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Math Problems
Precalculus
Evaluate rational exponents
4
a
1
2
4
3
2
a
3
4
\frac{4 a^{\frac{1}{2}}}{4^{\frac{3}{2}} a^{\frac{3}{4}}}
4
2
3
a
4
3
4
a
2
1
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1
−
tg
(
3
π
8
+
i
ln
2
4
)
1-\operatorname{tg}\left(\frac{3 \pi}{8}+i \frac{\ln 2}{4}\right)
1
−
tg
(
8
3
π
+
i
4
l
n
2
)
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6
−
1
3
?
6^{-\frac{1}{3}} ?
6
−
3
1
?
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Find the sum.Give your answer in simplest form.
\newline
1
48
+
5
6
\frac{1}{48}+\frac{5}{6}
48
1
+
6
5
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Find the derivative of
cot
−
1
(
1
8
x
+
9
)
\cot^{-1}\left(\frac{1}{8x+9}\right)
cot
−
1
(
8
x
+
9
1
)
.
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48
48
48
. Find the exact value of the given expression.
\newline
cos
(
2
tan
−
1
12
5
)
\cos \left(2 \tan ^{-1} \frac{12}{5}\right)
cos
(
2
tan
−
1
5
12
)
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Find square root.
64
121
\sqrt{\frac{64}{121}}
121
64
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5
x
+
7
2
=
3
x
2
−
14
5x + \frac{7}{2} = \frac{3x}{2} - 14
5
x
+
2
7
=
2
3
x
−
14
Find `x`
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Evaluate
∑
m
≥
1
(
1
−
1
m
)
m
2
=
\sum_{m \geq 1}\left(1-\frac{1}{m}\right)^{m^{2}}=
∑
m
≥
1
(
1
−
m
1
)
m
2
=
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Find the derivative of
tan
−
1
(
1
8
x
+
9
)
\tan^{-1}\left(\frac{1}{8x+9}\right)
tan
−
1
(
8
x
+
9
1
)
.
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(
3021
8
)
\left(\frac{3021}{8}\right)
(
8
3021
)
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sec
[
sin
−
1
(
−
3
4
)
]
\sec[\sin^{-1}(-\frac{3}{4})]
sec
[
sin
−
1
(
−
4
3
)]
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∂
f
∂
y
(
x
y
)
\frac{\partial f}{\partial y}(x^{y})
∂
y
∂
f
(
x
y
)
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Select the answer which is equivalent to the given expression using your calculator.
\newline
sin
(
arccos
5
250
)
\sin \left(\arccos \frac{5}{\sqrt{250}}\right)
sin
(
arccos
250
5
)
\newline
5
15
\frac{5}{15}
15
5
\newline
5
250
\frac{5}{\sqrt{250}}
250
5
\newline
15
5
\frac{15}{5}
5
15
\newline
15
250
\frac{15}{\sqrt{250}}
250
15
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Which of the following is a whole number?
\newline
Choices:
\newline
(A)
0
0
0
\newline
(B)
6.888
…
6.888\ldots
6.888
…
\newline
(C)
9
2
\frac{9}{2}
2
9
\newline
(D)
10
10
10
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2
⋅
4
x
−
1
2
−
5
⋅
6
x
+
2
3
⋅
9
x
+
2
=
0
2 \cdot 4^{x - \frac{1}{2}} - 5 \cdot 6^{x} + \frac{2}{3} \cdot 9^{x+2} = 0
2
⋅
4
x
−
2
1
−
5
⋅
6
x
+
3
2
⋅
9
x
+
2
=
0
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arccos
(
cos
(
−
3
π
4
)
)
\arccos \left(\cos \left(-\frac{3 \pi}{4}\right)\right)
arccos
(
cos
(
−
4
3
π
)
)
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x
2
x
2
−
c
2
=
c
2
x
2
−
c
2
+
39
\frac{x^{2}}{\sqrt{x^{2}-c^{2}}}=\frac{c^{2}}{\sqrt{x^{2}-c^{2}}}+39
x
2
−
c
2
x
2
=
x
2
−
c
2
c
2
+
39
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4
4
y
−
7
=
2
9
y
\frac{4}{4}y-7=\frac{2}{9}y
4
4
y
−
7
=
9
2
y
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(
8
−
2
log
8
12
y
3
)
\left(8^{-2 \log _{8} 12 y^{3}}\right)
(
8
−
2
l
o
g
8
12
y
3
)
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56
z
7
\sqrt{56z^{7}}
56
z
7
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Fully simplify.
\newline
13
x
y
2
(
−
9
x
4
y
)
13 x y^{2}\left(-9 x^{4} y\right)
13
x
y
2
(
−
9
x
4
y
)
\newline
Answer:
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uation.
−
2
3
m
=
8
27
-\frac{2}{3} m=\frac{8}{27}
−
3
2
m
=
27
8
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10
−
4
5
8
10-4 \frac{5}{8}
10
−
4
8
5
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R
(
x
)
=
ln
(
3
+
x
2
−
x
2
)
R(x)=\ln \left(\frac{3+x}{2-x^{2}}\right)
R
(
x
)
=
ln
(
2
−
x
2
3
+
x
)
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f
(
v
)
=
tan
−
1
(
3
−
2
v
)
f(v)=\tan ^{-1}(3-2 v)
f
(
v
)
=
tan
−
1
(
3
−
2
v
)
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re
y
=
sin
−
1
(
1
2
x
+
5
)
y=\sin ^{-1}\left(\frac{1}{2 x+5}\right)
y
=
sin
−
1
(
2
x
+
5
1
)
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Find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
where
y
=
sin
−
1
(
1
2
x
+
5
)
y=\sin ^{-1}\left(\frac{1}{2 x+5}\right)
y
=
sin
−
1
(
2
x
+
5
1
)
.
