with the help of your calculator
write these in your calculator and get your answer
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:
theta = all real values
Step-by-step explanation:
sec theta + tan theta = cos theta / (1-sin theta )
sec theta = 1/cos theta
tan theta = sin theta/cos theta
1/cos theta + sin theta /cos theta= cos theta/ (1-sin theta)
(1+ sin theta) / cos theta = cos theta /( 1-sin theta)
using cross products
(1+sin theta) * (1-sin theta) = cos theta * cos theta
1 +sin theta - sin theta- sin^2 theta= cos ^2 theta
1 - sin ^2 theta= cos ^2 theta
cos ^2 theta= cos ^2 theta
this is an identity so it is true for all theta
{x,y} = {-2,3}
[1] 2x + 4y = 8
[2] x - 3y = -11
4y + 2x = 8
-3y + x = -11
Solve equation for the variable x
[2] x = 3y - 11
Plug this in for variable x in equation [1]
[1] 2•(3y-11) + 4y = 8
[1] 10y = 30
Solve equation [1] for the variable y
[1] 10y = 30
[1] y = 3
By now we know this much :
x = 3y-11
y = 3
Use the y value to solve for x
x = 3(3)-11 = -2
Solution :
{x,y} = {-2,3}
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~Savannah
