Answer:
All of them
Step-by-step explanation:
According to the ratio test, for a series ∑aₙ:
If lim(n→∞) |aₙ₊₁ / aₙ| < 1, then ∑aₙ converges.
If lim(n→∞) |aₙ₊₁ / aₙ| > 1, then ∑aₙ diverges.
(I) aₙ = 10 / n!
lim(n→∞) |(10 / (n+1)!) / (10 / n!)|
lim(n→∞) |(10 / (n+1)!) × (n! / 10)|
lim(n→∞) |n! / (n+1)!|
lim(n→∞) |1 / (n+1)|
0 < 1
This series converges.
(II) aₙ = n / 2ⁿ
lim(n→∞) |((n+1) / 2ⁿ⁺¹) / (n / 2ⁿ)|
lim(n→∞) |((n+1) / 2ⁿ⁺¹) × (2ⁿ / n)|
lim(n→∞) |(n+1) / (2n)|
1/2 < 1
This series converges.
(III) aₙ = 1 / (2n)!
lim(n→∞) |(1 / (2(n+1))!) / (1 / (2n)!)|
lim(n→∞) |(1 / (2n+2)!) × (2n)! / 1|
lim(n→∞) |(2n)! / (2n+2)!|
lim(n→∞) |1 / ((2n+2)(2n+1))|
0 < 1
This series converges.
Use similar triangles
distance of man from puddle = 0.5 m.
distance of puddle from tower = 13 - 0.5 = 12.5 meters
so we have 2 similar triangles
one has height 2 m and base 0.5 m and the other has height x m ( the tower) and base 12.5 m
Corresponding sides are in the same ratio, so
2 / x = 0.5 / 12.5
0.5x = 2*12.5 = 25
x = 25 / 0.5 = 50 m
The tower is approx 50 m high.
Answer:
The points on the perpendicular bisector of a side of a triangle are equidistant from the vertices of the side it bisects.
Step-by-step explanation:
It is the last option. The perpendicular bisector theorem states that if a point lies on the bisector of a segment it is equidistant from the endpoints.
Meaning
If a perpendicular bisector is a line of the side of the triangle , it bisects the sides forming two right angles .
The first three choices are incorrect because
1) the figure shows a triangle bisected into two triangles and option 1 tells about 1 isosceles triangle.
2) The base angles of any triangle can be different or same .
3) the three perpendicular bisectors meet at a point called the circumeter. We have 1 perpendicual bisector which is dividing the triangle into two equal triangles.
The Answer is 181.688312 Because if you Use the ladder Method
The price of the truck is 4500 dollars.
But he paid it into breakdown:
=> 1500 dollars first payment
=> 350 dollars = 10 months => 350 * 10 = 3500 dollars
=> Total = 3500 + 1500 = 5000 dollars
=> 5000 - 4500 = 500 dollars additional for 10 months
=> 500 / 10 = 50 dollars per month
=> 50 * 12 = 600 dollars for 1 year
=> 600 / 4500 = 13.33% of the yearly interest.
