Since
are in arithmetic progression,




and since
are in geometric progression,




Recall that


It follows that

so the left side is

Also recall that

so that the right side is

Solve for
.

Now, the numerator increases more slowly than the denominator, since


and for
,

This means we only need to check if the claim is true for any
.
doesn't work, since that makes
.
If
, then

If
, then

If
, then

There is only one value for which the claim is true,
.
The domain of the graph is everything x is allowed to equal. Parentheses are used to show that x can be everything up to, but not including that number. Brackets are used to show x can be anything up to, and including, that number. The comma between the two numbers indicates that x can be anything between those two numbers.
Here, the time goes on the x axis and the distance will go on the y axis.
Time: 0 1 2 3 4 5 6 7 8 9 10
<span>Distance: 0.0 5.5 12.0 20.0 28.5 36.0 44.0 56.5 64.0 75.0
</span>
Since we are dealing with the domain, we really only need to focus on the time.
Time: 0 1 2 3 4 5 6 7 8 9 10
From this, we see that the values go from 0 to 10. This means that x can be anything from 0 to 10. Because there are y values that correlate with the numbers 0 and 10, we know that the domain will include 0 and 10. This indicates we must use brackets.
Knowing all of this information, we can now write our domain as:
[0, 10]
Answer:
523.6 km
Step-by-step explanation:
Let x represent the distance traveled by train. Then 1020-x is the distance traveled by bus. The travel times are given by the relation ...
time = distance/speed
Then the total travel time in hours is ...
x/160 +(1020-x)/105 = 8
21x +32640 -32x = 26880 . . . . . multiply by 3360
5760 = 11x . . . . . . . . . add 11x -26880
523.6 ≈ x . . . . . . . . . . divide by 11
Aidan traveled about 523.6 km by train.
Answer:
720
Step-by-step explanation:
I got it from Quora
We can use 6 people without repetition, which means we simply have to use counting principle 1.
A number of n objects can be arranged in n! ways.
Total number of combinations possibles = 6! =720
2,523 is your investment for 15%
1,611 will be your investment for the 6%