Count the number of positive integers less than 100 that do not contain any perfect square factors greater than 1.
Possible perfect squares are the squares of integers 2-9.
In fact, only squares of primes need be considered, since for example, 6^2=36 actually contains factors 2^2 and 3^2.
Tabulate the number (in [ ])of integers containing factors of
2^2=4: 4,8,12,16,...96 [24]
3^2=9: 9,18,....99 [11]
5^2=25: 25,50,75 [3]
7^2=49: 49,98 [2]
So the total number of integers from 1 to 99
N=24+11+3+2=40
=>
Number of positive square-free integers below 100 = 99-40 = 59
Answer:
V =1236.4 ft^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
The radius is d/2 =15/2 = 7.5
V = 3.14 (7.5)^2 * 7
V = 1236.375
Rounding to the nearest tenth
V =1236.4 ft^3
Answer:
5 feet squared
Step-by-step explanation:
Answer:
The value of x = -1 makes the denominator of the function equal to zero. That is why this value is not included in the domain of f(x)
Step-by-step explanation:
We have the following expression
Since the division between zero is not defined then the function f(x) can not include the values of x that make the denominator of the function zero.
Now we search that values of x make 0 the denominator factoring the polynomial 
We need two numbers that when adding them get as a result -1 and when multiplying those numbers, obtain -2 as a result.
These numbers are -2 and 1
Then the factors are:
We do the same with the numerator
We need two numbers that when adding them get as a result 4 and when multiplying those numbers, obtain 3 as a result.
These numbers are 3 and 1
Then the factors are:
Therefore
Note that 
only if 
So since 
is not included in the domain the function has a discontinuity in
Answer:A
Step-by-step explanation: the diagonals face each other making them perpendicular making both sides parallel to each other, being straight.
