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Math Problems
Algebra 2
Evaluate exponential functions
If
f
(
1
)
=
1
f(1)=1
f
(
1
)
=
1
and
f
(
n
+
1
)
=
f
(
n
)
2
+
2
f(n+1)=f(n)^{2}+2
f
(
n
+
1
)
=
f
(
n
)
2
+
2
then find the value of
f
(
3
)
f(3)
f
(
3
)
.
\newline
Answer:
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If
f
(
1
)
=
6
f(1)=6
f
(
1
)
=
6
and
f
(
n
+
1
)
=
−
5
f
(
n
)
+
2
f(n+1)=-5 f(n)+2
f
(
n
+
1
)
=
−
5
f
(
n
)
+
2
then find the value of
f
(
3
)
f(3)
f
(
3
)
.
\newline
Answer:
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If
f
(
1
)
=
1
f(1)=1
f
(
1
)
=
1
and
f
(
n
)
=
−
5
f
(
n
−
1
)
−
n
f(n)=-5 f(n-1)-n
f
(
n
)
=
−
5
f
(
n
−
1
)
−
n
then find the value of
f
(
3
)
f(3)
f
(
3
)
.
\newline
Answer:
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Write an explicit formula that represents the sequence defined by the following recursive formula:
\newline
a
1
=
100
and
a
n
=
−
1
5
a
n
−
1
a_{1}=100 \text { and } a_{n}=-\frac{1}{5} a_{n-1}
a
1
=
100
and
a
n
=
−
5
1
a
n
−
1
\newline
Answer:
a
n
=
a_{n}=
a
n
=
Get tutor help
Write an explicit formula that represents the sequence defined by the following recursive formula:
\newline
a
1
=
1
and
a
n
=
6
a
n
−
1
a_{1}=1 \text { and } a_{n}=6 a_{n-1}
a
1
=
1
and
a
n
=
6
a
n
−
1
\newline
Answer:
a
n
=
a_{n}=
a
n
=
Get tutor help
Given that events A and B are independent with
P
(
A
)
=
0.45
P(A)=0.45
P
(
A
)
=
0.45
and
P
(
B
)
=
0.82
P(B)=0.82
P
(
B
)
=
0.82
, determine the value of
P
(
A
∣
B
)
P(A \mid B)
P
(
A
∣
B
)
, rounding to the nearest thousandth, if necessary.
\newline
Answer:
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Given
f
(
x
)
=
3
x
2
+
x
−
17
f(x)=3 x^{2}+x-17
f
(
x
)
=
3
x
2
+
x
−
17
, find
f
(
1
)
f(1)
f
(
1
)
\newline
Answer:
Get tutor help
If
f
(
1
)
=
3
f(1)=3
f
(
1
)
=
3
and
f
(
n
)
=
−
4
f
(
n
−
1
)
−
2
f(n)=-4 f(n-1)-2
f
(
n
)
=
−
4
f
(
n
−
1
)
−
2
then find the value of
f
(
3
)
f(3)
f
(
3
)
.
\newline
Answer:
Get tutor help
In general,
f
−
1
(
f
(
x
)
)
=
f
(
f
−
1
(
x
)
)
=
f^{-1}(f(x))=f\left(f^{-1}(x)\right)=
f
−
1
(
f
(
x
))
=
f
(
f
−
1
(
x
)
)
=
Get tutor help
Write an explicit formula for
a
n
a_{n}
a
n
, the
n
th
n^{\text {th }}
n
th
term of the sequence
150
,
30
,
6
,
…
150,30,6, \ldots
150
,
30
,
6
,
…
.
\newline
Answer:
a
n
=
a_{n}=
a
n
=
Get tutor help
For the following equation, find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
.
\newline
f
(
x
)
=
−
4
x
4
+
x
f(x)=-4 x^{4}+x
f
(
x
)
=
−
4
x
4
+
x
\newline
Answer:
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
For the following equation, find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
.
\newline
y
=
−
5
x
5
+
5
x
3
+
2
x
y=-5 x^{5}+5 x^{3}+2 x
y
=
−
5
x
5
+
5
x
3
+
2
x
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
For the following equation, find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
.
\newline
f
(
x
)
=
−
8
x
3
+
x
f(x)=-8 x^{3}+x
f
(
x
)
=
−
8
x
3
+
x
\newline
Answer:
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
Given
f
(
x
)
=
2
tan
(
x
)
f(x)=2 \tan (x)
f
(
x
)
=
2
tan
(
x
)
, find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
.
\newline
Answer:
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
Given the function
f
(
x
)
=
(
6
x
2
+
9
)
4
f(x)=\left(6 x^{2}+9\right)^{4}
f
(
x
)
=
(
6
x
2
+
9
)
4
, find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
in any form.
