=±22
x
=
±
2
x
2
Using the fact that 2=ln2
2
=
e
ln
2
:
=±ln22
x
=
±
e
x
ln
2
2
−ln22=±1
x
e
−
x
ln
2
2
=
±
1
−ln22−ln22=∓ln22
−
x
ln
2
2
e
−
x
ln
2
2
=
∓
ln
2
2
Here we can apply a function known as the Lambert W function. If =
x
e
x
=
a
, then =()
x
=
W
(
a
)
.
−ln22=(∓ln22)
−
x
ln
2
2
=
W
(
∓
ln
2
2
)
=−2(∓ln22)ln2
x
=
−
2
W
(
∓
ln
2
2
)
ln
2
For negative values of
x
, ()
W
(
x
)
has 2 real solutions for −−1<<0
−
e
−
1
<
x
<
0
.
−ln22
−
ln
2
2
satisfies that condition, so we have 3 real solutions overall. One real solution for the positive input, and 2 real solutions for the negative input.
I used python to calculate the values. The dps property is the level of decimal precision, because the mpmath library does arbitrary precision math. For the 3rd output line, the -1 parameter gives us the second real solution for small negative inputs. If you are interested in complex solutions, you can change that second parameter to other integer values. 0 is the default number for that parameter.
Answer:
I believe its A
Step-by-step explanation:
A. 3
Hope this helps
Answer:
720 cubic units
Step-by-step explanation:
Answer:
36-e
Step-by-step explanation:
-
Answer:
12
Step-by-step explanation:
The least common multiple (LCM) is the lowest (least) postive number that two or more numbers can be divided into without a remainder. To find it, you can list the multiples, in order, of the given numbers. For 6, you would list {6, 12 , 18, 24...}. For 4, you would list {4, 8, 12 , 16, 20, 24...}. Then you look for the lowest positive number that these two sets share. In this case, it is 12. As you can see, 12 is the first number which appears in each set. The number 24 is also shared, but it is not the first common multiple, so the answer is 12.