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Math Problems
Algebra 2
Sin, cos, and tan of special angles
y
=
3
7
x
−
12
7
y=\frac{3}{7}x-\frac{12}{7}
y
=
7
3
x
−
7
12
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z
=
7
+
3
i
z=7+3 i
z
=
7
+
3
i
\newline
Find the angle
θ
\theta
θ
(in degrees) that
z
z
z
makes in the complex plane. Round your answer, if necessary, to the nearest tenth. Express
θ
\theta
θ
between
−
18
0
∘
-180^{\circ}
−
18
0
∘
and
18
0
∘
180^{\circ}
18
0
∘
.
\newline
θ
=
□
∘
\theta=\square^{\circ}
θ
=
□
∘
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∫
2
x
+
4
d
x
\int 2 x+4 d x
∫
2
x
+
4
d
x
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Solve the equation. Check your solution.
\newline
18
=
6
−
(
z
+
8
)
18=6-(z+8)
18
=
6
−
(
z
+
8
)
\newline
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Solve for
x
x
x
:
15
=
−
5
3
x
15 = -\frac{5}{3}x
15
=
−
3
5
x
\newline
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Determine the value of
y
y
y
, if
x
x
x
is
12
12
12
.
\newline
y
=
(
x
−
10
)
2
y=(x-10)^{2}
y
=
(
x
−
10
)
2
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
2
-2
−
2
.
\newline
y
=
x
2
−
5
y=x^{2}-5
y
=
x
2
−
5
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
5
5
5
.
\newline
y
=
(
x
−
3
)
2
y=(x-3)^{2}
y
=
(
x
−
3
)
2
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
6
-6
−
6
.
\newline
y
=
(
x
+
8
)
2
y=(x+8)^{2}
y
=
(
x
+
8
)
2
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
8
-8
−
8
.
\newline
y
=
x
2
−
2
y=x^{2}-2
y
=
x
2
−
2
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
12
-12
−
12
.
\newline
y
=
x
2
−
10
y=x^{2}-10
y
=
x
2
−
10
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
11
-11
−
11
.
\newline
y
=
(
x
+
4
)
2
y=(x+4)^{2}
y
=
(
x
+
4
)
2
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
5
5
5
.
\newline
y
=
(
x
−
5
)
2
y=(x-5)^{2}
y
=
(
x
−
5
)
2
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
5
-5
−
5
.
\newline
y
=
(
x
−
5
)
2
y=(x-5)^{2}
y
=
(
x
−
5
)
2
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
4
-4
−
4
.
\newline
y
=
(
x
−
5
)
2
y=(x-5)^{2}
y
=
(
x
−
5
)
2
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
3
-3
−
3
.
\newline
y
=
x
2
+
3
y=x^{2}+3
y
=
x
2
+
3
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
11
-11
−
11
.
\newline
y
=
x
2
+
4
y=x^{2}+4
y
=
x
2
+
4
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
9
-9
−
9
.
\newline
y
=
x
2
−
12
y=x^{2}-12
y
=
x
2
−
12
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
4
-4
−
4
.
\newline
y
=
x
2
−
5
y=x^{2}-5
y
=
x
2
−
5
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
8
-8
−
8
.
\newline
y
=
27
x
+
11
y=\frac{27}{x+11}
y
=
x
+
11
27
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
10
10
10
.
\newline
y
=
46
x
−
8
y=\frac{46}{x-8}
y
=
x
−
8
46
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
7
7
7
.
\newline
y
=
44
x
−
29
y=\frac{44}{x-29}
y
=
x
−
29
44
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
1
-1
−
1
.
\newline
y
=
46
x
−
1
y=\frac{46}{x-1}
y
=
x
−
1
46
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
5
5
5
.
\newline
y
=
34
x
−
7
y=\frac{34}{x-7}
y
=
x
−
7
34
\newline
Answer:
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sin
u
cos
2
u
cos
3
u
\frac{\sin u \cos 2 u}{\cos ^{3} u}
c
o
s
3
u
s
i
n
u
c
o
s
2
u
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sin
2
u
cos
2
u
\frac{\sin ^{2} u}{\cos ^{2} u}
c
o
s
2
u
s
i
n
2
u
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For which values of
x
\mathrm{x}
x
is the expression undefined?
