Answer:
radius=11.5
diameter=23
Step-by-step explanation:
The volume of a sphere is V=4/3 Pi r^3
We can use this to solve for the radius.
555.4= 4/3 (3.14)r^3
Solve for r how you would any other equation. Multiply 4/3 and 3.14.
555.4=4.187 r^3
Divide both sides by 4.187
132.65=r^3
To get rid of the ^3, find the cube root of both sides on a calcualtor.
r= 11.5
The diameter is the radius time two.
11.5 (2)=23.
Hope this helps!
Note: When I say both sides, I mean both sides of the = sign.
Answer:
627200LJ
Step-by-step explanation:
Height of box=5 m
Side of square base=4 m
Volume of rectangular box=
Using the formula
Volume of rectangular box=
Density of material=
We know that
Using the formula
Mass of rectangular box=
Gravity=
Weight of rectangular box,F=
Let L be the vertical distance traveled by box
Total work done =
Therefore,total work done against gravity =
=627200 L J
Hence, the box requires work against gravity=627200LJ
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.
