Here is an image to maybe help see this:
|sum of green angles = 4 * 180°||because the sum of interior angles in each triangle is 180°|
|sum of pink angles = 360°||because the sum of interior angles in a quadrilateral is 360°|
|(see this by drawing two triangles inside a quadrilateral.)|
sum of purple angles = sum of pink angles
|because vertical angles are congruent.|
sum of orange angles = sum of green angles - sum of purple angles
sum of orange angles = 4 * 180° - 360°
sum of orange angles = 360°
(I apologize if you are colorblind!!)
The sum of the measures of the interior angles of the quadrilateral in the middle is 180(4-2) =360. This makes the sum of the four angles inside the four triangles that are opposite to the quadrilateral's interior angles, the ones that are not orange, also 360 degrees. The sum of the interior angles of the four triangles is 4(180)= 720. So the orange angles must add up to 720-360= 360 as well.
x = y^2 + y + 1 (1)
5y = 2 - x - x^2 (2)
Square both sides of (1)
x^2 = (y^2 + y + 1) (y^2 + y + 1)
x^2 = y^4 + y^3 + y^2 + y^3 + y^2 + y + y^2 + y + 1
x^2 = y^4 + 2y^3 + 3y^2 + 2y+ 1 (3)
Sub (1) and (3) into (2) for x^2 and x
5y = 2 - (y^2 + y + 1) - ( y^4 + 2y^3 + 3y^2 +2y + 1)
5y = 2 - y^2 - y - 1 - y^4 - 2y^3 - 3y^2 - 2y - 1
5y = -y^4 - 2y^3 - 4y^2 -3 y
y^4 + 2y^3 + 4y^2 + 8y = 0 factor
y^3 ( y + 2) + 4y ( y + 2) = 0
(y^3 + 4y) ( y + 2) = 0
y ( y^2 + 4) ( y + 2) = 0
The second factor does not provide real solutions
The other two solutions are
y = 0 and y + 2 = 0
y = -2
When y = 0 x = (0)^2 + 0 + 1 = 1
When y = -2 x = (-2)^2 - 2 + 1 = 3
So....the solutions are
(1, 0) and ( 3, -2) .....as EP found graphically !!!!
This is a formula that he uses \(A=rs\)
s = semi-perimeter
A = area
r = inradius
Using his method (heron's formula) we can find the value of A.
Using the given info on the triangles side, we can find the semi-perimeter by finding the perimeter and dividing by 2.
Then with that info, we plug it into the formula and solve for R.
he is the same guest that posts homework questions.
Apparently my answer was wrong, but he doesn't know why because he didn't take time to understand my method, and simply plugged in the answer I got.
Then he gets mad at us for giving wrong answers, and that he didnt get full points on his "homework".
So basically he is this greedy jerk that blames you for his own problems
There is only one way of getting a total of 5 from 5 dice , or 1+1+1+1+1 =5. Then there 5 ways of getting a 6, or 2+1+1+1+1, 1+2+1+1+1, 1+1+2+1+1, 1+1+1+2+1, 1+1+1+1+2......and so on for every number from 5 up to 21.
Then you add them all up like this:
1+5+15+35+70+126+205+305+420+540+651+735+780+780+735+651+540 =6,594 / 6^5 =~84.8% probability.
I’m probably the only person on this forum that has a clue about what you are referencing.
The reason I have a clue is I’m a genetically enhanced chimp with advanced mind reading skills.
This skill is a great advantage for interpreting babble and bullshit questions that lack a contextual preface.
You can use a variable to store the constant of the Golden ratio. I’ve use the Golden ratio and many other constants in the forum’s calculator –sometimes several constants simultaneously. They are easy to change on the fly, too. I’ve posted at least three examples. You can peruse through my profile and find them.
Oh, and those “physic thingies that don't make any sense,” are very useful when needed. There are over 300 of them in the constants list. Your values have to be limited because if there were 30,000 of them, then it would take you a long time to find the one you need –you may as well just type it in.
There is one constant that should be on the list: The constant for Quantum Dumbness at a distance. It works well for dumbness infectious via the net.
a^2 -3a + 9 = 0 subtract 9 from both sides
a^2 - 3a = -9 complete the square on a
a^2 - 3a + 9/4 = -9 + 9/4
(a - 3/2)^2 = -27/4 take both roots
a - 3/2 = ±√ [-27] / 2
a = [3 ± 3i√3 ]
When a = [ 3 + 3i√ 3]
__________ then a^3 =
( [ 3 + 3i√ 3] / 2)^2 ( [3 + 3i√ 3 ] / 2 ) =
[ 9 + 18i√3 + 9i^2 (3) ]
_______________ * ( [ 3 + 3i√3] / 2) =
[ -18 + 18i√3 ]
_____________ ( [ 3 + 3i√3 ] / 2 ) =
[ -9 + 9i√3] [ 3 + 3i√3]
__________ * __________ =
[-27 + 27i√3 + 27i√3 - 27*3 ] [ -27 * 4 ]
______________________ = __________ = -27
The same result is obtained for a^3 when a = ( 3 - 3i√3 ) / 2
Please do not discuss this problem! This is an active homework problem.
To the original poster: I realize that homework may be challenging. If you wish to receive some help from the staff or other students, I encourage you to use the resources that the online classes provide, such as the Message Board. Thanks.
JESUS CHRIST!! Are you having a bad day or are you just fucking stupid?
Read my goddamn post! I clearly answer your question! The answer is in boldface.
I have questions for you:
How did you ever figure out how to post on this forum?
How is it that you are still alive?
Darwin’s natural selection takes too long!