36/99 because 36 divided by 99 is 0.363636363636
Answer:
a. yes
b. Q
c. line MP
Step-by-step explanation:
a. "Collinear" means "on the same line". The diagram shows point K on the same line with M and P, so ...
yes, M, P, and K are collinear
__
b. N, W, and U are the corners of face NUWQ, so point Q is also in that plane.
__
c. The plane MPQ includes face MPQN. The plane TVP includes face TVPM.
Line MP (or PM) is the line where these planes intersect.
Answer:
Solve for y 3/7=15. 37y=15 3 7 y = 15. Multiply both sides of the equation by 73 7 3. 73.37 y=73.15 7 3. 3 7 y = 7 3. 15
Step-by-step explanation:
Solve for y by simplifying both sides of the equation, then isolating the variable. Y=35
I guess the sequence is
![a_n=\dfrac{1^2}{n^3}+\dfrac{2^2}{n^3}+\cdots\dfrac{n^2}{n^3}](https://tex.z-dn.net/?f=a_n%3D%5Cdfrac%7B1%5E2%7D%7Bn%5E3%7D%2B%5Cdfrac%7B2%5E2%7D%7Bn%5E3%7D%2B%5Ccdots%5Cdfrac%7Bn%5E2%7D%7Bn%5E3%7D)
which we can write as
![a_n=\displaystyle\frac1{n^3}\sum_{k=1}^nk^2=\frac{n(n+1)(2n+1)}{6n^3}=\dfrac{2n^2+3n+1}{6n^2}](https://tex.z-dn.net/?f=a_n%3D%5Cdisplaystyle%5Cfrac1%7Bn%5E3%7D%5Csum_%7Bk%3D1%7D%5Enk%5E2%3D%5Cfrac%7Bn%28n%2B1%29%282n%2B1%29%7D%7B6n%5E3%7D%3D%5Cdfrac%7B2n%5E2%2B3n%2B1%7D%7B6n%5E2%7D)
converges if it is bounded and monotonic. Consider the function,
![f(x)=\dfrac{2x^2+3x+1}{6x^2}=\dfrac13+\dfrac1{2x}+\dfrac1{6x^2}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7B2x%5E2%2B3x%2B1%7D%7B6x%5E2%7D%3D%5Cdfrac13%2B%5Cdfrac1%7B2x%7D%2B%5Cdfrac1%7B6x%5E2%7D)
which has derivative
![f'(x)=-\dfrac1{2x^2}-\dfrac1{3x^3}](https://tex.z-dn.net/?f=f%27%28x%29%3D-%5Cdfrac1%7B2x%5E2%7D-%5Cdfrac1%7B3x%5E3%7D)
for all
, so
is monotonically decreasing on
, and as
we have
![\displaystyle\lim_{x\to\infty}f(x)=\dfrac13](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bx%5Cto%5Cinfty%7Df%28x%29%3D%5Cdfrac13)
So we know that
is monotonically decreasing and bounded below by
.
To find the limit, we can also write
![a_n=\dfrac{2+\frac3n+\frac1{n^2}}6](https://tex.z-dn.net/?f=a_n%3D%5Cdfrac%7B2%2B%5Cfrac3n%2B%5Cfrac1%7Bn%5E2%7D%7D6)
As
, the rational terms vanish and we're left with
![\displaystyle\lim_{n\to\infty}\frac26=\frac13](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bn%5Cto%5Cinfty%7D%5Cfrac26%3D%5Cfrac13)
Answer:
7 and 5
Step-by-step explanation:
NONE