Name And A Cartesian Equation For It. Graph The Cartesian Traced By The .
Berkeley City College Due: HW - Chapter 10 - Parametric Equations and Polar Coordinates Name Parametric equations and a parameter interval for the motion of a particle in the xy-plane are given. Identify the particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph traced by the particle and the direction of motion. 1) x 4 cos t, y 4 sin t, ! t 2! 5 y 4 3 2 1 -4 -3 -2 -1 1 2 3 4 x -1 -2 -3 -4 -5 2) x 2 sin t, y 3 cos t, 0 t 2! y 5 4 3 2 1 -4 -3 -2 -1 1 2 3 4 x -1 -2 -3 -4 -5 Instructor K. Pernell 1
3) x 25t2, y 5t, - t y 5 4 3 2 1 -4 -3 -2 -1 1 2 3 4 x -1 -2 -3 -4 -5 Obtain the Cartesian equation of the curve by eliminating the parameter. 4) x t, y 2t 8 5) x 3 t - 7 , y 9 8 - t 6) x t3 - 5t, y t2 - 5 2
7) x 9 sin 2 t, y 9 cos2 t; 0 t 2! Find dy/dx without eliminating the parameter. 8) x 5t2, y 11 t3; t 0 9) x 6 tan t - 2, y 4 sec t 3, t (2n 1)! 2 10) x ln(2t), y e2t 11) x 1/t6, y -3 ln t Find d2y/dx2 without eliminating the parameter. 12) x 5t2, y 10 t3; t 0 3
13) x 1 - 2 sin t, y 1 7 cos t, t n! 14) x ln(2t), y ln(8t)3, t 0 2 2 15) x t 8t, y t - 2t, t -8 2 2 Find an equation for the line tangent to the curve at the point defined by the given value of t. 16) x sin t, y 6 sin t, t ! 3 Find the length of the parametric curve defined over the given interval. 17) x 6t - 6, y 12t 1, 0 t 1 4
Find the area of the surface generated by revolving the curves about the indicated axis. 18) x sin t, y 3 cos t, 0 t 2!; x-axis 19) x t 2 6, y t 2 6t, - 6 t 6; y-axis Change the given polar coordinates (r, θ) to rectangular coordinates (x, y). 20) ( 3, !/6) 21) (-4, -!/3) Find a set of polar coordinates for the point for which the rectangular coordinates are given. 22) (-5 3, 5) A) 10, 2! 3 B) 10, 5! 6 C) 5, 5! 6 5 D) 5, 2! 3
For the given rectangular equation, write an equivalent polar equation. 23) x2 y2 64 24) x2 y2 - 10x 0 For the given polar equation, write an equivalent rectangular equation. 25) r cos θ 11 26) r -9 csc θ 27) r 1 7 cos θ - 3 sin θ 28) r2sin 2θ 24 6
Find the area of the specified region. 29) Inside one leaf of the four-leaved rose r 3 sin 2θ Find the length of the curve. 30) The spiral r 5θ 2, 0 θ 2 3 Graph the polar equation. 1 31) r 1 - sin θ 5 4 3 2 1 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 1 2 3 4 5 r Find an equation for the line tangent to the curve at the point defined by the given value of t. 32) x 6t2 - 3, y t5, t 1 7
Obtain the Cartesian equation of the curve by eliminating the parameter. 33) x cos θ, y -4 sin 22θ 34) x 9 sec t , y 7 tan t Find the length of the curve. 35) The spiral r e4θ , 0 θ " 36) The circle r 7 cos θ 8
Answer Key Testname: MATH3B HWCH10 1) x2 y2 16 y 5 4 3 2 1 -4 -3 -2 -1 1 2 3 4 x -1 -2 -3 -4 -5 Counterclockwise from (-4, 0) to (4, 0) Objective: (10.1) Graph Parametric Equations and Eliminate the Parameter 2) x2 y2 1 4 9 y 5 4 3 2 1 -4 -3 -2 -1 1 2 3 4 x -1 -2 -3 -4 -5 Counterclockwise from (0, 3) to (0, 3), one rotation Objective: (10.1) Graph Parametric Equations and Eliminate the Parameter 9
Answer Key Testname: MATH3B HWCH10 3) x y 2 5 y 4 3 2 1 -4 -3 -2 -1 1 2 3 4 x -1 -2 -3 -4 -5 Entire parabola, bottom to top (from fourth quadrant to origin to first quadrant) Objective: (10.1) Graph Parametric Equations and Eliminate the Parameter 4) y 2x2 8 Objective: (10.4) Convert Parametric Equations to Cartesian Equation I 5) x2 y2 1 9 81 Objective: (10.4) Convert Parametric Equations to Cartesian Equation I 6) x2 y3 5y2 Objective: (10.4) Convert Parametric Equations to Cartesian Equation I 7) x y 9 Objective: (10.4) Convert Parametric Equations to Cartesian Equation II 8) 3 11 t 10 Objective: (10.4) Find dy/dx Given Parametric Equations 9) 2 sin t 3 Objective: (10.4) Find dy/dx Given Parametric Equations 10) 2te2t Objective: (10.4) Find dy/dx Given Parametric Equations 11) - t6 6 Objective: (10.4) Find dy/dx Given Parametric Equations 12) 3 10 100t Objective: (10.4) Find d2 y/dx 2 Given Parametric Equations 10
