Question

@mathmale help

Answer 1

#4

Answer 2

At first glance, Problem #4 strikes me as involving linear algebra. You're right; it has no connection whatsoever to #3.

Have you graphed systems of inequalities such as
5x - 4y equal to or less than 20
3x + y equal to or greater than 7

??

Answer 3

yes

Answer 4

i didn't know they were inequalities

Answer 5

That's part of the challenge of #4.
Actually, there are clues in the problem statement that the number of weapons and the number of batteries stored on board are not limitless.
How many total weapons can go on board?
What's the max number of batteries that the space ship can accommodate?

Answer 6

.. im confused

Answer 7

Clearly some info is missing from Problem #4. It's up to us to identify what is missing, so that we can ask Mr. Captain for that info. What do you think is missing? You're the one who decides how many of each kind of weapon goes on board and ensures that every single battery on board is used.

Answer 8

is the number of missiles missing

Answer 9

I do view this question as being a fair one, especially if you've worked with linear inequalities before.

Yes, we don't know how many missiles we should stash on board.

Answer 10

But our hero Plohrr has clipboard and fountain pen in hand and can ask all the questions he wants of Mr. Captain.

Answer 11

:D

Answer 12

so, we have to make out own number

Answer 13

Not quite make up our own number, but rather choose a variable to represent the # of missiles to be stashed on board. Later we'll find the numeric value of that variable.

Answer 14

oh like x ?

Answer 15

You bet. What next?

Answer 16

I see that our hero is becoming better and better day by day in dreaming up questions that get him where he wants to go.

Answer 17

haha so now we set up a system correct

Answer 18

Yes. Mr. Plohrr defines x as the number of missiles that go on board. Then he realizes that there's more than one unknown involved here, and with intense focus attempts to identify and name that unknown.

Answer 19

so there is a y too

Answer 20

No kidding, there is a y as well.

So, always desirous of being precise, Mr. P. lists his variables by name and defines each one. Then he starts pondering the age-old question of how those variables may be related to each other.

Answer 21

Our hero reviews his meticulously neat notebook to find something relevant, and comes up with the following:
"Not quite make up our own number, but rather choose a variable to represent the # of missiles to be stashed on board. Later we'll find the numeric value of that variable."
He then defines the second variable.

Answer 22

so now we solve the system.

Answer 23

Very soon. Hope my story isn't turning you off.
Having defined x and y, is there any data from the problem statement that you could use to write a relationship between x and y?

Answer 24

We don't yet have a system to solve, but are getting there.
There remains one more key question to ask of the captain before we'll be there.

Answer 25

..

Answer 26

There are two different types of weapons: missiles and guns.
Mr. Plohrr defines x as the number of missiles that go on board.
He then realizes that y represents the number of guns, and also realizes that the total number of weapons that can be stashed on board is limited ... to what figure?

Answer 27

hmm. only 15 weapons!

Answer 28

Right on. Thus, x + y = ?

Answer 29

15

Answer 30

Then the first inequality is
x+y equal to or less than 15.

Guns and missiles don't use the same number of batteries, do they? Some key info is missing here: How many batteries does a gun require? How many does a missile require?

You have the right to ask Mr. Captain for that info. Once he replies, how are you going to use that info to write a new inequality?

Answer 31

the ship only has 45 batteries

Answer 32

Right. And thus the total number of batteries required by the x missiles PLUS the total number of batteries required by the y missiles must sum up to 45; that's the upper limit.

Please try phrasing the question you're going to ask Mr. Captain at this point.

Answer 33

x + y = 15

x + y = 45? that doesn't look right

Answer 34

Right, it doesn't. The first equation is just fine.

(From before:) Guns and missiles don't use the same number of batteries, do they? Some key info is missing here: How many batteries does a gun require? How many does a missile require?

You have the right to ask Mr. Captain for that info. Once he replies, how are you going to use that info to write a new inequality?


Suppose that you learn from Mr. C. that each missile requires C batteries and each gun requires G batteries.

The total number of batteries available is 45.

Can you write the appropriate inequality now?

Answer 35

im not sure

Answer 36

There are x missiles, and each missile requires C batteries. Therefore the total number of batteries allocated to missiles is Cx.
Similarly, the total number of batts. allocated to guns is Gy.

Cx + Gy is equal to or less than 45 (the total number of batteries available).

Without knowing C and G, you can't do any more than this. But you do have a good system of equations to solve for x and y. This wraps up Problem #4. (Was that you, Mr. P., taking a deep breath?

Answer 37

x + y eq to or less than 15
Cx + Gy eq to or less than 45

is your system of ineq.

Answer 38

ohhh i see!

Answer 39

I strongly encourage you to go over this discussion several times until you find yourself able to do the problem completely on your own.

Move on to the next problem. First, would you please try phrasing some questions about what you believe you need to know to get started on a solution?

Answer 40

Peter, I've enjoyed this greatly; hope my attempts at humor and story-telling with you the lead character haven't been turn-offs for you.
I do need to get off my computer and join my friends for breakfast. You could either post Problem #5 in the usual way, or respond to my request (would you please try phrasing some questions about what you believe you need to know to get started on a solution?) through a private message.

Answer 41

ok, thanks again, always a great help !

Answer 42

My pleasure. We'll talk again soon, I'm sure. Bye for now!

Answer 43

bye !

Answer 44

there you are

Answer 45

Yeah, here I am. Learned something from you!

Answer 46

So, regarding the very last question, what are your current thoughts? As you get to know me, you'll see that I like most to build upon what you already know.

