7. Correct
- - -
9. By the ratio test, the series will converge if
The limit reduces to
where
because
is given. So the series converges when
This means the radius of convergence is
.
- - -
10. By the ratio test, the series converges if
The limit is
and so the radius of convergence is 1.
- - -
11. Incorrect. By the root test, the series converges for
![\displaystyle\lim_{n\to\infty}\sqrt[n]{\left|\frac{(x-2)^n}{n^n}\right|}=\lim_{n\to\infty}\frac{|x-2|}n=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bn%5Cto%5Cinfty%7D%5Csqrt%5Bn%5D%7B%5Cleft%7C%5Cfrac%7B%28x-2%29%5En%7D%7Bn%5En%7D%5Cright%7C%7D%3D%5Clim_%7Bn%5Cto%5Cinfty%7D%5Cfrac%7B%7Cx-2%7C%7Dn%3D0%3C1)
which means the series converges for all
, and so the interval of convergence is
.
- - -
For 14 and 16, it'll probably be too late to edit this post by the time you see this. You can try posting the remaining problems in a new question.
The numbers of chairs and tables that should be produced each week in order to maximize the company's profit is 15 chairs and 18 tables.
Since a furniture company has 480 board ft of teak wood and can sustain up to 450 hours of labor each week, and each chair produced requires 8 ft of wood and 12 hours of labor, and each table requires 20 ft of wood and 15 hours of labor, to determine, if a chair yields a profit of $ 65 and a table yields a profit of $ 90, what are the numbers of chairs and tables that should be produced each week in order to maximize the company's profit, the following calculation should be done:
16 chairs; 24 tables
Time used = 16 x 12 + 24 x 15 = 192 + 360 = 552
Wood used = 16 x 8 + 24 x 20 = 128 + 480 = 608
15 chairs; 18 tables
Time used = 15 x 12 + 18 x 15 = 180 + 270 = 450
Wood used = 15 x 8 + 18 x 20 = 120 + 360 = 480
12 chairs; 28 tables
Time used = 12 x 12 + 28 x 15 = 144 + 420 = 564
Wood used = 12 x 8 + 28 x 20 = 96 + 540 = 636
18 chairs; 20 tables
Time used = 18 x 12 + 20 x 15 = 216 + 300 = 516
Wood used = 18 x 8 + 20 x 20 = 144 + 400 = 544
Therefore, the only option that meets the requirements of time and wood used is that of 15 chairs and 18 tables, whose economic benefit will be the following:
15 x 65 + 18 x 90 = X
975 + 1,620 = X
2,595 = X
Therefore, the numbers of chairs and tables that should be produced each week in order to maximize the company's profit is 15 chairs and 18 tables.
Let’s find the volume of the small cubes.
1/3^3
1/27
Now multiply this by 567
567•(1/27)
21
The volume of the box is 21 inches cubed.
Answer:
Step-by-step explanation:
5 can cancel
