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Math Problems
Calculus
Find derivatives using implicit differentiation
3
+
5
x
=
k
+
6
x
3+5 x=\sqrt{k+6 x}
3
+
5
x
=
k
+
6
x
\newline
For what value of the constant
k
k
k
does the given equation have
x
=
0
x=0
x
=
0
as the only solution?
\newline
□
\square
□
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Choose the correct symbol to compare the expressions. Do not multiply.
\newline
3
?
3
×
2
4
3 ? 3 \times \frac{2}{4}
3
?
3
×
4
2
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
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Compare the numbers. Pick the correct sign.
\newline
−
2
?
8
-2 \,?\, 8
−
2
?
8
\newline
\newline
You can use the number line to help.
\newline
\newline
Choices:
\newline
(
A
)
>
(A) >
(
A
)
>
\newline
(
B
)
<
(B) <
(
B
)
<
\newline
(
C
)
=
(C) =
(
C
)
=
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Compare the numbers. Pick the correct sign.
\newline
−
5
?
2
-5 \,?\, 2
−
5
?
2
\newline
\newline
You can use the number line to help.
\newline
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Compare the numbers. Pick the correct sign.
\newline
−
5
?
3
-5 \,?\, 3
−
5
?
3
\newline
\newline
You can use the number line to help.
\newline
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
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A function
p
p
p
is defined as
p
(
x
)
=
(
x
−
a
)
(
x
−
15
)
(
x
−
20
)
+
15
p(x)=(x-a)(x-15)(x-20)+15
p
(
x
)
=
(
x
−
a
)
(
x
−
15
)
(
x
−
20
)
+
15
where
a
a
a
is a constant. Given that
p
(
7
)
=
15
p(7)=15
p
(
7
)
=
15
, what is the value of
a
a
a
?
\newline
□
\square
□
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Using implicit differentiation, find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
.
\newline
x
y
=
−
5
+
y
x
3
\sqrt{x y}=-5+y x^{3}
x
y
=
−
5
+
y
x
3
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Given the function
h
(
x
)
=
x
2
+
7
x
+
5
h(x)=x^{2}+7 x+5
h
(
x
)
=
x
2
+
7
x
+
5
, determine the average rate of change of the function over the interval
−
6
≤
x
≤
1
-6 \leq x \leq 1
−
6
≤
x
≤
1
.
\newline
Answer:
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