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If the sum of
(
2
x
y
+
4
x
y
)
(2 x y+4 x y)
(
2
x
y
+
4
x
y
)
is subtiracted from
(
2
x
2
y
+
10
x
y
)
\left(2 x^{2} y+10 x y\right)
(
2
x
2
y
+
10
x
y
)
What will be the Answer?
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Divide:
\newline
920
4
=
□
\frac{920}{4} = \square
4
920
=
□
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Solve for
x
\mathrm{x}
x
.
\newline
−
2
3
=
10
x
-\frac{2}{3}=\frac{10}{x}
−
3
2
=
x
10
\newline
Answer:
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Solve for
x
\mathrm{x}
x
.
\newline
−
3
2
=
30
x
-\frac{3}{2}=\frac{30}{x}
−
2
3
=
x
30
\newline
Answer:
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Solve for
x
\mathrm{x}
x
.
\newline
−
4
3
=
16
x
-\frac{4}{3}=\frac{16}{x}
−
3
4
=
x
16
\newline
Answer:
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Solve for
x
\mathrm{x}
x
.
\newline
−
2
17
=
x
34
-\frac{2}{17}=\frac{x}{34}
−
17
2
=
34
x
\newline
Answer:
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6
10
−
1
5
\frac{6}{10}-\frac{1}{5}
10
6
−
5
1
=
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Which value of
x
x
x
satisfies the equation
4
3
(
x
−
1
4
)
=
−
37
3
\frac{4}{3}\left(x-\frac{1}{4}\right)=-\frac{37}{3}
3
4
(
x
−
4
1
)
=
−
3
37
?
\newline
9
9
9
\newline
−
8
-8
−
8
\newline
8
8
8
\newline
−
9
-9
−
9
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Which expression is equivalent to
−
61.6
+
12.2
?
-61.6+12.2 ?
−
61.6
+
12.2
?
\newline
−
12.2
+
(
−
61.6
)
-12.2+(-61.6)
−
12.2
+
(
−
61.6
)
\newline
−
61.6
+
(
−
12.2
)
-61.6+(-12.2)
−
61.6
+
(
−
12.2
)
\newline
12.2
−
(
−
61.6
)
12.2-(-61.6)
12.2
−
(
−
61.6
)
\newline
12.2
−
61.6
12.2-61.6
12.2
−
61.6
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Which expression is equivalent to
−
47.7
−
64.5
-47.7-64.5
−
47.7
−
64.5
?
\newline
−
64.5
+
47.7
-64.5+47.7
−
64.5
+
47.7
\newline
47.7
+
(
−
64.5
)
47.7+(-64.5)
47.7
+
(
−
64.5
)
\newline
−
47.7
+
(
−
64.5
)
-47.7+(-64.5)
−
47.7
+
(
−
64.5
)
\newline
64.5
−
(
−
47.7
)
64.5-(-47.7)
64.5
−
(
−
47.7
)
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Which expression is equivalent to
−
3.7
−
54.7
-3.7-54.7
−
3.7
−
54.7
?
\newline
54.7
−
(
−
3.7
)
54.7-(-3.7)
54.7
−
(
−
3.7
)
\newline
−
54.7
+
3.7
-54.7+3.7
−
54.7
+
3.7
\newline
3.7
+
(
−
54.7
)
3.7+(-54.7)
3.7
+
(
−
54.7
)
\newline
−
3.7
+
(
−
54.7
)
-3.7+(-54.7)
−
3.7
+
(
−
54.7
)
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(
d
d
x
)
(
−
4
x
4
3
−
2
x
−
3
4
+
3
)
\left(\frac{d}{dx}\right)(-4x^{\frac{4}{3}}-2x^{-\frac{3}{4}}+3)
(
d
x
d
)
(
−
4
x
3
4
−
2
x
−
4
3
+
3
)
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Find
d
d
x
(
64
x
−
3
)
\frac{d}{dx}(\sqrt{64x^{-3}})
d
x
d
(
64
x
−
3
)
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Find
d
d
x
49
x
−
9
\frac{d}{dx}\sqrt{49x^{-9}}
d
x
d
49
x
−
9
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Convert
64
9
\frac{64}{9}
9
64
into a mixed number.
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ln
(
1
e
)
\ln \left( \frac{1}{e} \right)
ln
(
e
1
)
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log
3
(
7
−
2
x
)
=
5
(
4
x
+
11
)
\log 3^{(7-2x)}=5^{(4x+11)}
lo
g
3
(
7
−
2
x
)
=
5
(
4
x
+
11
)
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ln
x
2
+
1
x
3
+
5
\ln\sqrt{\frac{x^{2}+1}{x^{3}+5}}
ln
x
3
+
5
x
2
+
1
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3
5
−
3
10
\frac{3}{5}-\frac{3}{10}
5
3
−
10
3
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y
=
(
sin
−
1
(
5
x
2
)
)
3
y=(\sin^{-1}(5x^{2}))^{3}
y
=
(
sin
−
1
(
5
x
2
)
)
3
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Simplify
ln
(
1
e
)
\ln \left(\frac{1}{\sqrt{e}}\right)
ln
(
e
1
)
\newline
Answer:
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Simplify
ln
(
1
e
)
\ln \left(\frac{1}{e}\right)
ln
(
e
1
)
\newline
Answer:
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