Answer Key Testname: MATH3B HWCH10 13) - 7 sec3t 4 Objective: (10.4) Find d2 y/dx 2 Given Parametric Equations 14) 0 Objective: (10.4) Find d2 y/dx 2 Given Parametric Equations 15) 10 (t 8)3 Objective: (10.4) Find d2 y/dx 2 Given Parametric Equations 16) y 6x Objective: (10.4) Find Equation of Tangent Given Parametric Equations 17) 6 5 Objective: (10.4) Find Length of Parametric Curve I 18) 12"2 Objective: (10.4) Find Surface Area of Revolution 19) 248 " 3 Objective: (10.4) Find Surface Area of Revolution 3, 3 2 2 20) Objective: (10.5) Convert From Polar to Cartesian Coordinates 21) (-2, 2 3) Objective: (10.5) Convert From Polar to Cartesian Coordinates 22) B Objective: (10.5) Convert From Cartesian to Polar Coordinates 23) r 8 Objective: (10.5) Convert Cartesian Equation to Polar Form 24) r 10 cos θ Objective: (10.5) Convert Cartesian Equation to Polar Form 25) x 11 Objective: (10.5) Convert Polar Equation to Cartesian Form 26) y -9 Objective: (10.5) Convert Polar Equation to Cartesian Form 27) 7x - 3y 1 Objective: (10.5) Convert Polar Equation to Cartesian Form 28) y 12 x Objective: (10.5) Convert Polar Equation to Cartesian Form 29) 9" 8 Objective: (10.5) Find Area of Region Inside Polar Curve 11
Answer Key Testname: MATH3B HWCH10 30) 280 3 Objective: (10.5) Find Length of Polar Curve 31) 5 4 3 2 1 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 1 2 3 4 5 r Objective: (10.5) Graph Polar Equation II 32) y 5 x- 1 12 4 Objective: (10.4) Find Equation of Tangent Given Parametric Equations 33) y -16x2(1- x2) Objective: (10.4) Convert Parametric Equations to Cartesian Equation II 34) x2 - y2 1 81 49 Objective: (10.4) Convert Parametric Equations to Cartesian Equation II 35) 17 (e4" - 1) 4 Objective: (10.5) Find Length of Polar Curve 36) 7" Objective: (10.5) Find Length of Polar Curve 12
Objective: (10.4) Find d2y/dx2 Given Parametric Equations 14) 0 Objective: (10.4) Find d2y/dx2 Given Parametric Equations 15) 10 (t 8)3 Objective: (10.4) Find d2y/dx2 Given Parametric Equations 16) y 6x Objective: (10.4) Find Equation of Tangent Given Parametric Equations 17) 6 5 Objective: (10.4) Find Length of Parametric Curve I 18) 12"2
phase concentrations and volumes by Equations 8 to 10. Substituting Equations 8 to 10 into Equation 7 gives Equation 11. The compound concentrations in each phase may be related to the partition coefficient by Equation 12, which is a re-arrangment of Equation 1. Substituting Equation 12 into Equation 11 gives Equation 13 C S M S V S .
Page 6 of 18 A radical equation is an equation that has a variable in a radicand or has a variable with a rational exponent. ( 2) 25 3 10 3 2 x x radical equations 3 x 10 NOT a radical equation Give your own: Radical equation Non radical equation To solve a radical equation: isolate the radical on one side of the equation and then raise both sides of the
The Manning Equation is a widely used empirical equation that relates several uniform open channel flow parameters. This equation was developed in 1889 by the Irish engineer, Robert Manning. In addition to being empirical, the Manning Equation is a dimensional equation, so the units must be specified for a given constant in the equation.
The Manning Equation. is a widely used empirical equation that relates several uniform open channel flow parameters. This equation was developed in 1889 by the Irish engineer, Robert Manning. In addition to being empirical, the Manning Equation is a dimensional equation, so the units must be specified for a given constant in the equation.
Chapter 5 Flow of an Incompressible Ideal Fluid Contents 5.1 Euler’s Equation. 5.2 Bernoulli’s Equation. 5.3 Bernoulli Equation for the One- Dimensional flow. 5.4 Application of Bernoulli’s Equation. 5.5 The Work-Energy Equation. 5.6 Euler’s Equation for Two- Dimensional Flow. 5.7 Bernoulli’s Equation for Two- Dimensional Flow Stream .
At Your Name Name above All Names Your Name Namesake Blessed Be the Name I Will Change Your Name Hymns Something about That Name His Name Is Wonderful Precious Name He Knows My Name I Have Called You by Name Blessed Be the Name Glorify Thy Name All Hail the Power of Jesus’ Name Jesus Is the Sweetest Name I Know Take the Name of Jesus
a Cartesian swivel velocity decoder. It is unknown whether 4D postural control of the arm endpoint and swivel angle would be superior using a joint-based or Cartesian swivel based decoder. In this study, we directly compare closed-loop BCI con-trol of reaching using decoded Cartesian and joint velocities.
The London DayBreak Strategy is a day trading strategy that takes advantage of the London open trading range. It’s a momentum breakout strategy that only requires up to no more than 15-minutes of your time. The London DayBreak Strategy only makes use of two simple technical indicators: the MACD which is a trend-following momentum indicator and the 50-EMA. A buy signal is generated only when .
