Let
where we assume |r| < 1. Multiplying on both sides by r gives
and subtracting this from gives
As n → ∞, the exponential term will converge to 0, and the partial sums will converge to
Now, we're given
We must have |r| < 1 since both sums converge, so
Solving for r by substitution, we have
Recalling the difference of squares identity, we have
We've already confirmed r ≠ 1, so we can simplify this to
It follows that
and so the sum we want is
which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?
-8x-2y=-24
-2y=-24+8x
2y=24-8x
Y=12-4x
Y=-4x+12
Your answer ---> D . 2 2/9
<span>When given 3 triangle sides, to determine if the triangle is acute, right or obtuse:
</span>1) Square all 3 sides.
2) Sum the squares of the 2 shortest sides.
3) Compare this sum to the square of the 3rd side.
if sum > 3rd side² Acute Triangle
if sum = 3rd side² Right Triangle<span>
if sum < 3rd side² Obtuse Triangle
1) 1,296 2,401 3,600
2) Sum = 3,697
3) </span><span>3,697 is greater than 3,600
Therefore, the triangle is acute.
Source:
http://www.1728.org/triantest.htm
</span>
Answer:
66 degree
Step-by-step explanation:
given:
angle FAB = 48 degree
angle ECB = 18 degree
in triangle HBC , angle H is also 48 degree degree since the line is parallel the connection between angle H and angle A is alternate interior angle and alternate interior angle are always equal.
so angle H = 48 degree
in triangle HBC
angle H + angle C = angle ABC (sum of two interior opposite angles are equal to the exterior angle formed)
48 + 18 = angle ABC
66 = angle ABC