Answer:
Height ( h) = 12 units.
Step-by-step explanation:
Given : An equilateral triangle with side = 8 √3.
To find : What us the length of the altitude of the equilateral triangle .
Solution : We have given equilateral triangle with side = 8 √3.
By taking the half triangle,
By the Pythagorean theorem :
(Hypotenuse)² = ( adjacent)² + (opposite)².
Plug the values Hypotenuse = 8√3 , adjacent = 4√3 , opposite = h.
(8√3)² = ( 4√3)² + (h)².
192 = 48 + (h)².
On subtracting by 48 both sides.
192 -48 = (h)².
144 = (h)².
On taking square root .
h = 12 .
Therefore, Height ( h) = 12 units.
Answer: 1440
Step-by-step explanation:
To arrange 3 boys and 4 girls such that no two boys are together.
Since boys should be arranged between the girls.
So first arrange the girls.
Assume that the girls are placed, then there will be 5 spaces left for 3 boys.
The number of combinations to fill these places = 
Also, 3 boys can arrange themselves in 3! =3 x 2 x 1 = 6 ways
4 girls can arrange themselves in 4! = 4x 3 x 2 x 1 = 24 ways
Then, the total number of arrangements = 10 x 6 x 24 = 1440
Hence, the required number of arrangements = 1440
Answer:
2/3
Step-by-step explanation:
4 subs 6 people
4/6= 0.66 repeated
so each person got 2/3 sub
Answer: The required value of f(3) is 81.
Step-by-step explanation: We are given the following function :

We are to find the value of f(3).
Substituting x = 3 in equation (i), we get

Thus, the required value of f(3) is 81.
Answer:
I believe it's 4,080
Step-by-step explanation:
you just add the two numbers