Answer:
Volume of cylinder = 
Step-by-step explanation:
Given : A cylinder fits inside a square prism.
To find : The volume of cylinder
Solution : Refer the attached graph.
Area of circle = 
Area of square = 
Side of square = diameter of circle= 
Diameter = 2r
∴ Area of square= 
Area of circle is 
of area of square.
Volume is always = area × height
Volume of prism = Area of square × h = 
Volume of cylinder = Area of circle × h =
Now, rate
⇒Volume of cylinder is of Volume of prism.
Volume of Cylinder =
Volume of cylinder = 
Volume of cylinder =
We have an arithmetic progression:
an=number of item at row n
an=a₁+(n-1)d
d=common difference=an-a(n-1)=a₂-a₁=2-1=1
n=number of row
In this case:
an=1+(n-1)*1=n
The sum of an arithmetic serie is:
Sn=(a₁+an)n / 2
In this case:
a₁=1 (number of itms in the first row)
an=n (we have to calculate this before)
Sn=(1+n)n /2=(n+n²)/2
Therefore:
f(n)=Sn=number of items when we have n number of rows
f(n)=(n+n²)/2
Answer: f(n)=(n+n²)/2
To chek:
f(1)=(1+1²)/2=1
f(2)=(2+2²)/2=6/2=3
f(3)=(3+3²)/2=(3+9)/2=12/2=6
....
9514 1404 393
Answer:
b. 362,880
Step-by-step explanation:
There are 9 ways to choose the first batter, 8 ways to choose the second, and so on. There are a total of 9·8·7·6·...·2·1 = 9! = 362,880 ways to arrange the batting order.
Answer:
d. J
Step-by-step explanation:
Real numbers are the vast set of numbers that broadly categorize into Rational and Irrationals (and also the Transcendentals, which are irrational too). Every rational number and every irrational number are characteristicly different from each other. Following this order, all rationals and irrationals are real numbers. This order is best represented in the Figure J.
Answer:
We know that in a triangle, given two sides, the third one must be smaller than the sum of the given sides, but greater than their difference:
z < x + y
z > x - y
Therefore, the length of the third side will be between the difference and the sum of the other two sides. In our case:
x + y = 13
x - y = 3
Hence, the correct answer is: B) The side needs a fence that is longer than 3ft. and shorter than 13ft.
Step-by-step explanation:
