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Math Problems
Algebra 2
Find trigonometric ratios using reference angles
Fully simplify using only positive exponents.
\newline
15
x
4
y
2
3
x
y
4
\frac{15 x^{4} y^{2}}{3 x y^{4}}
3
x
y
4
15
x
4
y
2
\newline
Answer:
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Find
t
t
t
.
5
13
=
t
−
6
13
\dfrac{5}{13}=t-\dfrac{6}{13}
13
5
=
t
−
13
6
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99
x
12
25
y
12
\sqrt{\frac{99 x^{12}}{25 y^{12}}}
25
y
12
99
x
12
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g
(
x
)
=
−
1
5
(
x
+
5
)
2
−
2
g(x)=-\frac{1}{5}(x+5)^2-2
g
(
x
)
=
−
5
1
(
x
+
5
)
2
−
2
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x
2
+
3
+
9
−
x
2
=
x^{2}+3+9-x^{2}=
x
2
+
3
+
9
−
x
2
=
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Find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
where
y
=
csc
−
1
(
2
x
4
+
6
)
y=\csc ^{-1}\left(2 x^{4}+6\right)
y
=
csc
−
1
(
2
x
4
+
6
)
.
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Fully simplify using only positive exponents.
\newline
30
x
3
y
7
12
x
4
y
4
\frac{30 x^{3} y^{7}}{12 x^{4} y^{4}}
12
x
4
y
4
30
x
3
y
7
\newline
Answer:
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Factor the expression completely.
\newline
x
3
y
5
−
x
5
x^{3} y^{5}-x^{5}
x
3
y
5
−
x
5
\newline
Answer:
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Factor the expression completely.
\newline
x
y
5
−
x
3
y
4
x y^{5}-x^{3} y^{4}
x
y
5
−
x
3
y
4
\newline
Answer:
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(
4
11
)
(
4
−
8
)
=
(4^{11})(4^{-8})=
(
4
11
)
(
4
−
8
)
=
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−
6
−
∫
(
−
3
)
(
0
)
9
−
x
2
d
x
-6-\int_{(-3)}^{(0)}\sqrt{9-x^{2}}dx
−
6
−
∫
(
−
3
)
(
0
)
9
−
x
2
d
x
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∫
3
x
(
2
x
−
1
)
2
d
x
\int 3\sqrt{x}(2x-1)^{2}\,dx
∫
3
x
(
2
x
−
1
)
2
d
x
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a
−
13
a
−
6
=
□
\dfrac{a^{-13}}{a^{-6}}=\Box
a
−
6
a
−
13
=
□
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a
−
13
a
−
6
=
□
\dfrac{a^{-13}}{a^{-6}}=\Box
a
−
6
a
−
13
=
□
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If
2
+
y
3
=
x
y
3
2+y^{3}=x y^{3}
2
+
y
3
=
x
y
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
=
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