b) Given four points A(-2, 0, -3), B (1, -2, 1), C (-2,-³), D (,0). Find the equation of the plane through AB that is parallel to CD.
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- Find the parametric equation of the line that passes through P(-2, 0, 3) and is parallel to the line with parametric equations x = −1 + 3t , y = 2−2t, and z = 3+t. Which is the equation for x?3 A projectile is fired from a position on the ground. The motion of the projectile in two dimensions is represented by the parametric equations x=0e² and y= (1+0) ³: dy .3.1 Find an expression for the velocity of the projectile. dx d²y dx² 2.3.2 Find an expression for the acceleration- of the projectile.Find the solution. (D5- 2D3- 2D2- 3D - 2)y = 0. – 3x A y = (c, +c,r)e-*+cze-2* +e* (c _cosx+c 5$sinx) B y = (c,+c)e-2+c,e+e="(c,cosr+ ce,sinr) y = c,e"+c,e+c,ez+c,cosx+c gsinx D y = (c,+c,x)e¯*+cze"+c,cosx+€sinx
- Find parametric equations for the line that passes through the point (5, 2) and is parallel to the line y = −(7/2)x − 2.Generate a 3D plot based on the equation z=sin(x) +cos(y), both x and y range from 0 to 2 pi. Please use Matlab to solve.From the two parametric equations below, find dydx x = (2 − 3t)/ (1 + t), y =(3 + 2t)/(1 + t)
- A particle started at A(1,0) circled the origin once an d returned toA(1,0) .what were the change in its coordinates(7) (D² - 70° + 180² - 2004 200+8) V = 0The trajectory of a projectile launched from the origin at an initial speed of u at an angle of 0 degrees to the horizontal is given by the parametric equations x = v cos(0)t y=- 1 I 9t² where g is acceleration due to gravity, typically 32 feet per second per second or 9.8 meters per second per second. +vsin (0)t Find parametric equations for the trajectory of a golf ball with an initial speed of 80 feet per second at an angle of 60° to the horizontal. Enter either exact value coefficients (in radians!!!) or correct to at least three decimal places. Y 80 cos 60 7 ) 180 t sin (60 180) . How many seconds will the ball be -16² +80 sin 60- the air before it hits the ground? seconds How far will it travel horizontally in total? feet
- Find the parametric equation of the line ( x-3, y+6 )•( 2,-3 ) = 0x(t) = Convert the line given by the parametric equations y(t) Enter the symmetric equations in alphabetic order. = = 2 - 10t -2 + 3t to symmetric equations. 1 + 10tA watermelon is launched by a catapult with an initial velocity of 89 feet per second and an angle of 61∘ to the horizontal. If the watermelon is launched with an initial height of 9 feet, thus the parametric equations for the watermelon's motion is x(t)=(89cos61∘)t, y(t)=−16t2+(89sin61∘)t+9. After how many seconds does the watermelon reach its maximum height? (Round your answer to the nearest tenth if necessary.)