Question

Can some one Plzz help?!!
Activity 1). An archer releases an arrow from a shoulder height of 1.39 m. When
the arrow hits the target 18 m away, it hits point A. When the target is
removed, the arrow lands 45 m away. Find the maximum height of the
arrow along its parabolic path.

Answer 1

Activity 2). Archers need to use arrows that do not bend easily. Th e table shows how the weight of an arrow affects its spine, or the distance the center of the arrow bends when a certain constant weight is attached. Graph the data in the table to find a linear and a quadratic model for the data. Use the regression feature on your calculator to find each model. Which model is a better fit? Explain.
The table
Weight (in grams) 140,150, 170,175,205
Weight (in inches) 1.4, 1.25,.93, .78 ,.43
this is the picture of the target http://assets.openstudy.com/updates/attachments/507e201be4b0919a3cf31396-ducky_fresh-1350443065381-target.png

Answer 2

@Directrix plzz help

Answer 3

@Hero @myininaya @Zarkon @robtobey @RadEn @thomaster @jdoe0001 @tkhunny @Luigi0210 Can you plzz help me anyone

Answer 4

I think the idea is supposed to be that they give you three points and you find the parabola. Which you can totally do, and I can show you how to do.

What I'm not grasping is how point A contains any useful information. Do you know the height of the target?

Answer 5

its 1.52 m

Answer 6

Oh. Then, yeah, you have three points.

Answer 7

so how would i do it

Answer 8

Ok. The point where the arrow is launched, we'll call that x = 0 so it's (0, 1.39)
The target is 18m away and after doing all the subtraction it hits 1.28m up so that point is (18, 1.28)
And finally if the arrow just flies it hits the ground (y = 0) so that point is (45, 0)

Answer 9

so how would i put that in a form

Answer 10

I'm getting to that. If you just want me to give you the answer it's not going to happen. I'm going slowly so you actually understand.

Answer 11

okay lets start lol

Answer 12

The standard form for a parabola is \(ax^2 + bx + c = y\)
You have three x/y values up there. So you can plug them in and get a system of three linear equations, which you solve to find a, b, and c.
\[0 + c = 1.39\]\[a(18^2) + b(18) + c = 1.28\]\[a(45^2) + b(45) + c = 0\]

Answer 13

okay so c is 1.39

Answer 14

Right. Now you can plug that in and figure out a and b.

Answer 15

so how would you do that

Answer 16

The same way you solve any other linear equation.

Answer 17

Once you've done that, you'll have it in \(y = ax^2 + bx + c\) and have something that looks like this.

The maximum height of the arrow will be the vertex of the parabola.

The formula for the x value of the vertex of the parabola is \(\frac{-b}{2a}\) and of course from that you can find y... which is your answer.

Answer 18

1.41m right

Answer 19

im still lost i know the answer i just want to be explained how you would/what you would do to get that answer because i know the answer is 1.41m

Answer 20

I did explain it!
And I was just doing it to make sure I got that answer.

Answer 21

(And I did :D )

Answer 22

Do you not know how to solve a system of linear equations?

Answer 23

okay so can you show me the steps you did to get that answer like you showed me earlyier it was together

Answer 24

I did show you the steps.
However, at some point, something was unclear.

So let's go back. Do you understand how to solve a system of linear equations?

Answer 25

not really

Answer 26

Ok. Essentially, the process is that if you have n variables, you need n unique linear equations and you can find all of them. If you want to find a and b, for example, you'd need two equations.

For example, if we have
\[a + b = 10\]\[2a - b = 2\]We can find both a and b using that system. There are a variety of techniques but I tend to prefer substitution or elimination. It's a little complicated to try to teach the whole thing but I think you can get it.

We solve the first equation for b.
\[b = 10 - a\]Then we plug that into the second:
\[2a - (10 - a) = 2\]\[2a - 10 + a = 2\]\[3a = 12\]\[a = 4\]
Not that we know a, it's easy to find b.
\[4 + b = 10\]\[b = 6\]

The process is the same here. It is just three variables and three equations, and much uglier coefficients.

Answer 27

okay im copying ot to a sheet of paper to remember this

Answer 28

There are probably better lessons on solving systems of equations out there. This is the absolute basic idea.

(Calculators will also do it for you, which can help when the coefficients are ugly. But you should know how.)

Answer 29

okay i under stand now can you show me the exact way you did that example and show me how would i get the answer

Answer 30

Well, to be completely honest, I didn't feel like messing with it so I used this.
http://math.bd.psu.edu/~jpp4/finitemath/3x3solver.html
Like I said, this is something calculators can and will do quite readily.

But I actually know how to do it. You should probably study it if you don't know how. :D

Answer 31

i will so know would you so kindly help me to do the activity 2

Answer 32

Sorry, I can't. I've got to go.

That one even says "use your calculator" though so... do that.
Or if you don't have the right kind of calculator there are websites that will do that for you, too.
http://easycalculation.com/statistics/regression.php

Answer 33

@Luigi0210 can you help me with activity no.2

Answer 34

@Directrix now may you help me with the second activity

Answer 35

@willie12345678

Linear Regression Equation:

http://easycalculation.com/statistics/regression.php

Answer 36

do my answer is the stuff under results