Answer:
Step-by-step explanation:
1) Add the whole numbers first.
2) Join the denominators.
3) Simplify.
hence, the answer is 3 4/5.
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.
Answer:
The temperature needs to decrease by 7°F to return to the original temperature.
Step-by-step explanation:
The temperature starts at 33 degrees then increases by 10 then 12 then decreases by 15 which will equal 40.
33 + 10 = 43
43 + 12 = 55
55 - 15 = 40
40 - 33 = 7
The temperature needs to decrease by 7 degrees.
Answer:
Area = 60.0 units²
Step-by-step explanation:
First, let's find the height of the triangle using Pythagorean Theorem:
Height = √(11² - 8²)
= √57
Height = 7.5 (nearest tenth)
✔️Find the area:
Area = ½*base*height
Base = 2*8 = 16
Height = 7.5
Plug in the values
Area = ½*16*7.5
Area = 60.0 units² (nearest tenth)
10 ft i think. 5/9 of 180 (which is 12 x 15) is 100 and 10 x 10 is 100
