jboy314

A. The tricky part of this proof is that we must recognize that angles PAO and PBO are both right angles because they are formed by radii to tangents.  Therefore they are congruent.

Segment AO is congruent to segment BO as they are both radii.

Segment PO is congruent to itself by the reflexive property of congruence. This essentially means that it is a segment that is a side length of both triangles.  We should also note that is the hypotenuse. 

With these pieces of information hand we are able to say the triangles are congruent by the Hypotenuse Leg theorem of triangle congruence!

x intercepts are where the y value is zero.  Therefore to find the x intercept we let y=0

x^2-16=0

x^2=16

x=4 or -4

To find y intercept we need to recognize that it occurs where x=0 so we set x to 0

y=0^2 +16

y=16

Well it sort of depends.  I once asked a professor this question and he responded with, "it blows up, like a bomb."

One way I like to think of it is in a real context.  First of all lets say I had no hamburgers and five friends, and I wanted to share my hamburgers with my friends.  since there are six of us this is 0/6.  The question, then, is how much food do each of my friends get?  None of course because there is no food!   Now we flip the script.  Lets say i have six burgers but i have not friends to share them with.  How many burgers do each of my friends get?  Mathematically this looks like 6/0 and at first many people think this is also zero.  Consider it more closely though, the question was how many burgers do each of my friends get?  Since I have no friends in this context it the question makes no sense and therefore we cannot answer the questions.  When we run into things like this in math we say they are undefined.

another answer to this is infinity.  Pick a number, any number and divide it by 1.  Then divide by .5, then by .2 then .1.  Divide it by .01 and .001 and .0001 and notice the pattern.  The numbers get massive!  This is undoubtedly what my professor meant when he said it blows up like a bomb!

let's start testing factors and see what we get.  The factors of 24 are 2, 3, 4, 6, 8, 12, and 24

As it turns out the only one of these that is a factor of 74 is 2

whoohoo a bunch of rectangles and triangles!

Since the end triangles have side lengths of 6, 8, and 10 they are a pythagorean triple which implies that they are right triangles.  As such each has an area of 6(8)/2=24 m^2

The base is a rectangle with lengths 8 and 17 so its area is 8(17)=136 m^2

The "back" side has lengths of 6 and 17 so its area is 6(17)=102 m^2

And the "top" face has lengths of 10 and 17 so its area is 10(17)=170 m^2

Add them all together and we get 2(24)+136+102+170=456 m^2

Found with a quick google search:

"

• 108,000 km/h

   
• The orbital speed of the Earth around the Sun averages about 30 km/s ( 108,000 km/h, or 67,108 mph), which is fast enough to cover the planet's diameter (about 12,700 km, or 7,900 miles) in seven minutes, and the distance to the Moon of 384,000 km (239,000 miles) in four hours."

you would need to factor out something from within the radical. 

For example take sqrt(50)=sqrt(25)sqrt(2)   notice that 25(2)=50 so we are just factoring and giving each fraction its own radical.  if we simplify the sware root of 25 then we get

5sqrt(2)  whcih is not a simplified radical. 

5(8)+5=45

so the improper form (which is generally preferred) is 45/8

initially it was in degrees and it should be noted that the 180 on the right side was initially in degrees.  I'm sort of disappointed to hear that there is not an elegant way to solve this!

this is a reflection about the line y=x-2