Answer:
see below
Step-by-step explanation:
-33, -27, -21, -15,....
-33 +6 = -27
-27+6 = -21
-21+6 = -15
This is an arithmetic sequence
The common difference is +6
explicit formula
an=a1+(n-1)d where n is the term number and d is the common difference
an = -33 + ( n-1) 6
an = -33 +6n -6
an = -39+6n
recursive formula
an+1 = an +6
10th term
n =10
a10 = -39+6*10
= -39+60
=21
sum formula
see image
The sum will diverge since we are adding infinite numbers
Answer:
0 < y <= 6
Step-by-step explanation:
Given:
√(x² - 6x + 9)
if -3 <= x < 3
you can write (x² - 6x + 9)
as (x-3) * (x- 3) which is (x-3)²
so now you have √{(x-3)²}, which is the same as the absolute value of x-3. In mathematics it is written as:
| x - 3 |
So √(x² - 6x + 9) = | x - 3 |
See the graph in the attachment.
for -3 <= x < 3
you get the y values bigger then ( but not equal to) 0 and smaller then or equal to 6.
This is written as 0 < y <= 6
Answer:
The speed of current is 7 miles per hour
Step-by-step explanation:
Given as :
The distance cover by boat in downstream = D = 147 miles
The distance cover by boat in upstream = d = 147 miles
The time taken in downstream trip = T = 7 hours
The time taken in upstream trip = t = 21 hours
Let The speed of boat in still water = x mi/h
And The speed of current = y mi/h
The speed in downstream = S = (x + y) mi/h
The speed in upstream = s = (x - y) mi/h
<u>Now, According to question</u>
∵ Distance = speed × time
<u>For downstream</u>
D = S × T
Or, 147 miles = (x + y) mi/h × 7 hours
i.e 7 (x + y) = 147
Or, x + y =
∴ x + y = 21 ........A
<u>For upstream</u>
d = s × t
Or, 147 miles = (x - y) mi/h × 21 hours
i.e 21 (x - y) = 147
Or, x - y =
∴ x - y = 7 .......B
Now, Solving equations A and B
So, (x + y) + (x - y) = 21 + 7
Or, (x + x) + (y - y) = 28
Or, 2 x + 0 = 28
∴ x =
i.e x = 14 miles per hour
The speed of boat in still water = x = 14 mi/h
Now, putting the value of x into eq B
So, y = x - 7
Or, y = 14 - 7
i.e y = 7 miles per hour
The speed of current = y = 7 mi/h
Hence, The speed of current is 7 miles per hour . Answer