Quick inquiry....

W

WTF?

Junior Member
Joined
Sep 16, 2005
Messages
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I'm confused a bit, by these problems:

1)It says to simplify:
steppizzleoneizzle.jpg


I get this,
2ndsteppizzlewuzzizlelkj.jpg


Hope fully, it all simplifies to this \(\displaystyle 2i^2\) * \(\displaystyle 2\)

Then I get -2*2=-4,
I'm not sure about this, but am I doing something wrong?

Also, theres another problem:
10*sqroot(-50), I get 50i*sqroot(2)
 
WTF? said:
I'm confused a bit, by these problems:

1)It says to simplify:
steppizzleoneizzle.jpg


I get this,
2ndsteppizzlewuzzizlelkj.jpg


Hope fully, it all simplifies to this \(\displaystyle 2i^2\) * \(\displaystyle 2\)

Then I get -2*2=-4,
I'm not sure about this, but am I doing something wrong?

"Hopefully"? "Something wrong"? . . Looks brilliant to me.

Also, theres another problem:
10*sqroot(-50), I get 50i*sqroot(2)
Correct again.
Click to expand...
 
THE ANSWER COULD BE: UNDEFINED
What is the domain of definition?
Are we in the 'reals' or 'comlpex numbers'?
There is no answer without knowing domains!
 
Hello, it's me again and i'm in need of another push. :(

Teh problem:
Miriam wants to construct a rectangular pen alongside her house for her puppy Webster. Her father saidshe could use the 22 meters of chicken wire he had in his garage. what should be the dimensions of the pen if miriam wants Webster to have as much running area as possible.
I don't understand how one could put this in a quadratic form, this is a problem under quadratics, and the book says the answer is 5.5x11 meters :? , I'm totally confused as how that was done.

Another one. :(
A ball is hit by a bat when 3 feet off the ground. It is caught at the same height of 300 feet away from the batter. How far from the batter did it reach its maximum height?
Again, the book says 150ft. :?

Thanks for any posts regarding my confusion.
 
WTF? said:
Hello, it's me again and i'm in need of another push. :(

Teh problem:
Miriam wants to construct a rectangular pen alongside her house for her puppy Webster. Her father saidshe could use the 22 meters of chicken wire he had in his garage. what should be the dimensions of the pen if miriam wants Webster to have as much running area as possible.
I don't understand how one could put this in a quadratic form, this is a problem under quadratics, and the book says the answer is 5.5x11 meters :? , I'm totally confused as how that was done.
Click to expand...
We have:
Code: 
    |             |
    |             |
    |             |
  x |             | x
    |             |
    |_____________|
           y
Perimeter = ? [1]

Area = ? [2]

Use [1] to write [2] in terms of one variable. This gives you an upside down parabola. Determine where its maximum height, that is the greatest area, (its vertex) occurs.
 
WTF? said:
Another one. :(
A ball is hit by a bat when 3 feet off the ground. It is caught at the same height of 300 feet away from the batter. How far from the batter did it reach its maximum height?
Again, the book says 150ft. :?
Click to expand...
Ignoring air resistance, the ball will have a symmetrical, parabolic path.

The vertex of a parabola is always half-way between two points on the parabola if they have the same height.

Code: 
   /|\ y
    |                      *                            
    |                       
    |
    |           *- - - - - + - - - - -*
    |
    |      
    |     *- - - - - - - - + - - - - - - - -*            B: batter; C: catcher
    |
    | 
   3+ B- - - - - - - - - - + - - - - - - - - - -C
    | |<-      150       ->|<-      150       ->|
    | |                                         |
  --*-+--------------------+--------------------+-*---->
    | |<-  - - - - - - - - - - - - - - - - - - >|      x                                      
    |                     300
 
WTF? said:
P=22
A=?

So 22=x?

gahhhh.... :twisted:
Click to expand...
Yes, the perimeter is 22. I phrased that poorly.

But we can form an equation based on that.

From the diagram, and knowing the perimeter is 22, we know
2x + y = 22 [1]

as 2x + y is an expression for the perimeter.



Area = base * height = xy [2]

From [1], y = 22 - 2x

Substitute this expression for y into [2]:

xy becomes x(22 - 2x).

So, area = x(22 - 2x)

We know the area is therefore given by an upside parabola. Upside side down because expanding gives: 22x - 2x^2; the negative in front of x^2 tells us the parabola is upside down.

You can find the x-intercepts (the parabola's equation is already factorised) and use the symmetry of the parabola, as I tried to explain, to find the x-value where the parabola's highest point occurs.

That gave you the lengths of the left and right-hand side, use equation [1], that is the perimeter's equation, to find the bottom side, y.
 
Helllo again. :oops:

I have several quick questions that I need reassurance on.

15y=5x^2 -30x -21

It says to put it in vertex form, I get:
y+(26/15)=3(x-1/3)^2.

Also, I have these questions that ask for number of x-intercepts of the graph of the parabola.

y=7x^2 -2x +11 I put 0, since the discriminant is negative.

y=-2(x-8)^2 -1 I put 0 since the discriminant is negative

y=x^2 -20x +100 I put 0 since the discriminant is negative.

Thanks for any input.
 
WTF? said:

I have several quick questions that I need reassurance on.

15y=5x^2 -30x -21

It says to put it in vertex form, I get:
y+(26/15)=3(x-1/3)^2.
Unfortunately not.

Let's do some steps retracing.

15y = 5x^2 - 30x - 21

Add 21 to both sides

15y + 21 = 5x^2 - 30x

We prefer a coefficient of 1 in front of x^2, so divide both sides by 5:

3y + 21/5 = x^2 - 6x

Now complete the square on the right-hand side:

x^2 - 6x = (x - 3)^2 - 9
Remember we need to subtract 9 because (x - 3)^2 by itelsf equals x^2 - 6x + 9.

So we have

3y + 21/5 = (x - 3)^2 - 9

Now arrange into the vertex form, y = a(x - k)^2 + h.

Also, I have these questions that ask for number of x-intercepts of the graph of the parabola.

y=7x^2 -2x +11 I put 0, since the discriminant is negative.
Correct.

y=-2(x-8)^2 -1 I put 0 since the discriminant is negative
Correct. You can also see from the equation (which is in vertex form) that the parabola is upside down and has a vertex below the x-axis, this is its highest point.

y=x^2 -20x +100 I put 0 since the discriminant is negative.
The discrimant is zero! How many x-intercepts?
Click to expand...
 
WTF? said:
Is -13 irrational or rational?
Click to expand...
Do you know what a "rational" number is, or how "rational" versus "irrational" relates to fractions?

Eliz.
 
Familiarise yourself with the definition of a rational number to remove any uncertainty.

Mathworld said:
A rational number is a number that can be expressed as a fraction \(\displaystyle \mbox{ \frac{p}{q}}\) where \(\displaystyle \mbox{p}\) and \(\displaystyle \mbox{q}\) are integers and \(\displaystyle \mbox{q \neq 0 }\) ... Numbers that are not rational are called irrational numbers.
Click to expand...
 
Unco said:
Familiarise yourself with the definition of a rational number to remove any uncertainty.

Mathworld said:
A rational number is a number that can be expressed as a fraction \(\displaystyle \mbox{ \frac{p}{q}}\) where \(\displaystyle \mbox{p}\) and \(\displaystyle \mbox{q}\) are integers and \(\displaystyle \mbox{q \neq 0 }\) ... Numbers that are not rational are called irrational numbers.
Click to expand...
Click to expand...
'

Ah, thanks. So -13 is rational.
 
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