Please help! I'm lost......

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sunnygirl37

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Sep 13, 2009
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Hi...

I have two math problems that I am completely lost on and and need the answers to by tomorrow evening.

The first one is:

A canada goose flies at a speed of x mi/hr in still air. Write a function for the rate of the goose flying in the opposite direction as a 20 mi/hr wind.

A) f(x) =20x
B) f(x) =x-20
C) f(x) =x
D) f(x) =x+20
E) None of these

The next problem is:

The function of f(x) =40+x models the total number fo gallons of chocolate in a 50-gallon tub that has x gallons of new chocolate added to it when the tub already had 40 gallons of chocolate. The value of x is restricted to:

A) [0,40]
B) [0,50]
C) [0,10]
D) [10,40]
E} [none of these]

I appreciate any help offered. Thank you :)
 
sunnygirl37 said:
Hi...

I have two math problems that I am completely lost and and need the answers to by tomorrow evening.

The first one is:

A canada goose flies at a speed of x mi/hr in still air. Write a function for the rate of the goose flying in the opposite direction as a 20 mi/hr wind.

A) f(x) =20x
B) f(x) =x-20
C) f(x) =x
D) f(x) =x+20
E) None of these

The next problem is:

The function of f(x) =40+x models the total number fo gallons of chocolate in a 50-gallon tub that has x gallons of new chocolate added to it when the tub already had 40 gallons of chocolate. The value of x is restricted to:

A) [0,40]
B) [0,50]
C) [0,10]
D) [10,40]
E} [none of these]

I appreciate any help offered. Thank you :)
Click to expand...

Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.
 
For #1 - what does the answer (A) tell you?

For #2 - what does the answer (A) tell you?
 
Well on #1, I know that I'm looking for restricted values.
That's where I get lost...I don't know how to plug in any of the choices or even what I should be looking for.

Same with question #2...(Sorry :(
 
mmm4444bot said:
… A [Canadian] goose …
Click to expand...


Good grief! :lol:

What was I thinking.

WHOOPS, Microsoft Windows lost all of my previous text, in this reply, while I was trying to add the comment above. Oh, well. What else is new. :x
 
I checked and there is no wording of headwind or tailwind. It doesn't specify if the bird is flying with the wind or against it. I typed the problem exactly as it was written (which was poorly). I don't know what the square brackets mean...
 


Okay. Let's interpret the given statement to mean that the bird is flying in a direction opposite TO the 20 mph wind.

In other words, the bird is flying into a headwind.

So, we need to understand some basic physics, in this senario. I'm going to explain a similar situation.

A fish swims x mph in still water. What expression represents the fish's speed while swimming with or against a 5 mph river current.

When the fish goes "with the flow", its speed x is increased by 5 mph because the water helps "push" the fish along.

Speed swimming in the same direction of current: x + 5

When the fish goes "against the flow", its speed x is decreased by 5 mph because the water slows the fish by "pushing" against it.

Speed swimming in the opposite direction of current: x - 5

Does this "physics" make sense? Do you understand how it applies to the bird flying against a 20 mph wind?

In the second exercise, those square brackets indicate an interval of the Real number line. (It's called "Interval Notation".)

[0, 40] means the interval 0 ? x ? 40

In other words, it's a way of saying that the domain is the set of all Real numbers from 0 though 40. Both endpoints are included, in this interval, because a square bracket indicates inclusion.

(Interval notation uses a parenthesis to indicate exclusion.)

Now, does that particular choice for the domain make sense, for the given function? No, it does not. The vat holds only 50 gallons. If we add 40 gallons to the existing 40 gallons, there will be chocolate all over the floor because 40+40 is a total of 80 gallons.

What is the maximum number of gallons that can be added to 40 gallons without exceeding the capacity of 50 gallons?

 
Yes, I think I understand what you are saying on problem #1. I think the answer would be B) f(x) =x-20. The way you explained it in regards to the fish helped.

On problem #2, 10 gallons would be the maximum allowed since it already contains 40 gallons.
 
sunnygirl37 said:
… on problem #1 … I think the answer would be … f(x) = x - 20 …

Yes!

Here's the sort of information that comes out of function f.

If a particular goose flies 25 mph in still air, then x = 25. f(25) = 5, and this means the bird flies only 5 mph in a 20 mph headwind.

If a stronger goose flies 55 mph in still air, then x = 55. f(55) = 35, and this means that the bird flies only 35 mph in a 20 mph headwind.

If a weaker goose flies only 10 mph in still air, then x = 10. f(10) = -10, and this means that 10 is not in the domain of this function because the speed cannot be negative. (Well, "velocity" can be negative, but wait until you study vectors before considering "backwards" flight.)

In other words, this particular function f only works for determining the speed (in a 20-mph headwind) for geese that fly AT LEAST 20 mph in still air.

So, the domain of f is [20, ?) mathematically. Of course, in reality, there is an upper limit because geese cannot approach the speed of light. 8-)

On problem #2, 10 gallons would be the maximum allowed since it already contains 40 gallons.

Yup. So what are all of the possible amounts that could be added to the vat?

The answer to this question is the domain (i.e., the set of x values that make sense), and the domain can be expressed using interval notation.
Click to expand...
 
sunnygirl37 said:
On answer 2...I'm not sure if the answer is C or D ?
Click to expand...

A) [0,40]
B) [0,50]
C) [0,10] ----------- 0 ? x ? 10
D) [10,40]----------- 10 ? x ? 40
E) [none of these]

So then - which one you shouldn't choose? Why?
 


Why are you still guessing?

It seems to me that you still do not understand the exercise, OR you've decided to stop thinking.

There is a 50-gallon vat that already contains 40-gallons of chocolate. You previously told me that you understand this: no more than 10 gallons of chocolate can be added to the existing 40 gallons.



A) [0,40] ? This choice says that you can add any amount from 0 gallons to 40 gallons

B) [0,50] ? This choice says that you can add any amount from 0 gallons to 50 gallons

C) [0,10] ? This choice says that you can any amount from 0 gallons to 10 gallons

D) [10,40] ? This choice says that you can add any amount from 10 gallons to 40 gallons

E} [none of these] ? This choice says that you can not add any additional chocolate to the vat

Why is the correct answer not obvious to you? :?
 
sunnygirl37 said:
So am I correct that the answer would be C?
Click to expand...

Let me see if I've got this right.

You were down to choices C and D.

You were helped to see that D could not be correct.

And you're asking if C is right? I guess you aren't really thinking about this too much.
 
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