Answer:
Total space in the box is 75.2 cm³.
Step-by-step explanation:
Cone:
- It is three dimension shape.
- It has a vertex.
- The slant height of a cone
, 
= slant height, r= radius of the base, h= height - The lateral surface area is πrl
- The volume of a cone is
.
The artificial carrot that are cone shaped with a radius 1 cm and a height of 6 cm.
So, the volume of the cone is =
cm³
The volume 1 dozen carrots is = (12×2π) cm³
=75.4 cm³
The volume of the box= The volume of the 1 dozen carrot.
Total space in the box is 75.2 cm³.
Dilation because the sides will not be the same size as the original
<span>We let x be the length and y be the width of the rectangle. Then,
Perimeter = 2x + 2y
100 = 2x + 2y
50 = x + y
y = 50 - x
Area = xy
A = x(50 - x)
A = 50x - x^2
We then take the derivative; set it equal to zero:
A ' = 50 - 2x
0 = 50 - 2x
2x = 50
x = 25
y = 50 - x
y = 50 - 25
y = 25
Therefore, the dimensions are 25 and 25.</span>
Answer:
We have been given a unit circle which is cut at k different points to produce k different arcs. Now we can see firstly that the sum of lengths of all k arks is equal to the circumference:
Now consider the largest arc to have length \small l . And we represent all the other arcs to be some constant times this length.
we get :
where C(i) is a constant coefficient obviously between 0 and 1.
All that I want to say by using this step is that after we choose the largest length (or any length for that matter) the other fractions appear according to the above summation constraint. [This step may even be avoided depending on how much precaution you wanna take when deriving a relation.]
So since there is no bias, and \small l may come out to be any value from [0 , 2π] with equal probability, the expected value is then defined as just the average value of all the samples.
We already know the sum so it is easy to compute the average :
10% as a decimal would be .10
