Show that the curve such that the ratio of the di stance between the normal at any of its points and the origin to the distance between the sam e normal and the point (a, b) is equal to the constant k (k > 0, k = 1)is a circle.

Q: Find the distance between the origin and the normal to the curve y=e2x+x2 at the point where x=0…

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Q: Sketch the graphs of the following cylinders. Properly identify a cross-section on the appropriate…

A: Given: Let's consider the given equation and graph the following cylinders. y=2x-4

Q: Prove that all normal to the curve x=acos+atsint,y=asint-atcost.Are at a distance a from the origin

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Q: Show that at any point (x,y) on the curve y=bex/a ,the length of the subtangent cosgant and the…

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Q: Show that the normal line at any point of the circle x2 + y2 = a2 passes through the origin.

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Q: Find the length of the subtangent and sub-normal at a point of the curve y= bsin(x/a)

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Q: Find the tangent line to the given circle as directed. x² + y² + 10x – 6y – 2 = 0 parallel to y =…

A: Equation of the circlex2 + y2 +10x -6y -2 = 0⇒x2 + y2 + 10x -6y -2 + 25 - 25 + 9 -9 = 0           .…

Q: 1. Determine the angle between the normals of the intersecting surfaces (x – 2)² + 2y? + 2 = 3 and…

A: The equation for the given surfaces areP: (x-2)2+2y2+z2 = 3Q: 2(x-2)2+y2+2(z-1)2=5We have to find…

Q: If one uses the horizontal strip/element as a representative area, then the infinitesimal change may…

A: The area of the region under the curve can be calculated using the horizontal or the vertical…

Q: ind the tangent and normal to the curve y =2e at the point where the curve meets the y – axis

A: Find the equation of the tangent

Q: A simple curve has a central angle of 36 and a degree of curve of 6°. If the stationing of the point…

A: I=36∘D=6∘ R=1145.916D So, R=1145.9166=190.986m

Q: 2. Explore the asteroid given by the parameterization 1). Šketch its graph, determine the slope of…

A: Use a line integral to find the area of the region enclosed by the asteroid…

Q: What is the area of the triangle bounded by the x and y axes and the tangent to the curve xy^2=4 at…

A: xy2=4 Differentiating with respect to x, we get…

Q: Find equations for the tangent and normal to the cissoid of Diocles y2(2 - x) = x3 at (1, 1).

A: Find dy/dx using the given equation.

Q: For a χ2-curve with 22 degrees of freedom, find the χ2-value that has area a. 0.01 to its right. b.…

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Q: Show that at any point (x,y) on the curve y=bex/a , the length of the subtangent is constant and the…

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Q: Find the following for a q-curve with parameters κ = 4 and ν = 11. a. The q-value having area 0.05…

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Q: Prove that all normal to the curve x=acos+atsint,y=asint-atcost. Are at a distance a from the…

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Q: PR is tangent to circle Q at R and PS Is tangent to circle Q at S.Find mZP.

A: Given: PR is tangent to Q at R and PS is tangent to Q at S ∠P =  x° ∠Q =  4x° ∠R =  90° ∠S =   90°

Q: for the reparametri zations alt)= (t, Cosht, o), tER. Find two Curve %3D

A: Given curve is αt=t,cosht,0 We have to find the reparameterization for the given curve.…

Q: How many points are there on the surface 2 dx+y such that the tangent plane to the surface is…

A: We have given the a=6,b=9,c=9 d=max(a,b,c)=max(6,9,9)=9 The given surface is f(x,y,z)=9x2+y2-z We…

Q: In Exercises, use Table VII to find the required χ2-values. Illustrate your work graphically. For a…

A: a).Chi-square curve has degrees of freedom is 19 and the area to the right is 0.025.Software…

Q: :Find the length of nomal and sub-normal at a point on the curve y = 21

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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: A particular curve has unit tangent u= (-2 sin t, 2 cos t, 3) and unit normal n (-cost,- sin t,0).…

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Q: Prove that all normals to the curve x= acosx+atsint,y=asint-atcost are at a distance a from the…

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Q: Determine the following for a q-curve with parameters κ = 6 and ν = 13. a. The q-value having area…

A: Introduction: The studentized range distribution, the curve of which is called the q-curve, is the…

Q: Find the following for a q-curve with parameters κ = 9 and ν = 30. a. The q-value having area 0.01…

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Q: ind the equation for (a) the tangent plane and (b) the normal line at the point Po(8,0,8) on the…

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Q: Prove that the segment of the normal to the curve x = 2a sint +a sint cos't, y = -a cos't contained…

A: First find derivative then equation of normal line ,and point of coordinate axes and then use…

Q: Find the normal to the curve xy + 2x – y = 0 that are parallel to the line 2x + y = 0.

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Q: Show that at any point (x,y) on the curve y = be*, the length of the subtangent is constant and the…

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Q: Chebyshev's theorem is used when there is a bell shaped curve

A: Chebyshev's theorem is used when we want to find the the upper bound  of the probability. And they…

Q: In Exercises, use Table VII to find the required χ2-values. Illustrate your work graphically.…

A: Given that,Degrees of freedom =8

Q: Find reparametri zations two Curve aLt)=(t, Cosht, o, teR.

A: The general form of the parametric equation of the curve in three dimensional space is given by…

Q: A simple curve has a central angle of 36 and a degree of curve of 6°. f the stationing of the point…

A: Given, Central angle=36°Degree of curve=6°PC=10+020 For calculating PI the formula is, PI=PC+Length…

Q: Find the length of the subtangent and sub-normal at a point of the curve X y= bsin a

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Q: 2) Find and sketch the circle of curvature at the point on the curve y = x² where the tangent line…

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Q: Consider the sope old shown obove For the solution that sotrios y(1) -0.75, skotch the solon curve…

A: Given the slope field along with a point on the curve 1,0.75. We sketch a curve that is passing…

Q: Let R be the annulus defined by {1<x² +y² < 4}. Is R connected? Is it simply connected? Describe C =…

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Q: If x = 8cos3theta and y = 8sin3theta, find the total length of the curve swept out by the point…

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Q: Find the exact area between a large loop and the enclosed small loop of the curve r = 1+ 2 cos Areas…

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Q: The (blank) is the absolute distance between the estimate and the actual value of the estimated…

A: The residual is defined as the difference between the estimate and the actual value of the estimated…

Q: A curve is drawn on a sphere of radius "a' and the principal normal at a point P makes an angle 0…

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Q: Consider point (a, b) on the graph of y = ln x and triangle ABC formed by the tangent line at (a,…

A: Consider, y=lnx Differentiating with respect to x, we get dydx=1x Now slope of the tangent line at…

Q: Fined the arc leng th of the curve

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Q: Find and shade the area berween cach pair of z values. Given Curve 1. between --1.93 and 2- 1.55

A: Let Z be the random variable from normal distribution then we will find the following areas?

Q: Find the normals to the curve xy + 2x - y = 0 that are parallel to the line 2x + y = 0

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Q: The tangent line to the graph of y = ecos x is parallel to y = 0 at Select one: Oa. x = 1/2 O b. x =…

A: We are authorized to solve only 1 question, please repost remaining questions Tangent line

Q: determine the area of one leaf(petal) of the rosde curve r = 2sin(3Θ)

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