Answer:
134.5 degree
Step-by-step explanation:
first find the remaining side of a triangle
BY using cosine rule
C^2=A^2+B^2-2ABcosx
apply square root both sides
√c^2 =√[4^2+10^2-2(4)(10)cos29]
C=√(116-69.96958)
C=√46.03
C=6.8
Now find angle using cosine rule
C^2=A^2+B^2-2ABcosx
10^2=4^2+6.78^2-2(4)(6.78)cosx
100=16+45.9684-54.24cosx
100=61.9684-54.24cosx
100-61.9684=-54.24cosx
(38.0316)/-54.24=(-54.4cosx)/-54.24
-0.70117=cosx
X= cos inverse of -0.70117
x=134.5 degree
Answer:
216
Step-by-step explanation:
First find the base area
0.25 * √[(5 + 6 + 5) * (-5 + 6 + 5) * (5 - 6 + 5) * (5 + 6 - 5)] = 12
Equation:
12 * (5 + 6 + 5) + (2 * 12) = 216
1) given function
y = - 2 ^ ( -x + 2) + 1
2) domain: domain is the set of the x-values for which the function is defined.
The exponential function is defined for all the real numbers, so the domain of the given function is all the real numbers.
3) x-intercept => y = 0
=> y = - 2 ^ ( -x + 2) + 1 = 0 => 2^ ( -x + 2) = 1
=> - x + 2 = 0 => x = 2
The x-intercept is x = 0
4) y-intercept => x = 0
=> y = - 2 ^ ( -x + 2) + 1= - 2 ^ ( 0 + 2) 1 = - (2)^(2) + 1 =- 4 + 1 = - 3
=> The y-intercept is - 3
5) limit when x -> negative infinite
Lim f(x) when x -> ∞ = - ∞
6) limit when x -> infinite
Lim f(x) when x - > infinite = 1
=> asymptote = y = 1
7) range is the set of values of the fucntion: y
Given that the function is strictly decreasing from -∞ to ∞, the range is from - ∞ to less than 1
Range (-∞,1)
6 runners, 3 medals, how many ways to give them? well, runner say 2 could get gold or not, bronze or not and silver or not, and so can any other runnner, and the order "does matter", it makes a distinction, thus, is a Permutation
