Author Topic: How do I solve the following with CAS? (Read 1042 times) Tweet Share

dekoyl · « **on:** September 17, 2009, 01:42:34 pm »

How do I solve the following (with CAS) for A?

$\int_8^{T_c}\left(20-2tan^{-1}(t)\right).dt + 60.7 = (T_c-18)26.1782$

I did:

Code: [Select]

nSolve(∫(20-2*arctan(x),x,8,y) + 60.7 = 26.1782*(y-18),y) but it doesn't seem to work.

When I do it in CAS with nSolve after some fiddling around, it gives me 42.962 but the answer is meant to be ~15.

Thanks.

From this question:

TrueTears · « **Reply #1 on:** September 17, 2009, 03:14:30 pm »

Hmm I think answers are wrong because if you plug 15 in

$\int_8^{15} 20 - 2tan^{-1}(t) dt + 60.7 \approx 179.96$

$(15-18) \times 26.1782 \approx -78.53$

I got $42.962$ as well when I solved it. Thus the conclusion I reached above.

dekoyl · « **Reply #2 on:** September 17, 2009, 04:23:19 pm »

Hmm really? It's from VCAA 2007 Exam 2 - The very last question

TrueTears · « **Reply #3 on:** September 17, 2009, 04:28:10 pm »

Hmmz well unless the equation is wrong, 15 doesn't fit the equation.

dekoyl · « **Reply #4 on:** September 17, 2009, 04:30:35 pm »

Hmm yeah I think I'm wrong =\

Mao · « **Reply #5 on:** September 17, 2009, 05:15:11 pm »

Quote from: dekoyl on September 17, 2009, 04:23:19 pm

Hmm really? It's from VCAA 2007 Exam 2 - The very last question

I can't find the question =\

dekoyl · « **Reply #6 on:** September 17, 2009, 08:12:43 pm »

There you go. Thanks =]

Shameful bump.

ryley · « **Reply #7 on:** September 17, 2009, 08:54:44 pm »

I put in nSolve(nInt(20-2*arctan(t),t,0,z)=nInt(13*arccos((13-2t)/7),t,3,8)+13arccos((13-16)/7)*(z-8),z)

After a while, I got t=14.6374, so I think this is right.

ryley

Mao · « **Reply #8 on:** September 18, 2009, 07:52:51 am »

$v_{car} = \begin{cases} 20 & t < 0 \\ 20 - 2\tan^{-1} (t) & t \ge 0 \end{cases}$

$v_{police} = \begin{cases} 0 & t < 3 \\ 13 \cos^{-1} \left( (13-2t)/7 \right) & 3 \le t <8 \\ 13\cos^{-1} (-3/7) & t \ge 8 \end{cases}$

Hence, $x_{car} = \int_0^{T_c} 20 - 2\tan^{-1} (t)\; dt$ , and $x_{police} = \int_3^8 13 \cos^{-1} \left( (13-2t)/7 \right) \; dt + \int_8^{T_c} 13\cos^{-1} (-3/7)\; dt$ for $T_c\ge 8$

equating gives $\int_0^{T_c} 20 - 2\tan^{-1} (t)\; dt = \int_3^8 13 \cos^{-1} \left( (13-2t)/7 \right) \; dt + \int_8^{T_c} 13\cos^{-1} (-3/7)\; dt$ for $T_c\ge 8$

The most efficient way to do this on the calculator is ryley's method above. See http://vcenotes.com/forum/index.php?topic=17014.new#new

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Author Topic: How do I solve the following with CAS? (Read 1042 times) Tweet Share

dekoyl

How do I solve the following with CAS?

TrueTears

Re: How do I solve the following with CAS?

dekoyl

Re: How do I solve the following with CAS?

TrueTears

Re: How do I solve the following with CAS?

dekoyl

Re: How do I solve the following with CAS?

Mao

Re: How do I solve the following with CAS?

dekoyl

Re: How do I solve the following with CAS?

ryley

Re: How do I solve the following with CAS?

Mao

Re: How do I solve the following with CAS?

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