\newline
Answer:
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
Given the function
y
=
−
(
5
x
2
+
2
x
+
1
)
4
y=-\left(5 x^{2}+2 x+1\right)^{4}
y
=
−
(
5
x
2
+
2
x
+
1
)
4
, find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in any form.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
If
y
2
+
3
x
−
5
x
2
=
−
3
+
2
y
y^{2}+3 x-5 x^{2}=-3+2 y
y
2
+
3
x
−
5
x
2
=
−
3
+
2
y
then find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in terms of
x
x
x
and
y
y
y
.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
If
−
y
2
−
y
3
−
5
x
3
=
y
-y^{2}-y^{3}-5 x^{3}=y
−
y
2
−
y
3
−
5
x
3
=
y
then find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in terms of
x
x
x
and
y
y
y
.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
If
5
y
3
+
y
=
−
y
2
−
2
x
2
+
x
3
5 y^{3}+y=-y^{2}-2 x^{2}+x^{3}
5
y
3
+
y
=
−
y
2
−
2
x
2
+
x
3
then find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in terms of
x
x
x
and
y
y
y
.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
If
3
y
2
−
3
y
3
=
−
y
−
x
3
3 y^{2}-3 y^{3}=-y-x^{3}
3
y
2
−
3
y
3
=
−
y
−
x
3
then find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in terms of
x
x
x
and
y
y
y
.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
If
−
y
−
y
2
+
y
3
=
3
x
2
-y-y^{2}+y^{3}=3 x^{2}
−
y
−
y
2
+
y
3
=
3
x
2
then find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in terms of
x
x
x
and
y
y
y
.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
If
−
2
y
3
=
1
+
x
3
-2 y^{3}=1+x^{3}
−
2
y
3
=
1
+
x
3
then find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in terms of
x
x
x
and
y
y
y
.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
If
−
y
+
5
x
2
+
y
3
−
5
=
0
-y+5 x^{2}+y^{3}-5=0
−
y
+
5
x
2
+
y
3
−
5
=
0
then find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in terms of
x
x
x
and
y
y
y
.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
If
−
x
y
3
+
y
−
x
2
=
0
-x y^{3}+y-x^{2}=0
−
x
y
3
+
y
−
x
2
=
0
then find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in terms of
x
x
x
and
y
y
y
.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
If
5
=
−
x
y
3
−
3
y
3
−
3
x
5=-x y^{3}-3 y^{3}-3 x
5
=
−
x
y
3
−
3
y
3
−
3
x
then find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in terms of
x
x
x
and
y
y
y
.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
If
−
5
x
−
3
x
y
+
y
2
=
0
-5 x-3 x y+y^{2}=0
−
5
x
−
3
x
y
+
y
2
=
0
then find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in terms of
x
x
x
and
y
y
y
.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
If
x
y
+
5
y
2
−
x
3
=
0
x y+5 y^{2}-x^{3}=0
x
y
+
5
y
2
−
x
3
=
0
then find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in terms of
x
x
x
and
y
y
y
.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
If
−
y
2
−
x
3
+
4
+
5
x
=
0
-y^{2}-x^{3}+4+5 x=0
−
y
2
−
x
3
+
4
+
5
x
=
0
then find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in terms of
x
x
x
and
y
y
y
.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
If
−
x
2
+
2
y
3
+
3
y
=
y
2
+
5
-x^{2}+2 y^{3}+3 y=y^{2}+5
−
x
2
+
2
y
3
+
3
y
=
y
2
+
5
then find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in terms of
x
x
x
and
y
y
y
.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
If
3
y
2
−
4
x
3
=
3
x
2
3 y^{2}-4 x^{3}=3 x^{2}
3
y
2
−
4
x
3
=
3
x
2
then find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in terms of
x
x
x
and
y
y
y
.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
If
−
y
+
x
+
y
2
+
5
y
3
+
3
x
2
=
0
-y+x+y^{2}+5 y^{3}+3 x^{2}=0
−
y
+
x
+
y
2
+
5
y
3
+
3
x
2
=
0
then find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in terms of
x
x
x
and
y
y
y
.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
Given that
y
=
v
2
+
5
y=v^{2}+5
y
=
v
2
+
5
, find
d
d
v
(
5
v
3
−
2
sin
y
)
\frac{d}{d v}\left(5 v^{3}-2 \sin y\right)
d
v
d
(
5
v
3
−
2
sin
y
)
in terms of only
v
v
v
.
\newline
Answer:
Get tutor help
Find an explicit formula for the arithmetic sequence
\newline
−
11
,
−
3
,
5
,
13
,
…
-11,-3,5,13,\dots
−
11
,
−
3
,
5
,
13
,
…
\newline
Note: the first term should be
b
(
1
)
b(1)
b
(
1
)
.
\newline
b
(
n
)
=
□
b(n)=\square
b
(
n
)
=
□
Get tutor help
Given the function
f
(
x
)
=
x
1
−
x
3
f(x)=\frac{x}{1-x^{3}}
f
(
x
)
=
1
−
x
3
x
, find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
in simplified form.
