= 0,1] and d be the usual metric, d(x, y) = a -y %3D en d can not induces a norm on X True False

Q: Let X (2,3. 4) and de fined metrie on X as d(x, y) = |-y Find open ball B (2.2) = (0) O (2) 0 2.0…

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Q: Let d be metric on X, and de f ined di on X as di = max (d (r, ).0}, then dis semi metric but not…

A: Given d be an metric on X and d1 is defined on X by  d1=maxdx,y,0                     (i) To verify…

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Q: Bounded by the planes z= x, y =x, x+y=2 and z= 0

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Q: Evaluate the line integral x'z ds, where C is the line segment from (0, 5, 2) to (4, 6, 5).

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Q: 2. Show that the xy plane W = (x, y,0) in Rº is generated by: (i)u = and v = (ii)u : and v = 3

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Q: Compute the distance d from y to the plane in R' spanned by u1 and uz.

A: We have to find the distance d from y to the plane in R^3.

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Q: Write a homeomorphism between the unit closed disk A = {(r,y E R2 : a2 + y? < 1)} and the unit…

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Q: Let X=R2 and let d be the Euclidean metric.  Define d3:  R2 x R2 to R by d3(x, y) = min{1, d(x, y)}…

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Q: Consider a 2-space with the following metric ds² = rdr² + ydy? (a) Calculate the nonvanishing…

A: Given,A 2-space metric: ds2=x dx2+y dy2To find: a) Connection coefficients, Γ111 and Γ222…

Q: Consider the following mappings on RXR: d1(x,y) = e*-Y, d2(x,y) = |2x –yl and d3(x,y) V=yl O Both d1…

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Q: 4. Show that the set of points (z, w) e C with w2 = sin z is naturally a Riemann surface. %3D

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Q: a) F(x,y, z) : planes x = 0, x = 1, y = 0, y = 1, z = 0, and z = 1. 3xi + xyj + 2xzk and E is the…

A: Solution of (a) is in given below

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Q: Evaluate the line integral / x°z ds, where C is the line segment from (0, 2,4) to

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Q: Let f function from (R,d) to (R,d ) defined as f(x) = x , where d is .the discrete metric then f is…

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Q: Let d: Rx R*→[0, ∞) such that d(XF)=√(x, y)² show that (R.d) metric space.

A: `

Q: 4. Let r(s) be a unit speed curve with a curvature of zeroc fo. prove that the image r lies in a…

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Q: find volume 26. The wedge cut from the cylinder x2 + y? = 1 by the planes z = -y and z = 0

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Q: Exercise. a) For every ,r, y E R, let p(r, y) =| x² – y? |. Is pa metric U..... on R? b) For every…

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Q: t in 30 minute please duopoly with homogeneous goods. There ar

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Q: Let (x, y) and (z, w) be two points in R? state which of the following does not define metric on R?…

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Q: (10) Define the metric d on R² by d( (x₁, y₁), (x2, y2)) = max{ |x₁ − x2\,|y₁ - y2|}. Verify that…

A: The given problem is to verify that the given metric d on R2. Given metric…

Q: Let X = R and x, y E R. Admit for all x and y the metric d(x, y) = |arctan x arctan y|. | Compare…

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Q: IF en Inner pYoduct Space X iS Vea show thet condition Hnll=Hyll impLies +ye X-y>0c what does this…

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Q: 2. Show that the xy plane W = (x, y, 0) in R³ is generated by: (i)u = 2 and v= |1| (ii)u and v = 3…

A: Given the plane: W=(x,y,0) in ℝ3.Let (x,y,0) be any element from W. For a and b in ℝ, we…

Q: Suppose that u € C² (R²) and u(x, y) = 0 everywhere on the boundary of the square ((x,y): 0≤x≤ R,0 ≤…

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Q: Calculate ( (2x + y) dV , where V is a closed space bounded by the cylinder z = 4 – x? and the…

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Q: Consider 2-dimensional hyperbolic space with metric ds = dr'+dy and y > 0. The length of a line…

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Q: Verify Green's theorem Where C is the boundary of the triangle formed by x=3 , y=0 , x2= 3y

A: Verify Green's theorem Where C is the boundary of the triangle formed by x=3 , y=0 , x2= 3y

Q: 4. Show that ||y|| = maxxela.b]ly'(x)| defines a norm for the linear space Y - %3D {y e C' [a, b]: (…

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Q: 2. Assume that (X, dX) and (Y, dY ) are complete spaces, and give X × Y themetric d defined byd((x1,…

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Q: Find the kernel of linear map L:R R given by L(x,y,z)%3D(0,z,y)?

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: If X =R and d(x,y)= 1, then X not metric semi metric metric space

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Q: Integrate h (x. y) = yi+xj over the indicated path: r(u) = ui+ u²j. ue [0, 1).

A: Given hx,y=yi+xj and ru=ui+u2j, u∈0,1 We have to integrate hx,y=yi+xj along the path ru=ui+u2j…

Q: 4. Suppose that VxF= (0,1,-1), S is the plane x + y + z = 1 in the first octant and Cis the boundary…

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Q: Evaluate both sides of divergence theorem for A = pa,+ pcos(ø)a,+ zaz through the closed surface…

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Q: A solid G is bounded by the paraboloid z = 4 – r - y², the cylinder 2+ y = 4 and the plane z = 5.…

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Q: Verify that (S, d) is a metric space. 10.2 Prove that d(x, y) < d'(x, y)s/2 d(x, y) for all points'…

A: To prove dx,y≤d'x,y≤2dx,y for all points x,y∈ℝ×ℝ where d is the usual metric and d' is the…

Q: flz) = Im z is continuous %3D

A: The objective is to check f(z) =Im Z is continuous Or not.

Q: Use Green's Theorem to evaluate S. axy dy + cxy dy, where C is a counterclockwise oriented…

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Q: Show that a indeed perojective plane of gives 0rder BİBD (n+n+,n+),!

A: We need to prove that a projective plane of order n indeed gives a BIBD (n2+n+1, n+1, 1)

Q: Let d(x.y) = |1/x - 1/y be a metric on R(0)XR\(0). Then the open ball of center 1 and radius 1/4 is*…

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Q: Find My for a triangle whose vertices are located at (0,0), (1,0), (1,1) if the density of the…

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Q: Let X = {2,3, 4,..} and de fined metric on X as d (r, y) = |- yl %3D %3D Find орen ball B (2,2) =…

A: Follow the definition: B(2,2) = { x in X : d(x,2) &lt; 2 }

Q: Let X = {1,2,3, 4, ...} and de fined metric on X as d (r, y) |r-yl %3D Find open ballB (2,2) = o {2}…

A:

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.