Answer:
The mass of the substance that will remain after 5 years is 3.15 g
Step-by-step explanation:
Given;
initial mass of the radioactive substance, a = 10 g
remaining mass after 3 years, y = 5g
Generating a half-life equation;
After 5 years, the mass of the substance that will be present is given by;
y = 10(0.7937)⁵
y = 3.15 g
Therefore, the mass of the substance that will remain after 5 years is 3.15 g
Answer:
a
n
=
4
⋅
2
n
−
1
if it is a geometric sequence.
or could be:
a
n
=
1
3
(
2
n
3
−
6
n
2
+
16
n
)
if not.
Explanation:
There is a common ratio between successive pairs of terms:
8
4
=
2
16
8
=
2
32
16
=
2
So this looks like a geometric sequence with initial term
a
=
4
and common ratio
r
=
2
.
If so, the formula for the
n
th term is:
a
n
=
a
r
n
−
1
=
4
⋅
2
n
−
1
This is probably the answer expected by the questioner.
However, note that any finite sequence of terms does not determine an infinite sequence - unless you are told what kind of sequence it is - e.g. arithmetic, geometric, harmonic.
For example, we can match these first
4
terms with a cubic formula as follows:
Write down the sequence as a list:
4
,
8
,
16
,
32
Write down the sequence of differences between each pair of terms:
4
,
8
,
16
Write down the sequence of differences of this sequence:
4
,
8
Write down the sequence of differences of this sequence:
4
Having reached a constant sequence (albeit consisting of only one term), we can use the initial term of each of the sequences we have found as coefficients of a formula for the
n
th term:
a
n
=
4
0
!
+
4
1
!
(
n
−
1
)
+
4
2
!
(
n
−
1
)
(
n
−
2
)
+
4
3
!
(
n
−
1
)
(
n
−
2
)
(
n
−
3
)
=
4
+
(
4
n
−
4
)
+
(
2
n
2
−
6
n
+
4
)
+
(
2
3
n
3
−
4
n
2
+
22
3
n
−
4
)
=
2
3
n
3
−
2
n
2
+
16
3
n
=
1
3
(
2
n
3
−
6
n
2
+
16
n
Step-by-step explanation:
64 rounded to the nearest tenth is 60
Answer
I am going to answer the one thats like can you classifly each firgure
cone is the one on the far right
cylinder is the one thats a long circle kinda shape at the top
pyramid is the second to the left
prism is the one next to cylinder.
Step-by-step explanation:
2)
3x + y = 9 is equivalent to -15x - 5y = -45 by multiplying both sides by -5
<u>
</u> -15x - 5y = -45<u>
</u><u>+ </u><u>4x + 5y = 23</u>
-11x + 0y = -22
<u>
</u>-11x = -22
<em>x = 2</em>
3(2) + y = 9
6 + y = 9
<em>y = 3
</em>4)<em>
</em>2x + y = 17 is equivalent to -6x - 3y = -51 by multiplying both sides by -3
<em>
</em> 4x + 3y = 37
<u>+ (-6x - 3y = -51)
</u> -2x + 0y = -14
-2x = -14
<em>x = 7</em>
4(7) + 3y = 37
28 + 3y = 37
3y = 9
<em>y = 3</em><u>
</u>6)
x + 2y = 18 is equivalent to -10x - 20y = -180 by multiplying both sides by -10
10x - 3y = 19
<u>+ (-10x - 20y = -180)</u>
0x - 23y = -161
-23y = -161
<em>y = 7</em>
10x - 3(7) = 19
10x - 21 = 19
10x = 40
<em>x = 4
</em>
I hope this helped ^_^