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**hannahroxmysocks****Guest**

1) Find the length of the tangent from the point (12,0) to the circle x^2+y^2=4 (^means exponent)

2) Bob gave 4/5 of his pencils to Barbara, then he gave 2/3 of the remaining pencils to Bonnie. if he ended up with ten pencils for himself, with how many did he start?

3) A sheet of paper is 11 inches long. When it is folded in half on the dotted line(hamburger style) the width and length remains unchned. what was the width of the original sheet of paper?

if u know any answers plz tell me!!

**darthradius****Member**- Registered: 2005-11-28
- Posts: 97

1) I am not certain I am understanding this problem correctly, but here goes...

The graph of the equation x^2+y^2=4 is a circled centered at the origin, of radius 2.

A line drawn from the point (12,0) that is tangent to the circle would intersect the circle at one of the y intercepts.

By drawing this line, we create a right triangle, with a base of length 12 on the x-axis, and a height of 2 on the y-axis.

You can now plug these into the pythgorean formula, yielding the square root of 148

2) If we let x be the number of pencils Bob had to start with...

the number of pencils he had AFTER he gave some to Barbara is given: x-(4/5)x or equivalently, (1/5)x...

then, after he gives some pencils to bonnie, he has:

(1/5)x-(2/3)(1/5)x or (1/15)x

Now this last term is the number of pencils left after he has seen both Barbara and Bonnie, and we know from the problem that this number is ten...hence

(1/15)x=10 and x=150 (the # of pencils he had to start)

3) sorry...I don't know what hamburger style means

The greatest challenge to any thinker is stating the problem in a way that will allow a solution.

-Bertrand Russell

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Good post, darthradius. I wouldn't have seen how to do 1) like that.

Just one thing though, the length of 12 is the hypotenuse of the right-angled triangle, so the answer is actually √140, or 2√35 if you want.

And I also don't know what hamburger style means.

Why did the vector cross the road?

It wanted to be normal.

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**darthradius****Member**- Registered: 2005-11-28
- Posts: 97

???

I don't think the 12 is the hypotenuse....

The right angle is formed at the origin by the x and y-axes, isn't it?

The greatest challenge to any thinker is stating the problem in a way that will allow a solution.

-Bertrand Russell

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

The three points of the triangle are (0,0), (12,0) and another one somewhere on the circle. As (0,0) is the origin, the line from (0,0) to the point on the circle would be a radius.

We are also told that the line from (12,0) to the point on the circle is a tangent.

Circle rules say that radius + tangent = right-angle.

If the right-angle was at the origin, then the tangent would have to have a gradient of 0, but then it would miss (12,0), so that can't be it.

Why did the vector cross the road?

It wanted to be normal.

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**darthradius****Member**- Registered: 2005-11-28
- Posts: 97

oh my...you are absolutely right...I over-simplified the problem...whoops!

That's why you're the moderator and I'm just a member...;)

The greatest challenge to any thinker is stating the problem in a way that will allow a solution.

-Bertrand Russell

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**jdeschaine99****Member**- Registered: 2005-12-04
- Posts: 1

what would the awnser be to 7(6 - y) = -3(y-2)

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Multiply out of brackets: 42 - 7y = -3y + 6

Simplify: 36 = 4y

Solve: y = 9

And to check, let's put that back into the equation: -21 = -21.

Why did the vector cross the road?

It wanted to be normal.

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**Mozartmoses****Member**- Registered: 2006-04-26
- Posts: 10

ABC is a right-angled triangle, right angled at A and AD is the altitude on

BC. If AB : AC = 3 : 4, what is the ratio of BD to DC?

can anyone help me with this?

*Last edited by Mozartmoses (2006-05-14 09:41:23)*

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