Answer:
The mass of the grains = 120 ± 1 g
Step-by-step explanation:
we are given the following:
Total mass of container + grains = 185 grams
Mass of container = 65 grams
Therefore, mass of grains is calculated as follows:
Mass of grains = ( Mass of container + grains) - mass of container
= 185 - 65 = 120 grams.
since the scale has an absolute uncertainty of 1 g, the mass of the grains is written as 120 ± 1 g
Answer:
Decreased by 40%!
Step-by-step explanation:
At first it goes down by 10%, then 30%, so you just add them together and get decreased by 40%.
To be a function, it has to pass the vertical line test, which means a vertical line drawn anywhere in the graph should cut the graph only once, not more.
To be a one-to-one function, it has to pass the vertical line test as well as the horizontal line test, which means that a horizontal line drawn anywhere in the graph should cut the graph only once, not more.
<em>Of course, it passes the vertical line test, so its a function. </em>
<em>Does it pass the horizontal line test? </em><em>NO! </em><em>As shown in the attached picture, the blue line (horizontal line) cuts the graph at 3 places. We therefore eliminate choices A and B. We can eliminate choice C because nowhere is it required a function to pass through the origin for it to be one-to-one. Hence, the answer is D (blue line shows this).</em>
<em>ANSWER: D</em>
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.
