Math Is Fun Forum

basketballstar123

Member

Registered: 2016-08-10

Posts: 11

More Geo

Problem 1:  A rectangular box $P$ is inscribed in a sphere of radius $r$. The surface area of $P$ is 384, and the sum of the lengths of its 12 edges is 112. What is  $r$?

Problem 2:  The equation of the line passing through $(1,8)$ and $(5,6)$ can be expressed in the form
\[\frac{x}{a} + \frac{y}{b} = 1.\]
Find $a$.

Problem 3:  Let $P = (5,1)$, and let $Q$ be the reflection of $P$ over the line $y = \frac{1}{2} x + 2$. Find the coordinates of $Q$.

Problem 4:  The vertices of a triangle are the points of intersection of the line $y = -x-1$, the line $x=2$, and $y = \frac{1}{5}x+\frac{13}{5}$. Find an equation of the circle passing through all three vertices.

Problem 5:  In triangle $PQR$, we have $\angle P = 90^\circ$, $QR = 15$, and $\tan R = 5\cos Q$. What is $PQ$?

Problem 6:  Two circles of radius 1 are externally tangent at $Q$. Let $\overline{PQ}$ and $\overline{QR}$ be diameters of the two circles. From $P$ a tangent is drawn to the circle with diameter $\overline{QR}$, and from $R$ a parallel tangent is drawn to the circle with diameter $\overline{PQ}$. Find the distance between these two tangent lines.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: More Geo

Hi;

These look like Compuhigh problems and I have been instructed to not answer these questions. I am sorry.

Please show that it is not a Compuhigh problem and I will work on them. In the meantime I ask that no one else solve these, the answers will only be erased anyway.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

basketballstar123

Member

Registered: 2016-08-10

Posts: 11

Re: More Geo

What is a compuhigh problem?  Never heard of it...

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: More Geo

Hi;

Okay, I believe you. My apologies to you.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

basketballstar123

Member

Registered: 2016-08-10

Posts: 11

Re: More Geo

Thank you!!  I got 'em.  Can you help me with another prob plz:

In the diagram below, $WXYZ$ is a trapezoid such that $\overline{WX}\parallel \overline{ZY}$ and $\overline{WY}\perp\overline{ZY}$. If $YZ = 12$, $\tan Z = 1.5$, and $\tan X = 2$, then what is $XY$?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: More Geo

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: More Geo

hi basketballstar123

Using tan Z you can determine the value of WY and then, from Tan X, WX.

Then Pythagoras to get an equation for XY squared.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

basketballstar123

Member

Registered: 2016-08-10

Posts: 11

Re: More Geo

Is the answer 9sqrt(5)?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: More Geo

Hi;

That is what I am getting too.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

basketballstar123

Member

Registered: 2016-08-10

Posts: 11

Re: More Geo

Okay.  Thank you!!  I got it right.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: More Geo

Very good!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.