2 triangles are formed
sum of angle measures of a triangle is 180*
sum of angle measures of a swuare is 360*
Answer:
First term: 5
Fourth term: 5 1/2
Tenth term: 6 1/2
Step-by-step explanation:
Let's find the first, fourth and tenth terms of the arithmetic sequence described by the given rule:
A(n) = 5 + (n-1) (1/6)
First term:
A(1) = 5 + (1-1) (1/6)
A(1) = 5 + (0) (1/6)
A(1) = 5
Fourth term:
A(4) = 5 + (4-1) (1/6)
A(4) = 5 + (3) (1/6)
A(4) = 5 + 3/6 = 5 3/6 = 5 1/2 (simplifying)
Tenth term:
A(10) = 5 + (10-1) (1/6)
A(10) = 5 + (9) (1/6)
A (10) = 5 + 9/6 = 6 3/6 = 6 1/2 (simplifying)
The formula for simple annual interest is:
I = Prt
where,
I = Interest accumulated = $910.90
P = Principal Amount = $62000
r = Interest rate = 9.4% = 0.094
t = time in years
Using the values in above equation, we get:
910.90 = 62000 x 0.094 x t
⇒ t = 910.90/(62000 x 0.094) = 0.156
This is the time in years. Since there are 365 days in a year, the time in days will be:
t = 0.156 x 365 = 57 (rounded to nearest day)
This means, Nate kept the borrowed money for 57 days
Answer: it will trave 56.89 meters before coming to rest.
Step-by-step explanation:
This is a geometric progression since the distance travelled (height) by the ball is reducing by a constant ratio, r. Since the number of times that the ball will bounce is infinite, then we would apply the formula for determining the sum of the terms in a geometric progression to infinity which is expressed as
S = a/(1 - r)
where
S = sum of the distance travelled by the ball
a = initial distance or height of the ball
r = common ratio
From the information given,
a = 128/9
r = (32/3)/(128/9) = 0.75
Therefore,
S = (128/9)/(1 - 0.75) = 56.89 meters
