Answer:
i don't know this type of work.
Step-by-step explanation:
i'm only in 10th grade
Answer:
SA = 402.14 square inches
Step-by-step explanation:
Imagine you unroll the cylinder. You will be left with a rectangle and two "lids" (disks).
The rectangular area will be of dimension:
Ar = (height)*(circumference of the disk)
Ar = (12 in) * (8 in) *pi = 301.60 in^2
The area of one disk will be
Ad = pi*(radius^2) = pi*(4^2 in^2) = 50.27 in^2
So the total surface area will be
SA = Ar + 2* Ad = 402.14 in^2 (square inches)
When you rearrange the equation, you find that the solution is b)
Step-by-step explanation:
It is given that,
An aquarium is in the shape of a rectangular prism. The area of the base of the aquarium is 250 square inches.
We need to find the volume of the aquarium.
The formula for the volume of the rectangular prism is given by :
V = lbh
Where, l is length, b is width and h is height
Let the height of the prism is h inches. So,
V = A × h (As Area, A = lb)
V = 250× h
= (250h) inch³
By substituting the value of h, we can find its volume.
Hence, the volume of the aquarium is (250h) inch³.
You can use the root test here. The series will converge if
![L=\displaystyle\lim_{n\to\infty}\sqrt[n]{\frac{(4-x)^n}{4^n+9^n}}](https://tex.z-dn.net/?f=L%3D%5Cdisplaystyle%5Clim_%7Bn%5Cto%5Cinfty%7D%5Csqrt%5Bn%5D%7B%5Cfrac%7B%284-x%29%5En%7D%7B4%5En%2B9%5En%7D%7D%3C1)
You have
![L=\displaystyle\lim_{n\to\infty}\sqrt[n]{\frac{(4-x)^n}{4^n+9^n}}=|4-x|\lim_{n\to\infty}\frac1{\sqrt[n]{4^n+9^n}}](https://tex.z-dn.net/?f=L%3D%5Cdisplaystyle%5Clim_%7Bn%5Cto%5Cinfty%7D%5Csqrt%5Bn%5D%7B%5Cfrac%7B%284-x%29%5En%7D%7B4%5En%2B9%5En%7D%7D%3D%7C4-x%7C%5Clim_%7Bn%5Cto%5Cinfty%7D%5Cfrac1%7B%5Csqrt%5Bn%5D%7B4%5En%2B9%5En%7D%7D)
Notice that
![\dfrac1{\sqrt[n]{4^n+9^n}}=\dfrac1{\sqrt[n]{9^n}\sqrt[n]{1+\left(\frac49\right)^n}}=\dfrac1{9\sqrt[n]{1+\left(\frac49\right)^n}}](https://tex.z-dn.net/?f=%5Cdfrac1%7B%5Csqrt%5Bn%5D%7B4%5En%2B9%5En%7D%7D%3D%5Cdfrac1%7B%5Csqrt%5Bn%5D%7B9%5En%7D%5Csqrt%5Bn%5D%7B1%2B%5Cleft%28%5Cfrac49%5Cright%29%5En%7D%7D%3D%5Cdfrac1%7B9%5Csqrt%5Bn%5D%7B1%2B%5Cleft%28%5Cfrac49%5Cright%29%5En%7D%7D)
so as
, you have
, which means you end up with
This is the interval of convergence. The radius of convergence can be determined by finding the half-length of the interval, or by solving the inequality in terms of
so that
is the ROC. You get
