Answer:
The volume of the solid is 
Step-by-step explanation:
In this case, the washer method seems to be easier and thus, it is the one I will use.
Since the rotation is around the y-axis we need to change de dependency of our variables to have
. Thus, our functions with
as independent variable are:
For the washer method, we need to find the area function, which is given by:
![A=\pi\cdot [(\rm{outer\ radius)^2 -(\rm{inner\ radius)^2 ]](https://tex.z-dn.net/?f=A%3D%5Cpi%5Ccdot%20%5B%28%5Crm%7Bouter%5C%20radius%29%5E2%20-%28%5Crm%7Binner%5C%20radius%29%5E2%20%5D)
By taking a look at the plot I attached, one can easily see that for a rotation around the y-axis the outer radius is given by the function
and the inner one by
. Thus, the area function is:
![A(y)=\pi\cdot [(\sqrt{y} )^2-(y^2)^2]\\A(y)=\pi\cdot (y-y^4)](https://tex.z-dn.net/?f=A%28y%29%3D%5Cpi%5Ccdot%20%5B%28%5Csqrt%7By%7D%20%29%5E2-%28y%5E2%29%5E2%5D%5C%5CA%28y%29%3D%5Cpi%5Ccdot%20%28y-y%5E4%29)
Now we just need to integrate. The integration limits are easy to find by just solving the equation
, which has two solutions
and
. These are then, our integration limits.

Answer:
24.68 gram
Step-by-step explanation:
Given that :
Volume = 182.8 ml
Density of liquid = 0.135 gram/ml
Recall :
Density = mass (g/ml) / volume (ml)
Substitute the value into the equation :
0.135 = mass / 182.8
Mass = 0.135 * 182.8
Mass = 24.678 gram
Hence, weight = 24.678 grams
Answer:
Option (1) increase.
Step-by-step explanation:
Let an exponential function is having common ratio = 3 ( greater than 1) and y-intercept = -1
So the function is, 
Now we prepare a table for the values of x and f(x),
x -1 0 1 2
f(x) -1.67 -1 1 7
We find from the table that the values of the function are increasing with the increase in the values of x.
Therefore, Option (1) increase will be the answer.