We are told in the question that 1 carat is equal to 200 mg.
The Hope Diamond is 44.5 carats. Let's multiply the weight of 1 carat by 44.5 to get the weight of the Hope Diamond in mg:

The total weight of the Hope Diamond is 8,900 mg. However the question asks for the weight in grams. There are 1000 mg in 1 gram, so let's divide the known weight of the Hope Diamond in mg by 1000 to get the weight converted to grams:

Now we know that
the weight of the Hope Diamond is equal to 8.9 grams.
We will use integration by substitution, as well as the integrals
∫
1
x
d
x
=
ln
|
x
|
+
C
and
∫
1
d
x
=
x
+
C
∫
x
3
x
2
+
1
d
x
=
∫
x
2
x
2
+
1
x
d
x
=
1
2
∫
(
x
2
+
1
)
−
1
x
2
+
1
2
x
d
x
Let
u
=
x
2
+
1
⇒
d
u
=
2
x
d
x
. Then
1
2
∫
(
x
2
+
1
)
−
1
x
2
+
1
2
x
d
x
=
1
2
∫
u
−
1
u
d
u
=
1
2
∫
(
1
−
1
u
)
d
u
=
1
2
(
u
−
ln
|
u
|
)
+
C
=
x
2
+
1
2
−
ln
(
x
2
+
1
)
2
+
C
=
x
2
2
−
ln
(
x
2
+
1
)
2
+
1
2
+
C
=
x
2
−
ln
(
x
2
+
1
)
2
+
C
Final answer
Its upsidedown, witch one do you need help with?
Answer:
¾
Step-by-step explanation:
Length of Kerry string = 7(½) = 15/2
Length of John string = 6(¾) = 27/4
15/2 - 27/4
30 - 27/4
3/4
Question 3 is: D. All integers are rational numbers.
Question 4 is: C. the counting number is 4. Hope this helped :)