jboy314

try solving the following based on the techniques that I posted in response to one of your earlier questions!  If you get stuck or want to verify your work feel free to post and we can discuss

6890<C<8840

6890<39m+2600<8840

Remember how in basic algebra anything that we do to one side of an equation we do to the other as well to keep it balanced?    The same applies here with one caveat: if you multiply or divide by a negative number you must flip the inequality signs.  Here is an example of why this is important/

take 2<4, an obviously true statement and multiply both sides by -1 so we have -2<-4,  this is now not true!  If we flip the inequality so it says -2>-4 we have preserved out relation however. 

Secondly, its not so much about sides in algebra as it is about hitting every "chunk" of math that is separated by a relation symbol.  With that, back to your initial question.

Let's subtract four, not from both sides, but from all three "pieces"

-12<-2x<=-9      Now we divide by -2, dont forget to flip the signs!

6>x=>9/2      And we are done!

It can also be written as  x<6 and x>=9/2

There are a handful of reasons.  Let's start with a relatively basic one and see where the conversation goes.  In geometry we learn that the sine ratio is equal to the ratio of the lengths of the opposide side and hypotenuse of a right triangle.  Let's apply this to an arbitrary right triangle.  When we select the right angle as our angle for the sine function something odd happens.  It turns out that the opposite side, in this case, is the hypotenuse!

sin(90)=o/h

o=h

Therefore o/h=1

If you make it a little bit farther in math you could consider the unit circle.  On the unit circle 90 degrees represents a vector of magnitude 1 pointing straight up from the origin to the point (0,1).  Since sin(x)=y it follows by substitution that since y=1, sin(90)=1

Using the quadratic formula is a method that ALWAYS works.  Isn't it nice when you find something that always works?

There are a few ways to start thinking about this but here is the one that feels most natural to me.  We note that since a hexagon has 6 sides the sum of its interior angles will be 720 degrees and since there are six of them, each must be 120 degrees.  Now let's draw in the radius and apothem somewhere next to eachother on our figure (you should draw this out so you can see).  When we draw the radius and apothem we have created a right triangle.  The radius bisects a 120 degree angle so the interior angle of the triangle at that vertex is 60 degrees, while the final angle of the triangle is 30.  A 30-60-90 triangle!  Lucky us!  Since the hypotenuse(radius) is 11, the shortest leg of the triangle will be half as much.  5.5 in this case.    in a 30-60-90 triangle it always holds the relationship that the longer leg is  greater than the shorter leg by a factor of sqrt(3).  Therefore your apothem has length 5.5sqrt(3)

This is in slope intercept form,y=mx+b ,  where m is slope and b is y-intercept.  Therefore the slope of this one is 3.

notice that both 46 and 69 are divisible by 23 so the simplified fraction is 2/3 multiplied by 100.  When you perform the multiplication your answer is 200/3

First we should simplify f(x)

f(x)=2+3+x=5+x    Now we want to get rid of the function notation so that the algebra is as friendly as possible

y=5+x

To find an inverse we replace each x with y, replace each y with x, and solve for you as follows

x=5+y

x-5=y

And there is your inverse function!

The inverse function property is likely the one that says that if two functions f and g are inverses of one another then f(g(x))=g(f(x))=x  Lets test it!

f(g(x))=f(x+7)=(x+7)-7=x   It checks out so these functions are indeed inverses of one another.

In kinematics there is a formula to describe this

d=v_i+(1/2)at^2    where distance is in meters, v_i is initial velocity, a is acceleration, and t is time in seconds.

for your problem we are going to focus on the vertical direction and first answer how long it takes the player to fall 8 meters. 

8=0+(1/2) (9.8)t^2     V_i is p because the ostrich is not falling the moment it leaves the platform, and A is 9.8 because it is a gravitiational constant.

16=9.8t^2

t=sqrt(16/9.8)=1.28 seconds    This is the time the ostrich and player are in freefall before hitting the ground.

Assuming you are not programming air resistance and drag into your game the ostrich moving at 10m/s will travel 10 m/s  *  1.28 s =12.8 Meters horizonally.

As a side note, the ostrich will likely have broken legs after such a fall!