: GK || HI K

A: Given that, GK→ bisects ∠JGI and m∠H=m∠I To prove  GK¯ ∥ HI¯

Q: If ge R [a,6] 'ib h) < gcx) exapt gex) except for a finite number 8 points in (a, b] then prove that

A: The partition from a to b should be first divided to form a set of integrals.

Q: 2. Given u = (–4, 4, −4) and ✓ = (−5, 6, 2) find: a. u.v b. ux v c. proj(u onto v) (the projection…

A:

Q: Suppose that flath) -flx) = Cahx?+ Chx t Th3x = Ch ? Sh3 + Th3x -Cah=5h 2. 2. find fcx)

A: f(x+h)-f(x)=6hx2+6hx+7h2x-6h2-5h3 we know that f'(x) is  f'(x)=limh-&gt;0f(x+h)-f(x)h

Q: Prove that a. V. (A + B) = V.A + V.B b. V. (ØA) = (V. Ø). A + Ø(V. A)

A:

Q: 2.4. If a7 on [a, b], prove that we have а) f da = f da + f dz, (a < c < b), b) f + g) da < | f da +…

A: We will use the basic knowledge of Riemann sums and the theory of integration of real-valued…

Q: y (b, f (b)) (a, f (a))

A:

Q: Consider AGRT and AARE in the figure to the right. Given: R is the midpoint of AG and ET. Prove:…

A: Given: A figure with two triangles EAR and GTR. As R is the midpoint of AG, therefore, GR=AR As,…

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.