When x gets large, you can ignore everything except the highest-degree terms of the numerator and denominator. Effectively, you want the value of
-2x/x
= -2
The horizontal asymptote is -2.
Answer:
- AP
- tₙ = (n-2)k² + (2n - 3)k + n
Step-by-step explanation:
<u>Given sequence:</u>
- -k² - k + 1, k + 2, k² + 3k + 3, 2k² + 5k + 4, ...
We can see apart from the second term all terms are 2nd degree trinomial so it is not a GP.
Let's find the difference: to determine if it is a AP:
- k + 2 - (-k² - k + 1) = k + 2 + k² + k -1 = k² + 2k + 1
- k² + 3k + 3 - (k + 2) = k² + 3k + 3 - k - 2 = k² + 2k + 1
- 2k² + 5k + 4 - (k² + 3k + 3) = 2k² + 5k + 4 - k² - 3k - 3 = k² + 2k + 1
As we see the difference is common and it confirms the sequence is AP.
<u>First term is </u>
<u>Common difference is </u>
<u>nth term is:</u>
- tₙ = a₁ + (n-1)d
- tₙ = -k² - k + 1 + (n-1)(k² + 2k + 1) =
- -k² - k + 1 + (n-1)k² + (n-1)*2k + n-1 =
- (n-2)k² + (2n - 3)k + n
Answer: £1.18
Step-by-step explanation: 9.44/8 = 1.18
Answer:
$20 per day with a $50 fee
Step-by-step explanation:
For 1 day, the gold fee is $70. For 2 days, the gold fee is $90. This can be written as the ordered pairs (1, 70) and (2, 90).
To find the daily fee, we will find the slope between the points:
Next we will use point-slope form:
y-y₁ = m(x-x₁)
y-70 = 20(x-1)
Use the distributive property:
y-70 = 20(x)-20(1)
y-70 = 20x-20
Add 70 to each side:
y-70+70 = 20x-20+70
y = 20x+50
This means the fee is $50.
New Orleans is an example of a city that experienced both a high decrease in population and a high increase in population in the span of three years. Explain the factors that led to these rapid population changes.