Welcome :: Homework Help and Answers :: Mathskey.com
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,435 questions

17,804 answers

1,438 comments

774,938 users

Calc w/ Parametric Curves HELP?

0 votes

I keep getting -1 as my answer, but that answer is not one of the possible options... Please show your work on how to solve. Thank you!!

asked Jul 20, 2014 in CALCULUS by anonymous

1 Answer

0 votes

x = 5sint

Apply derivative to each side.

d/dt = d/dt (5sint) = 5cost.

y = 5cost

Apply derivative to each side.

dy /dt = d/dt (5cos) = -5sint.

dy / dx = (dy /d) / (d/d)

           = -5sint / 5cost

           = - tant

---------------------

x = 5sint

sint =x/5

t = sin-1 (x/5 )

dy / dx =- tan(sin-1 (x/5 ))

               =-(x/5)/√(1-(x/5)2)                                          (Since tan(sin-1 (x)) =x/√ (1-x2))

                  =-x/√(25-x2)

Take the derivative both sides

d2y / dx2  =-(d/dx)(x/√(25-x2))

                 =-(√(25-x2)(1)-x(-1/(2√(25-x2))(2x))/(25-x2)

                 =-(√(25-x2)-x2(-1/(√(25-x2))/(25-x2)

                  =-((25-x2)+x2)/(25-x2)3/2

                     =-25/(25-x2)3/2

At t = 3π/4

x= 5sin3π/4 =5/√2

d2y / dx2  =-25/(25-x2)3/2

                    =-25/(25-(5/√2)2)3/2

                     =-25/(25-(25/2))3/2

                      =-25/(25/2)3/2

                       =-25*23/2/125

                 =-2√2/5

Option (c) is correct.

 

answered Jul 24, 2014 by joly Scholar
edited Jul 24, 2014 by bradely

Related questions

asked Aug 5, 2014 in CALCULUS by anonymous
asked Jul 22, 2014 in CALCULUS by anonymous
asked May 1, 2015 in CALCULUS by anonymous
asked Nov 5, 2014 in CALCULUS by anonymous
asked Aug 19, 2014 in CALCULUS by anonymous
asked Jul 23, 2014 in CALCULUS by anonymous
asked Aug 3, 2017 in ALGEBRA 1 by anonymous
...