The answer to this is 12.
One third of 12 is 4.
12+4=16
Comment if you have ANY questions!
Hope this helps!
<h3>Given</h3>
tan(x)²·sin(x) = tan(x)²
<h3>Find</h3>
x on the interval [0, 2π)
<h3>Solution</h3>
Subtract the right side and factor. Then make use of the zero-product rule.
... tan(x)²·sin(x) -tan(x)² = 0
... tan(x)²·(sin(x) -1) = 0
This is an indeterminate form at x = π/2 and undefined at x = 3π/2. We can resolve the indeterminate form by using an identity for tan(x)²:
... tan(x)² = sin(x)²/cos(x)² = sin(x)²/(1 -sin(x)²)
Then our equation becomes
... sin(x)²·(sin(x) -1)/((1 -sin(x))(1 +sin(x))) = 0
... -sin(x)²/(1 +sin(x)) = 0
Now, we know the only solutions are found where sin(x) = 0, at ...
... x ∈ {0, π}
When multiplying fractions, just multiply straight across
10 x 11 = 110
3 x 12 = 36
110/36 is your answer
3 1/18 is simplified mixed fraction
hope this helps
Using the least common factor, it is found that:
- a) 60 packages should be bought.
- b) There will be 5 filled goody bags.
<h3>
Least Common Factor:</h3>
- The sizes of the packages are: 10, 6, 15 and 12.
- To fill each bag and have no left-overs, the number of packages is the <u>least common factor</u> of these amounts.
- The least common factor is found factoring the numbers into prime factors.
Item a:
10 - 6 - 15 - 12|2
5 - 3 - 15 - 6|2
5 - 3 - 15 - 3|3
5 - 1 - 5 - 1|5
1 - 1 - 1 - 1
Hence, lcf(10,6,15,2) = 2 x 2 x 3 x 5 = 60.
60 packages should be bought.
Item b:
Goody bags are in packages of 12, hence:
60/12 = 5.
There will be 5 filled goody bags.
To learn more about the least common factor, you can take a look at brainly.com/question/24873870
