express followibg function in parameters
2nd problem;; line of intersection of two functions
express followibg function in parameters 2nd problem;; line of intersection of two functions (a) y2 =...
2. We say that two curves intersect orthogonally if they intersect and their tangent lines are orthogonal at each point in the intersection. For example, the curve y = 0 intersects the curve x2 + y2-1 orthogonally at (-1,0) and (1,0). Let H be the set of curves y2-2.2-b with b є R. (a) Prove that the tangent line of each curve in H at a point (x, y) with y 0 has slope - (b) Let y-f(x) be a...
2. We say that two curves intersect orthogonally if they intersect and their tangent lines are orthogonal at each point in the intersection. For example, the curve y = 0 intersects the curve x2 + y2-1 orthogonally at (-1,0) and (1,0). Let H be the set of curves y2b with b ER. (a) Prove that the tangent line of each curve in H at a point (r, y) with y / 0 has slope (b) Let y -f(x) be a...
1. 2. Which vector function represents the curve of intersection of the surfaces x = y2 and y² + x2 25 ? = Find a vector that is parallel to both of the planes 2 – y + 2z = 2 and x + y + 3z = 13.
Chapter 13, Section 13.7, Question 017 (a) Find all points of intersection of the line x = -2+1, y = 3 +t, z = 2t +21 and the surface z= x2 + y2 (b) At each point of intersection, find the cosine of the acute angle between the given line and the line normal to the surface. Enter your answers in order of ascending x-coordinate value. (a) (b) (x1,91,21) = (003 Edit cos 01 = ? Edit (x2, Y2, 22)...
python 1 import matplotlib.pyplot as plt 2 import numpy as np 3 4 abscissa = np.arange(20) 5 plt.gca().set_prop_cycle( ’ color ’ , [ ’ red ’ , ’ green ’ , ’ blue ’ , ’ black ’ ]) 6 7 class MyLine: 8 9 def __init__(self, * args, ** options): 10 #TO DO: IMPLEMENT FUNCTION 11 pass 12 13 def draw(self): 14 plt.plot(abscissa,self.line(abscissa)) 15 16 def get_line(self): 17 return "y = {0:.2f}x + {1:.2f}".format(self.slope, self.intercept) 18 19 def __str__(self):...
LARLALUI 2.5.021. MY Consider the following. x2 + y2 - 81 (a) Find two explicit functions by solving the equation for y in terms of x. (positive function) X Y2 = (negative function) Y V
Consider the following. z = x2 + y2, z = 36 − y, (6, -1, 37) (a) Find symmetric equations of the tangent line to the curve of intersection of the surfaces at the given point. x − 6 12 = y + 1 −2 = z − 37 −1 x − 6 1 = y + 1 12 = z − 37 −12 x − 6 = y + 1 = z − 37 x − 6 12 =...
Given y1, y2, and y3 as a function of x. In the same graph plot the three functions for x ?[-3,3] . Follow the form given below. function y1 Line style: solid, color: blue function y2 Line style: dashed, color: black function y3 Line style: dotted, color: red Label the x and y axis; x axis as (x), and the y axis as (y1,y2,y3), title the graph as (problem5), add a legend on the plot. y1=x^4-e^(-x) y2=x^2-x^3+25 y3=30-12x,
(1 pt) Express the function y V as a composition y f(g(x)) of two simpler functions y f(u) and help (formulas) g(x) help (formulas)
Find a normal vector and an equation for the tangent plane to the surface: x3 - y2 - z2 - 2xyz + 6 =0 at the point P : (−2, 1, 3). Determine the equation of the line formed by the intersection of this plane with the plane x = 0. [10 marks] (b) Find the directional derivative of the function F(x, y, z) = 2x /zy2 , at the point P : (1, −1, −2) in the direction of...