Answer:
k = 10
Step-by-step explanation:
The sum of k terms of a geometric sequence with first term a1 and common ratio r is given by ...
... Sk = a1·(1 -r^k)/(1 -r)
For the given numbers, this is ...
... 118096 = 78732·(1 -(1/3)^k)/(1 -1/3)
Manipulating this to get the term containing k, we have
... 1 -(2/3)(118096/78732) = (1/3)^k
... 1/59049 = (1/3)^k
Taking logarithms, we get
... -log(59049) = -k·log(3)
... log(59049)/log(3) = k = 10
Answer:
840
Step-by-step explanation:
The 3 by 3 grid below shows nine 1 cm x 1 cm squares and uses 24cm of wire
24 cm of wire
is 3 (3 + 1) + 3(3 + 1)
= 3 x 4 + 3 x 4
= 12 + 12
= 24 cm
length of wire is required for a similar 20 by 20 grid
= 20(20 + 1) + 20(20 + 1)
= 20 x 21 + 20 x 21
= 420 + 420
= 840 cm
Answer:
x^2 + 2x = 1 = - 1
Step-by-step explanation:
x^2 + 2x + 3 = 1
x^2 + 2x + 3 - 2 = 1 - 2
x^2 + 2x + 1 = - 1
P' = (-1, 8) (the x coordinate stays the same and the y coordinate = (distance between -4 and 2) + 2 = 6+2 = 8).
using the same process:-
Q' = (4, 8)
R' = (8, 5)
S' = (3, 5)