\newline
Answer:
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
Given the function
f
(
x
)
=
x
5
−
3
x
4
f(x)=\frac{x}{5-3 x^{4}}
f
(
x
)
=
5
−
3
x
4
x
, find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
in simplified form.
\newline
Answer:
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
Given the function
f
(
x
)
=
x
3
−
2
x
3
f(x)=\frac{x}{3-2 x^{3}}
f
(
x
)
=
3
−
2
x
3
x
, find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
in simplified form.
\newline
Answer:
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
Given the function
y
=
(
10
x
+
10
)
(
x
3
−
x
2
+
1
)
y=(10 x+10)\left(x^{3}-x^{2}+1\right)
y
=
(
10
x
+
10
)
(
x
3
−
x
2
+
1
)
, find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in any form.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
f
(
x
)
=
x
2
f(x)=x^{2}
f
(
x
)
=
x
2
\newline
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
Find
lim
x
→
4
x
3
−
4
x
2
x
2
−
16
\lim _{x \rightarrow 4} \frac{x^{3}-4 x^{2}}{x^{2}-16}
lim
x
→
4
x
2
−
16
x
3
−
4
x
2
.
\newline
Choose
1
1
1
answer:
\newline
(A)
2
2
2
\newline
(B)
1
1
1
\newline
(C)
−
4
-4
−
4
\newline
(D) The limit doesn't exist
Get tutor help
Find
lim
x
→
−
4
x
2
−
16
x
2
+
4
x
\lim _{x \rightarrow-4} \frac{x^{2}-16}{x^{2}+4 x}
lim
x
→
−
4
x
2
+
4
x
x
2
−
16
.
\newline
Choose
1
1
1
answer:
\newline
(A)
2
2
2
\newline
(B)
−
2
-2
−
2
\newline
(C)
0
0
0
\newline
(D) The limit doesn't exist
Get tutor help
Find
lim
x
→
−
4
7
x
+
28
x
2
+
x
−
12
\lim _{x \rightarrow-4} \frac{7 x+28}{x^{2}+x-12}
lim
x
→
−
4
x
2
+
x
−
12
7
x
+
28
.
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
7
7
7
\newline
(C)
−
1
-1
−
1
\newline
(D) The limit doesn't exist
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What is the expression for
f
(
x
)
f(x)
f
(
x
)
when we rewrite
3
5
x
+
3
⋅
2
7
x
3^{5 x+3} \cdot 27^{x}
3
5
x
+
3
⋅
2
7
x
as
3
f
(
x
)
3^{f(x)}
3
f
(
x
)
?
\newline
f
(
x
)
=
f(x)=
f
(
x
)
=
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Which expressions are equivalent to
z
0.2
z^{0.2}
z
0.2
?
\newline
Choose all answers that apply:
\newline
A
z
\sqrt{z}
z
\newline
B
z
5
\sqrt[5]{z}
5
z
\newline
C
(
z
2
)
−
10
\left(z^{2}\right)^{-10}
(
z
2
)
−
10
\newline
D None of the above
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Rewrite the expression in the form
b
n
b^{n}
b
n
.
\newline
(
b
2
)
3
7
=
□
\left(b^{2}\right)^{\frac{3}{7}}=\square
(
b
2
)
7
3
=
□
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Rewrite the expression in the form
a
n
a^{n}
a
n
.
\newline
1
a
−
5
6
=
\frac{1}{a^{-\frac{5}{6}}}=
a
−
6
5
1
=
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Rewrite the expression in the form
a
n
a^{n}
a
n
.
\newline
a
2
5
⋅
a
−
3
=
a^{\frac{2}{5}} \cdot a^{-3}=
a
5
2
⋅
a
−
3
=
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Rewrite the expression in the form
z
n
z^{n}
z
n
.
\newline
z
−
1
3
z
−
5
6
=
□
\frac{z^{-\frac{1}{3}}}{z^{-\frac{5}{6}}}=\square
z
−
6
5
z
−
3
1
=
□
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Rewrite the expression in the form
x
n
x^{n}
x
n
.
\newline
x
−
10
3
x
3
=
□
\frac{x^{-\frac{10}{3}}}{x^{3}}=\square
x
3
x
−
3
10
=
□
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Rewrite the expression in the form
y
n
y^{n}
y
n
.
\newline
(
y
−
1
2
)
4
=
□
\left(y^{-\frac{1}{2}}\right)^{4}=\square
(
y
−
2
1
)
4
=
□
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Rewrite the expression in the form
x
n
x^{n}
x
n
.
\newline
x
−
2
⋅
x
11
9
=
x^{-2} \cdot x^{\frac{11}{9}}=
x
−
2
⋅
x
9
11
=
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