Answer 47

wait a minute that is not the whole question

Answer 48

there is a graph

Answer 49

I find myself asking questions:
(1) where are we on the Headquarters orbit x^2 + y^2 = 200^2 at the moment?
(2) Since no time is involved, only coordinates of location, are we to assume that the HQ and the satellite are stationary (I don't think so).

Any way in which you could post that graph? Let's be creative here.

Answer 50

I can't attach but I can email like you said

Answer 51

wrgnsc@rit.edu

Answer 52

Let me know when you've e-mailed the illustration.

Answer 53

emailed

Answer 54

Sounds as though you'll end up with two intersecting straight lines. If so, this problem should be pretty easy to complete. Looking at the table given, how would you go about coming up with an equation representing this (linear) data?

Answer 55

Well one is a graph and we can make a graph using that table

Answer 56

Use any method you like to come up with an equation representing the data in that table. Probably we could solve this problem without coming up with an equation, but instinctively I'd say the results would be more accurate and more satisfying if you did have such an equation.

Answer 57

slope intercept from ok?

Answer 58

That would work fine. If you go that way, find the slope of the line represented by the data points, and then plug the slope and the coordinates of one of the points in the table into the slope-intercept formula.

I'd use the point-slope formula myself, but either will succeed.

Answer 59

y = x+ 0

Answer 60

OK, now please choose any point from the table. Substitute the x- and y-coordinates into your equation y = x + 0 and determine whether or not the resulting equation is true.

Answer 61

it isn't true

Answer 62

I subbed y as 1 and x as 2

Answer 63

Yes, and is the resulting equation true or false?

Answer 64

OH, excuse me, I see y ou've already answered that. Sorry.
In that case, something went wrong. Let's go back and redo the derivation of the equation representing the data in the table.

Answer 65

What are the first 2 points represented in the table? Type them out as points (x,y).

Answer 66

(1,0)

Answer 67

yes, and the next one?
I'd like for you to determine the slope of the line segment connecting these two points. Or, maybe we could skip that step, because you already have the slope correct: it is +1.

Answer 68

(1,0) is the first point; the next one is ( ? , ? )

Answer 69

(2,1)

Answer 70

Right. Either go through the calculations again to determine the slope of the line segment connecting those 2 points, or just accept your previous answer: m=1. Which will it be?

Answer 71

Just a bit of advance notice: My pal here in Calgary, Alberta, and I are going out on errands in just a few minutes, but I promise to be available later in the day. In the meantime I'd encourage you do do as much as you can towards solving the current problem.

Answer 72

m =1

Answer 73

You have two points: (1,0) and (2,1). You've correctly found the slope of the line connecting these 2 points. All you need to do now is to determine the y-intercept, b. Yes, m=1.

So, choosing the first point (arbitrarily): y = m x + b
0 = (1)(1) + b.

What's b?

Answer 74

1

Answer 75

false 0 doesn't equal 2

Answer 76

After you've substituted this value of b into y=mx+b, you'll have the equation of the straight line repres. the data in your table. Please check that: b is actually negative here, not positive. Illustrate your work so that I can give you feedback on it.

Answer 77

It's great that you're checking y our own work as you go along. Way to go!!

Answer 78

For example: Peter writes:
y = m x + b and then substitutes the knowns x=1 and y=0:
0 = 1 (1) + b.
Peter subtracts 1 from both sides of this equation and ends up with:

Answer 79

Just a bit of advance notice: My pal here in Calgary, Alberta, and I are going out on errands in just a few minutes, but I promise to be available later in the day. In the meantime I'd encourage you do do as much as you can towards solving the current problem. Share it with me via e-mail, or by private message, or by responding right here. I'll definitely respond later today.

Answer 80

ok so does 0=0

Answer 81

so it's true

Answer 82

You'll end up with the equations of 2 straight lines. All you have to do is to determine the coordinates of the point at which they intersect.

See you soon, Peter! So, you got b=-1? Absolutely correct.
thus, y=x-1 is the correct equation!

Bye for now! 'til later.

Answer 83

the other line is y = 2x - 5

Answer 84

so now I'm guessing I have to solve the system ?

Answer 85

Im not sure where to go from here so I'll wait until you're back ! thanks again

Answer 86

:)

Answer 87

Hi, Peter!
Yes, you're to solve the system of linear equations:
y=2x-5
y=x-1

with one caveat: the slope of the first equation is actually 2.5, or 5/2. Best way to check that out is to pick any point on the given line (trajectory) that has integer coordinates and determine whether or not the equation is true or not.

So: think of having to solve y=(5/2)x-5 and y=x-1 as a system of linear equations.

I'd encourage you to consider what options you'd have here: substitution, elimination by addition/subtraction, graphing, matrices and determinants. Any of these sound sufficiently familiar to you to encourage you to try them?

Answer 88

ive only learned substitution and elimination so far

Answer 89

Which would you prefer to try now?

Answer 90

substitution

Answer 91

so it would be x - 1 = 2x - 5

Answer 92

and solve for x

Answer 93

y=(5/2)x-5 and y=x-1 could be equated to one another, thereby eliminating the y. Make sense? if so, please try it. Your goal is to find x that satisfies the resulting equation. Right (except that you want y=(5/2)x-5, not 2x-5).

Answer 94

oh ok so x = -1

Answer 95

Haven't done it myself, but I'll guide you through checking it. If your x=-1, then use either equation to predict y.

Answer 96

no i did it wrong

Answer 97

im at a hotel so im doing this all in my head ..