\newline
3
x
−
12
x
2
−
25
\frac{3 x-12}{x^{2}-25}
x
2
−
25
3
x
−
12
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Find all horizontal asymptotes of the following function.
\newline
f
(
x
)
=
x
−
4
10
x
2
−
56
x
+
64
f(x)=\frac{x-4}{10 x^{2}-56 x+64}
f
(
x
)
=
10
x
2
−
56
x
+
64
x
−
4
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Solve the differential equation
d
y
d
x
=
−
e
x
8
\frac{d y}{d x}=-\frac{e^{x}}{8}
d
x
d
y
=
−
8
e
x
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Fully simplify using only positive exponents.
\newline
30
x
y
8
10
x
7
y
8
\frac{30 x y^{8}}{10 x^{7} y^{8}}
10
x
7
y
8
30
x
y
8
\newline
Answer:
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Factor the expression completely.
\newline
y
5
+
x
2
y
5
y^{5}+x^{2} y^{5}
y
5
+
x
2
y
5
\newline
Answer:
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Factor the expression completely.
\newline
x
y
+
x
5
y
5
x y+x^{5} y^{5}
x
y
+
x
5
y
5
\newline
Answer:
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Evaluate. Write your answer as a whole number or as a simplified fraction.
\newline
2
2
⋅
2
2
=
□
2^{2} \cdot 2^{2} = \square
2
2
⋅
2
2
=
□
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Find the derivative of
y
y
y
with respect to
θ
\theta
θ
:
y
=
(
5
−
5
θ
)
tanh
−
1
(
θ
)
y = (5 - 5\theta)\tanh^{-1}(\theta)
y
=
(
5
−
5
θ
)
tanh
−
1
(
θ
)
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Given the function
y
=
x
−
x
sin
x
y=x-x\sin x
y
=
x
−
x
sin
x
, find
d
y
d
x
\frac{dy}{dx}
d
x
d
y
in any form.
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Find
d
y
d
x
\frac{dy}{dx}
d
x
d
y
.
4
x
y
=
sin
(
x
+
y
)
4xy=\sin(x+y)
4
x
y
=
sin
(
x
+
y
)
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Find the derivative of
y
y
y
with
y
=
(
5
−
5
θ
)
tanh
−
1
(
θ
)
y=(5-5\theta)\tanh^{-1}(\theta)
y
=
(
5
−
5
θ
)
tanh
−
1
(
θ
)
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If
y
2
cos
(
1
x
)
=
a
2
y^{2}\cos\left(\frac{1}{x}\right)=a^{2}
y
2
cos
(
x
1
)
=
a
2
, then find
d
y
d
x
\frac{dy}{dx}
d
x
d
y
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Solve the differential equation.
\newline
d
y
d
x
=
6
x
y
\frac{dy}{dx}=6\sqrt{xy}
d
x
d
y
=
6
x
y
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(i)
\newline
lim
x
→
0
(
tan
2
x
−
sin
2
x
x
3
)
\lim_{x \to 0} \left( \frac{\tan 2x - \sin 2x}{x^{3}} \right)
lim
x
→
0
(
x
3
t
a
n
2
x
−
s
i
n
2
x
)
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Determine the value of
y
y
y
, if
x
x
x
is
10
10
10
.
\newline
y
=
46
x
−
8
y=\frac{46}{x-8}
y
=
x
−
8
46
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Find the derivative of the function.
\newline
g
(
t
)
=
1
(
7
t
+
1
)
6
g(t)=\frac{1}{(7t+1)^{6}}
g
(
t
)
=
(
7
t
+
1
)
6
1
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Evaluate. Write your answer in simplified, rationalized form. Do not round.
\newline
cos
9
0
∘
=
\cos 90^\circ =
cos
9
0
∘
=
____
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