S={xER:x2 - 4<0} with the usual metric is A. Compact. B. connected. C. Not connected D. Sequentially compact.

Q: Show that the square of the length of subtangent at any point on the curve by2=(x+a)2 (b is not…

A: Here given curve  by2=x+a2

Q: show that the square of the length of subtangent at any point on the curve by2=(x+a)3(b is not equal…

A:

Q: Prove that for any point (a, b) ≠ (0, 0) on the parabola y = x2 , the normal line intersects the…

A: The given equation of parabola is y=x2  For the point (a,b)≠ (0, 0), the slope of normal is and at…

Q: \si E2. is a metric on 1. Prove that d[(s), (t)] = 1=-00

A: To prove, ds,t=∑i=-∞∞si-ti2i is metric on ∑2. A metric space is a set X together with a function d…

Q: Determine the length of the tangent to the circle x2 + y2 − 4x − 5 = 0 from (8, −2)

A:

Q: The curvature of any line with slope m in 2-space at any point on it is TTL

A:

Q: Let C be the curve in space given by the following parameterization. Then d + 2dy +adz is equal to…

A: Given ∫xdx+2dy+zdz = ∫(xi+2j+zk).(dx i + dy j + dz k) = ∫F.dr Here F = (xi+2j+zk)…

Q: Find the equahion a Hhe tangent Lie FlX) =482- 5X +7 when R=1

A:

Q: 10) Define the metric d on R² by d (x₁, y₁), (x2, y2)) = max{|x₁ - x₂], ly₁ - yal}. Verify that this…

A: This is a question of topology.

Q: Homework 4. Show that the following are metric on R": d₁(x, y) = max₁sisn |X₁-yil; d₂(x, y) = -1 |x₁…

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Q: Show that if P lies on the intersection of the two curves x2 − y2 = c and xy = d (c, d constants),…

A: Solution:Givenx2-y2=c     and   xy=dTo prove tangent curve at P are…

Q: 3. 8.5 W 20

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: For a χ2-curve with 19 degrees of freedom, find the χ2-value that has area a. 0.025 to its right. b.…

A: a) Degrees of freedom is 19 The chi-square value that has area 0.025 to its right is given below:…

Q: 11. 12

A: 11. The figure of the circle is given by To evaluate : The value of x

Q: Use this formula to find the curvature. y = 3x4 к(x) %3 K(x)

A:

Q: 8how that the square of the leng point on the curve by = (x + a)° , length of the subnormal at that

A: Subnormal and Sub tangent: Allow y=f(x) to be the differentiable curve at point P. Let the tangent…

Q: Find the curvature K of r(t)= 2ti +t²j - k 3

A: We know that, the expression for the curvature; kt=r→'t×r→''tr→'t3 Given r→t=2ti→+t2j→-13t3k→

Q: Which of the following has more area under a curve with µ=5 and σ = 4 A.  µ ± 3σ  B.  µ ± 2σ  C.…

A: # given random variable x with mean =5 and standard deviations=4  Then to check under which range…

Q: Let (a, b) be an arbitrary point on the graph of y = 1/x, x &gt; 0. Prove that the area of the…

A: The given function for the curve is, y=1x The slope (m) of the tangent at the curve is,…

Q: Assume the distance metric is Euclidean, what is the Y-coordinate value for the FIRST iteration of…

A: From the given information, Location Coordinate(xi) Coordinate(yi) Weight(Wi) 1 2…

Q: Find the curvature k of the circle C: (T – 2)² + (y + 3)² = 25 at the point (5, 1).

A:

Q: The tangent to the circle x? + y? +3x+3 y = 38 at the point (2 ,4) is Select one: O11 y- 7x = 58 011…

A: Equation of the circle is : x2 + y2 + 3x + 3y = 38 at point (2,4)

Q: Suppose a point X lies in the exterior of a disk, and suppose that two lines are drawn from X…

A:

Q: Find the curvature k of the circle C:(x – 2)2 + (y +3) = 25 - at the point (5, 1).

A: circle equation is x-22+y+32=25 and point 5,1find curvature k

Q: Use this formula to find the curvature. y = 3x4 K(x) =

A:

Q: (b) Suppose C is a curve of length N, and ||F|| < M, where M is some positive number. Prove that F.…

A:

Q: If z = x + iy, then the inequality |z + il < 3 is a: A. Circle with center at (0,1) and radius 3. B.…

A:

Q: Find the exact length of the curve. y = In(1 - x²), o s x s

A: Solve the problem using definite integral

Q: The tangent to the circle x2 +y2 +10 x+5 y= 60 at the point (2 ,4) is Select one: O None O 13 y +…

A: Given that:x2+y2+10x+5y=60

Q: Find the length of the curve given by r(t) = for -5 <t<5. O 5/19 O 10/10 O 10/19 O 5/10 O 10

A:

Q: If YZ is a tangent, then according to Pythagorean Theorem, the length of XZ should be Therefore, YZ…

A: Given  XY = 11.4 in. YZ = 15.2 in If XYZ is right triangle than length of XZ by pythogoras theorem…

Q: %3D d Chy) = (Ĉ 1 Xi-y) do you metric space ornot ??

A:

Q: Let a cubic B-spline curve have knots 000 1 2 2 3 3 444. The domain knot values are between 0 and 4.…

A: The Solution is given below

Q: Find the length of the tangent to the circle x² + y² − 2x − 3y − 1 = 0 from the point (2, 5)

A: Solution- The equation of the circle x2+y2-2x-3y-1=0 The point =2,5 length of the tangent

Q: 47. Determine if AP is tangent to circle 0. A A. yes B. no 5 12 13

A: Given.

Q: d (x, y) = (x - y)^2 does the function define a metric o

A:

Q: Find the curvature k of the circle C : (x – 2)² + (y+ 3)² 16 at the point (2, 1).

A: Use the formula of curvature to solve this problem.

Q: The curvature of y=x is: None .a O 1 (1+x?)/2 .b O (1-x*)/2 .c O -1 (1+x²)/2 .d o

A: We will use the fact that the curvature of y=f(x) is given by…

Q: Show that the square of the length of subtangent at any point on the curve by =(x+a)°.(b÷0) varies…

A: We will prove it as following.

Q: For each KeR+, HeR make a curve-C3 y:R –→ R³such that it has a constant curvature K and a constant…

A: We produce a curve γ:ℝ→ℝ3 , so we have γt=cost, sint,t.  Now finding its first and double…

Q: The center of curvature C (h,k) is at A (2, 1) (B) (3, 0) © (4, -1) (5,-2) (D)

A:

Q: Which of the following points do not lie on any tangent line of the parabola y = x2 + 2? (2,6) O…

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Q: The curvature of any line with slope m in 2-space at any point on it is 0

A:

Q: O A parhcle moves on a straight Iimes with velouty funchon V() = Sinwt uslwt f ind its position…

A: To find the position function from the given velocity function.

Q: For the function graphed below, estimate the point of greatest curvature 1.

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Q: (b) Find the curvature for the space curve r(t) =(1.",)at the point.1.11 using the formula 10.

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Q: t that is only of the total distance she

A: Here, x is total distance.

Q: A circle, with area A = Tr2, is expanding with time. dr If = 6 cm 2/s, what is dt dA when r= 2? dt…

A: