Answer:
exponential
Step-by-step explanation:
exponential functions will always have a horizontal asymptote
Area of a rectangle = length * width
A = 1.6 *1.2 = 1.92 m²
Answer:
a-135 hot dogs and 245 sodas were sold.
Step-by-step explanation:
Our equations are:
1.25h + 0.75s = 352.50
h + s = 380
Let's use substitution to solve for this system. In the second equation, let's write h in terms of s:
h + s = 380
h = 380 - s
Now, let's plug in 380 - s for h in the first equation:
1.25h + 0.75s = 352.50
1.25(380 - s) + 0.75s = 352.50
We can now solve for s fairly easily:
1.25(380 - s) + 0.75s = 352.50
475 - 1.25s + 0.75s = 352.50
0.5s = 122.5
s = 245 sodas
We can already see which answer choice will match: A, and that is our answer.
Answer:
∑ (-1)ⁿ⁺³ 1 / (n^½)
∑ (-1)³ⁿ 1 / (8 + n)
Step-by-step explanation:
If ∑ an is convergent and ∑│an│is divergent, then the series is conditionally convergent.
Option A: (-1)²ⁿ is always +1. So an =│an│and both series converge (absolutely convergent).
Option B: bn = 1 / (n^⁹/₈) is a p series with p > 1, so both an and │an│converge (absolutely convergent).
Option C: an = 1 / n³ isn't an alternating series. So an =│an│and both series converge (p series with p > 1). This is absolutely convergent.
Option D: bn = 1 / (n^½) is a p series with p = ½, so this is a diverging series. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.
Option E: (-1)³ⁿ = (-1)²ⁿ (-1)ⁿ = (-1)ⁿ, so this is an alternating series. bn = 1 / (8 + n), which diverges. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.
