Step-by-step explanation:
a2 = a1×r
a3 = a1×r²
a1×r + a1×r² = 6×a4 = 6×a1×r³
1.
r + r² = 6r³
6r³ - r² - r = 0
r×(6r² - r - 1) = 0
the first solution is obvious : r = 0.
but this is no useful ratio for a geometric sequence.
the other 2 solutions are in
6r² - r - 1 = 0
the general solutions for a quadratic equation are
(-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 6
b = -1
c = -1
so,
(1 ± sqrt(1 - 4×6×-1))/12
r = (1 ± sqrt(25))/12
r = (1 ± 5)/12
r1 = (1+5)/12 = 6/12 = 1/2
r2 = (1-5)/12 = -4/12 = -1/3
2.
we can ignore r2 (negative) and just focus on r1 (1/2).
the second term is 8. that means
a2 = 8 = a1×r = a1×1/2
a1 = 2×a2 = 16
so, we have
a1 = 16
a2 = 8
a3 = a2×1/2 = 8×1/2 = 4
a4 = a3×1/2 = 4×1/2 = 2
a5 = a4×1/2 = 2×1/2 = 1
a6 = a5×1/2 = 1×1/2 = 1/2
a7 = a6×1/2 = 1/2 × 1/2 = 1/4
Answer:
Step-by-step explanation:
Given
Required
Distance of F'G'
The transformation that give rise to F'G' from FG are:
The above transformations are referred to as rigid transformation, and as such the side lengths remain unchanged.
i.e.
Calculating FG, we have:
Where:
--- 
--- 
Take positive square root
Recall that:
A is 45 b is 90 and c if 90
Answer:
free points pog
Step-by-step explanation:
have a good one my guy
Answer:
f(0) = -3
x increases by 1 f(x) increase by 2
f(x) = 2x -3
Step-by-step explanation:
Looking at the graph
f(0) means when x =0 the value of y = ?
when x = 0 y = -3
f(1) means when x = 1 y = ?
When x = 1 y = -1
y increased from -3 to -1 so it increased by 2
f(x) = ax+b where a is the increase and b is the value at x =0
f(x) = 2x -3
