Answer:
Step-by-step explanation:
In order to solve this we can start by drawing a sketch of the problem (see attached picture)
So fist, let's take the general form of a sinusoidal movement:
where:
A= amplitude
= angular frequency
x= time
= horizontal shift
b= vertical shift.
In this case, the amplitude will be the maximum distance between the center of the wheel and the highest or lowest point of the trajectory, in this case:
A= 13in - 0.5in =12.5 in
The angular frequency is how many radians the wheel will turn in a minute, so we get:
Generally, the sin function will start at the center of the circular movement. In this case, since it starts on the lowest point, we can say that the graph moves right by 
, so in this case:
and finally, the vertical shift is the distance between the center of the circular movement and the ground so in this case:
b=13in
so when putting it all together we get our equation to be:
v= (4/3)* pi *(d/2)^3 = (4/3) * pi * (3/2)^3 = about 14.14 cu ft Hope this helps you
Answer: 8(4p + 3)
Step-by-step explanation: Let's first rewrite this as 32p + 24.
If you're asked to factor a polynomial, the first thing you want to look for is the greatest common factor between the terms that are involved.
So what is the greatest common factor between 32p and 24?
Well if you use a factor tree, you'll figure out that the greatest common factor between 32p and 24 is 8.
What that means is that 2 factors out of this polynomial and what you're left with is each of these terms divided by the number that factors out.
In other words 32p divided by 8 or 4p and 24 divided by 8 which is 3.
So your answer is 8(4p + 3) and that is a factored version of 24 + 32p.
Answer: Second one
Step-by-step explanation: The median is 20, so it can only be the first or second one, but the highest number in the data is 27, and the highest number in the data of the first one is 30, so it must be the second one.
the answer is written like this
(4, -3)
