Answer:
It diverges.
Step-by-step explanation:
We are given the inetegral: ![\int\limits^{\infty}_2 \frac{1}{x} (\ln x)^2 dx](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%7B%5Cinfty%7D_2%20%5Cfrac%7B1%7D%7Bx%7D%20%28%5Cln%20x%29%5E2%20dx)
![\int\limits^{\infty}_2 \frac{1}{x} (\ln x)^2 dx=\int\limits^{\infty}_2 (\ln x)^2 d(\ln x)=\\\\=\lim_{t \to \infty} \int\limits^t_2 (\ln x)^2d(\ln x)=\lim_{t \to \infty} \frac{(\ln t)^3}{3} |^t_2=\infty-\frac{(\ln 2)^3}{3} =\infty](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%7B%5Cinfty%7D_2%20%5Cfrac%7B1%7D%7Bx%7D%20%28%5Cln%20x%29%5E2%20dx%3D%5Cint%5Climits%5E%7B%5Cinfty%7D_2%20%28%5Cln%20x%29%5E2%20d%28%5Cln%20x%29%3D%5C%5C%5C%5C%3D%5Clim_%7Bt%20%5Cto%20%5Cinfty%7D%20%5Cint%5Climits%5Et_2%20%28%5Cln%20x%29%5E2d%28%5Cln%20x%29%3D%5Clim_%7Bt%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B%28%5Cln%20t%29%5E3%7D%7B3%7D%20%7C%5Et_2%3D%5Cinfty-%5Cfrac%7B%28%5Cln%202%29%5E3%7D%7B3%7D%20%3D%5Cinfty)
So it is divergent.
Hi,
1) D
Working :
If the bell rings for 2 weeks straight that means it rings for 14 days.
The bell rings 48 times a day (2 * 24).
The answer is then: 48*14 = 672
2) C
Working:
144 cookies * 8 batches = 864 cookies
864 divided into boxes of 8 = 864 / 8 = 108
Answer:
A and B
Step-by-step explanation:
The surface area is found by calculating the 6 faces of a 3-d object. Since A and B are the only ones that cause you to use the whole object for the given task the answers are A and B.
The answer is 75.
Let's look at your problem shall we:
Odd number: It should end with the numbers 1,3,5,7, and 9.
The number is less than 100: It should be from the number 1-99
Sum of digits: 12
Multiple of 15: 15, 30, 45, 60, 75, and 90.
We can rule out 30, 60, and 90 because they are even.
1+5 = 6; 4+5=9; 7+5 = 12
You are left with 75.
So each house can hold 1000 cubes that are 1 meter in length. The house is also shaped like a cube, so you need to cube-root 1000. The cube-root of 1000 is 10. So the cube house has a length, width, and height of 10 meters.