Look at the factors in the 5 numbers. there are 3 factors, and each
number is the product of 2 of them (or 1 of them, twice). There is one
"pair" missing. Hope this helps!!!
The answer should be 3 square root 2
(1- cos2x) dx
= x - 1/2 sin2x + c
= x - 1/2 ( 2*sinx cosx) +c
= x - ((sinx) (cosx)) +c
Since 8 students take both, that leaves only 4 students who take Algebra I alone.
Likewise since 8 students take both, that leaves 10 who only take Algebra 2
So out of the 60, twenty two are taking either Alg I Alg Ii or both.
That leaves 38 people who are not taking either.
b. 38
You can set this up using a 2 circle venn diagram. Just be sure to put the 8 who take both in first.
Since both terms are perfect cubes, factor using the difference of cubes formula,
a
3
−
b
3
=
(
a
−
b
)
(
a
2
+
a
b
+
b
2
)
a
3
-
b
3
=
(
a
-
b
)
(
a
2
+
a
b
+
b
2
)
where
a
=
x
2
a
=
x
2
and
b
=
y
b
=
y
.
(
x
2
−
y
)
(
(
x
2
)
2
+
x
2
y
+
y
2
)
(
x
2
-
y
)
(
(
x
2
)
2
+
x
2
y
+
y
2
)
Multiply the exponents in
(
x
2
)
2
(
x
2
)
2
.
