John Y.

asked • 06/12/15

Precalculus word problem for final exam review

Jerry kicks a soccer ball 160 m with a max height 40 m. How high is the soccer ball when it is 145 m from jerry?
 
i realize this may be hard to explain via electronics but anything helps I want everything to be perfect for final exams and I  am using your answers to check my own . Thanks

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Mark M. answered • 06/12/15

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The maximum height occurs half way through the kick, at 80 m. So the vertex of the parabola is (80, 40)
 
f(x) = -a(x - h)2 + k
f(x) = -a(x - 80)2 + 40
 
Two other points are the kick (0, 0) and the landing (160, 0)
 
f(160) = -a(160 - 80)2 + 40
0 = -a(80)2 + 40
-40 = -640a
1/16 = a
 
f(x) = (-1/16)(x - 80)2 + 40
 
Substitute 145 for x to find the height.
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David W.

Wow!   1 2/3 football fields with a height 0f 120 ft!  If Jerry has any accuracy, he can earn millions as a place kicker in the NFL.   (some teachers make up really wild problems and students/tutors dutifully answer them; this could have been an arrow.
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06/12/15

Mark M.

Oh, how true!
And some tutors dutifully carp about them!
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06/12/15

John Y.

I got a height of 2 m this isn't correct though is it..
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06/18/15

JOHN F.

0 = -a(80)2 + 40
-40 = -6400a
1/160 = a
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07/11/15

JOHN F. answered • 07/11/15

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f(x)= -1/160 *(145-80)2 + 40
 
= -1/160 * 652 + 40
 
= 13.59375 m high when it's 145m from Jerry.
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David W.

Now, surely you would express the height in some value less exact than 13,59375 m (what does one use to measure that amount?).  What is practical for both the problem description and the math being taught?
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07/11/15

JOHN F.

That was the exact height.  John from Miami, OK wanted to check his answer against what was gotten here (he wanted everything to be perfect), so HE can choose how to present his answer.
 
If I was giving the test and did not specify a number of digits to which to round the answer, 13.59375 is what I'd check my students' answers against, wherever they may have chosen to round theirs.
 
Do you ever provide answers, or do you only give snide commentary?  I don't even have to leave this answer thread to see I'm not the first to receive your wise counsel.
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07/11/15

David W.

WyzAnt is working on a "tutor's forum" that should allow discussions much like those that occur in a teacher's lounge.  I may chat with you there someday.
 
I've found that tutors read this forum much more closely than students.  I posted errors and most other tutors have posted errors (you've noticed that, too).  Thankfully, some tutors have improved quite a bit recently -- checking a student's previous postings before answering, stopping short of a complete answer, including context information and alternatives, and writing some very encouraging words for discouraged students.  However, some tutors seem very proud (and thus would make terrible students) --- better approaches, computer solutions, checking answers, and working together with other tutors are not part of their repertoire.  Perhaps, later, you will able to effect positive change in tutors with your encouraging words.
 
This specific problem starts with numbers that must already have been rounded (160 m, 140m, and 45 m), so including resolution information (+/-) throughout the problem is good math, good computer calculations, etc.  That means that an answer with 5 digits after the decimal point is wrong! (it matters not whose answer that is, it is wrong).  At some point, these students may become engineers, bankers, etc. and deserve to be told what math is being taught and what use it has (so they can answer that age-old question, "Why do we need to learn this stuff?").
 
Now, if you review some problems and answers on this forum, you will find the whole gamut of serious to flippant problems, good to bad answers, pleasant to obnoxious tutor comments to each other, etc.  It is quite a chat room.  WyzAnt monitors it and seeks improvements.  It was originally intended to help link students to tutors and their have experimented with a pop-up chat box to make such a connection, but there is not a direct connection of a tutor to a student yet.  Again, perhaps multiple answers to an initial problem could initiate a paid-for tutoring session online (beneficial to WyzAnt and the tutor).
 
On this forum, I give free answers to students (PLZ feel free to check my resources) and sage advice to tutors (unless, of course, they are too proud to receive it, then I stop -- you've just joined that group).  Fortunately, all postings are public!
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07/11/15

JOHN F.

Proud?  You say that like it's a bad thing.  Yes, I'm proud enough to know when I don't need someone's advice.  Your pride drives you to minimize the work of others when you haven't attempted to do the work yourself.  Oh, and writing a program to answer somebody's question helps nobody but you.  What good have you done them by avoiding the math they're supposed to be learning?
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07/11/15

David W.

Alas, I remember my professors and some real engineers saying, "If you use a calculator instead of a slide rule and the Newton-Raphson method of finding a square root, students will not learn to calculate square roots!"  Well, true, but the concept of "levels of abstraction" is important!  Students can drive a car without knowing how to work on the engine (note: I bought metric wrenches to work on my VW first car, but my current car makes working on it pretty hard).  A few years ago, I was shocked when my 4-year old grandson showed me how to play Angry Birds.  This kid didn't know anything about binary or operating systems or interrupts or ...
 
The "math they're supposed to be learning" is changing and I want introduce students to future (well, no, current) methods for learning/applying it.  I'm writing LMS instruction modules that are graphic, colorful, animated, have sound, etc.  Students can learn the "math they're supposed to" in a half to a third the time [note: current metrics, but I'm shooting for better].
 
Cool!  You have a productivity "hot button."
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07/12/15

David W. answered • 06/12/15

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David W.

If we, like Jerry, "want everything to be perfect," then we often resort to "wanting everything/everyone else to be perfect" because we have realized that we ourselves clearly are not perfect (which is annoying, so we annoy others, too).

I'm testing out various methods for gaining a readership and I now have some devoted readers on this forum. I can't create the Microsoft/Apple/Google/Facebook/etc. approach of "you gotta have it," but if I can make the product/service good enough that others dutifully read/use it (if only to find errors), that works.
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06/12/15

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