Step-by-step explanation:
Answer:
and 
Step-by-step explanation:
(a)
A = 
× 4
× 
= 2 ×
= 
× 
← rationalise the denominator
= units²
(b)
Using Pythagoras' identity in the right triangle
let hypotenuse be h , then
h² = (4 )² + ( )²
= 32 + 
= 
+
= 
( take the square root of both sides )
h = 
= 
× ← rationalise the denominator
h =
Answer:
1083 seats
Step-by-step explanation:
this is an arithmetic sequence :
an = an-1 + c
in our case
a1 = 10 (10 seats in the first row)
a2 = a1 + 1 = 10 + 1 = 11
a3 = a2 + 1 = a1 + 1 + 1 = 10 + 1 + 1 = 12
an = an-1 + 1 = a1 + (n-1)×1 = a1 + n - 1 = 10 + n - 1 = 9 + n
a38 = a1 + 37 = 10 + 37 = 47 seats.
altogether this means the sum of the arithmetic sequence of a1 to a38.
the general sum of an arithmetic sequence from a1 to an is
n×(a1 + an)/2
in our case
38×(10 + 47)/2 = 19×57 = 1083 seats
