55 lating circles and the parabola on the same screen.53. At what point on the curve x = t³, y = 3t, z = t¹ is thenormal plane parallel to the plane 6x + 6y - 8z = 1?CAS 54. Is there a point on the curve in Exercise 53 where theosculating plane is parallel to the plane x + y + z = 1?[Note: You will need a CAS for differentiating, for simplify-ing, and for computing a cross product.]55. Find equations of the normal and osculating planes of thecurve of intersection of the parabolic cylinders x = y² andZ = = x² at the point (1, 1, 1).slabog925556. Show that the osculating plane at every point on the curver(t) = (t + 2, 1 t, 1t²) is the same plane. What can youconclude about the curve?-57. Show that at every point on the curver(t) = (e' cos t, e' sin t, e¹)the angle between the unit tangent vector and the z-axis isthe same. Then show that the same result holds true for theunit normal and binormal vectors.58. The rectifying plane of a curve at a point is the plane thatcontains the vectors T and B at that point. Find the recti-fying plane of the curve r(t) = sin ti + cos tj + tan t k atthe point (√√2/2, √2/2, 1).59. Show that the curvature K is related to the tangent andnormal vectors by the equationdTds=KNBAUDIA

Answered: 55. Find equations of the normal and…

55. Find equations of the normal and osculating planes of the curve of intersection of the parabolic cylinders x = y² and z = x² at the point (1, 1, 1).

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Similar questions

What is the difference of the meaning of the word ray in math and in computer science? In both areas, the meaning is that a ray is a directed line segment. In both areas, the meaning is that a ray is “half” of a line that has an origin and extends infinitely in one direction. Computer science: A ray is “half” of a line that has an origin and extends infinitely in one direction. Math: A ray is a directed line segment. Computer science: A ray is a directed line segment. Math: A ray is “half” of a line that has
Correct answer will be upvoted else Multiple Downvoted. Computer science. The train framework can be addressed as directions on a 2D plane. The I-th train beginning at the base end is at first at (i,0) and will be at (i,T) after T minutes, and the I-th train beginning at the left end is at first at (0,i) and will be at (T,i) after T minutes. All trains show up at their objections following 101 minutes. In any case, Gildong observed that a few trains booked to leave at a particular time, at the same time, are extremely hazardous. As of now, n trains are planned to leave from the base end and m trains are booked to withdraw from the left end. In the event that two trains are both at (x,y) simultaneously for some x and y, they will collide with one another. In this way, he is requesting you to observe the base number from trains that ought to be dropped to forestall every such accident. Input Each test contains at least one experiments. The main line contains the number of…
PLEASE EXPLAIN ALL STEPS: This question has been answered multiple times, clearly by the same tutor, but I am seeing inconsistencies within the values, the explanation does not explain how these steps are accomplished, and I would very much appreciate another approach so that I do not continue to waste questions on explanations that are not providing any real understanding. Simplify the boolean equations using FIRST a truth table (one table for a, one table for b) and THEN forming a k-map (one k-map for a, one k-map for b): a. xz + (xy + ~z) b. ~xyz + yz + x~y
4- Write the steps of 3D plot for the equation z * Plot z = sin(r)/r with r= √² + y², -8 < x≤8, -8 ≤ y ≤ 8. Your answer
5. F has one-tó-one correspondence. F {(-5, p), (10, w), (15, n), (20, m), (25, u), (30, b)}. Draw an arrow diagram for F. %3D
Correct answer will be upvoted else downvoted. Computer science. in case there are two planes and a molecule is shot with rot age 3 (towards the right), the cycle is as per the following: (here, D(x) alludes to a solitary molecule with rot age x) the primary plane delivers a D(2) to the left and lets D(3) progress forward to the right; the subsequent plane delivers a D(2) to the left and lets D(3) progress forward to the right; the primary plane lets D(2) forge ahead to the left and creates a D(1) to the right; the subsequent plane lets D(1) progress forward to one side (D(1) can't create any duplicates). Altogether, the last multiset S of particles is {D(3),D(2),D(2),D(1)}. (See notes for visual clarification of this experiment.) Gaurang can't adapt up to the intricacy of the present circumstance when the number of planes is excessively huge. Help Gaurang find the size of the multiset S, given n and k. Since the size of the multiset can be extremely huge, you…
This is a Computer Graphics Question on Phong's Lighting Model. Question: A light source with intensity 50 and radius of influence 100 is located at (4,2,93) from which you are called to calculate the illumination of a point on the yz plane. For no shiny surface and negligible ambient light, find the point on the surface with the highest illumination and light intensity at that point. Given the diffuse coefficient is 0.7.
Correct answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. You have n particular focuses (x1,y1),… ,(xn,yn) on the plane and a non-negative integer boundary k. Each point is a tiny steel ball and k is the draw in force of a ball when it's charged. The draw in power is something very similar for all balls. In one activity, you can choose a ball I to charge it. When charged, all balls with Manhattan distance all things considered k from ball I move to the situation of ball I. Many balls may have a similar facilitate after an activity. All the more officially, for all balls j with the end goal that |xi−xj|+|yi−yj|≤k, we dole out xj:=xi and yj:=yi. An illustration of an activity. Subsequent to charging the ball in the middle, two different balls move to its position. On the right side, the red dab in the middle is the normal situation of those balls. Your errand is to observe the base number of activities to move all balls to a similar…
Correct answer will be upvoted else Multiple Downvoted. Computer science. You might want to pick k glasses and gather however much water in them as could reasonably be expected. With that impact you can pour water starting with one glass then onto the next however many occasions as you like. In any case, as a result of the glasses' abnormal shape (and absolutely disconnected to your regular awkwardness), each time you attempt to move any measure of water, a big part of the sum is spilled on the floor. Officially, assume a glass I at present contains ci units of water, and a glass j contains cj units of water. Assume you attempt to move x units from glass I to glass j (normally, x can not surpass ci). Then, at that point, x/2 units is spilled on the floor. After the exchange is done, the glass I will contain ci−x units, and the glass j will contain min(aj,cj+x/2) units (abundance water that doesn't fit in the glass is likewise spilled). Each time you move water, you can…
Given two objects represented by the tuples (25, 5, 52, 14) and (10, 0, 36, 8):(a) Compute the Euclidean distance between the two objects.(b) Compute the Manhattan distance between the two objects.(c) Compute the Minkowski distance between the two objects, using q=3
What is the function of the reflection vector in computer graphics? At least two examples must be used to prove the correctness of your assertion.
Suppose images f(x,y) and g(x,y) have histograms h; and hg. Suppose you form image k(x,y) as the sum of these two images: k(x,y) = f(x,y) + g(x,y). (a) Under what conditions (on images f and g) can you determine the histogram hų of image k in terms of the histograms hf and hg? (That is, under what conditions can you determine hu if you are only given hj and he? Hint: this turns out to be fairly restrictive.) (b) Explain how you would derive hỵ in this case.