Answer:
Step-by-step explanation:
Put in the form of y = Ax + B
x + 2y = 10
2y = -x + 10
y = -½x + 5
has a slope of -½ and a y intercept of 5
-x + 4y = 8
4y = x + 8
y = ¼x + 2
has a slope of ¼ and a y intercept of 2
Step-by-step explanation:
Equation of line is y-y1 = m(x-x1), where m is the slope and (x1,y1) is the given point.
y-2 = 1/4*(x-(-4))
y-2 = 1/4 * (x+4)
4*(y-2) = x+4
Equation of the line is,
x-4y = -12
We know that
case 1)
Applying the law of sines
a/Sin A=b/Sin B
A=56°
a=12
b=14
so
a*Sin B=b*Sin A----> Sin B=b*Sin A/a---> Sin B=14*Sin 56°/12
Sin B=0.9672
B=arc sin (0.9672)------> B=75.29°-----> B=75.3°
find angle C
A+B+C=180°-----> C=180-(A+B)----> C=180-(56+75.3)----> C=48.7°
find c
a/Sin A=c/Sin C----> c=a*Sin C/Sin A----> c=12*Sin 48.7°/Sin 56°)
c=10.87-----> c=10.9
the answer Part 1)
the dimensions of the triangle N 1
are
a=12 A=56°
b=14 B=75.3°
c=10.9 C=48.7°
case 2)
A=56°
a=12
b=14
B=180-75.3----> B=104.7°
find angle C
A+B+C=180°-----> C=180-(A+B)----> C=180-(56+104.7)----> C=19.3°
find c
a/Sin A=c/Sin C----> c=a*Sin C/Sin A----> c=12*Sin 19.3°/Sin 56°)
c=4.78-----> c=4.8
the answer Part 2)
the dimensions of the triangle N 2
are
a=12 A=56°
b=14 B=104.7°
c=4.8 C=19.3°
Answer:
There's a lot of them.
There are many different ways to calculate 
. The ones used by computers to generate tons of digits are usually infinite series.
The series that has been prominent in recent records for the most digits of pi is the Chudnovsky algorithm.
The algorithm is this:
For faster performance, it can be simplified to this:
Other algorithms have been used, but right now this is the one that is being used to set the recent records.
There are also some approximations that are used because they are very easy to calculate.
first, 
can be used to calculate a fairly accurate pi, but a better rational approximation is 
This fraction is actually accurate to 6 digits and it is the best approximation of in simplest form and with a denominator below 30,000.
There are several other approximations and if you want to learn more I would recommend looking at the Wikipedia page which has tons of algorithms for pi.
