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Math Problems
Precalculus
Evaluate rational exponents
Which of the following expressions are equivalent to
−
8
11
−
3
4
−
1
4
-\dfrac{8}{11}-\dfrac{3}{4}-\dfrac{1}{4}
−
11
8
−
4
3
−
4
1
?
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Simplify to create an equivalent expression.
2
(
3
y
+
6
)
−
3
(
−
4
−
y
)
\qquad{2(3y+6)-3(-4-y)}
2
(
3
y
+
6
)
−
3
(
−
4
−
y
)
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Simplify:
\newline
1100
−
(
374
−
87
)
1100-(374-87)
1100
−
(
374
−
87
)
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Solve for s:
−
7
=
s
+
(
−
13
)
-7=s+\left(-13\right)
−
7
=
s
+
(
−
13
)
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−
57
=
d
6
−
72
-57=\frac{d}{6}-72
−
57
=
6
d
−
72
Find the value of
b
b
b
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y
=
ln
x
−
2
x
+
2
y=\ln \frac{x-2}{x+2}
y
=
ln
x
+
2
x
−
2
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Simplify the expression :
a
b
∗
arctan
(
cot
x
b
)
ab*\arctan\left(\frac{\cot x}{b}\right)
ab
∗
arctan
(
b
c
o
t
x
)
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Solve for
x
x
x
:
\newline
x
=
25
100
x=\sqrt{\frac{25}{100}}
x
=
100
25
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Evaluate:
70
÷
(
6
+
2
2
)
70\div(6+2^{2})
70
÷
(
6
+
2
2
)
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Evaluate:
\newline
(
8
−
6.24
)
2
(8-6.24)2
(
8
−
6.24
)
2
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Factorise:
\newline
x
2
−
6
x
+
8
=
0
x^{2}-6x+8=0
x
2
−
6
x
+
8
=
0
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Write a question that could give an answer of
(
a
3
b
−
3
)
/
(
c
3
)
(a^{3}b^{-3})/(c^{3})
(
a
3
b
−
3
)
/
(
c
3
)
.
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lim
n
→
∞
(
a
−
1
+
b
n
a
)
n
\lim _{n \rightarrow \infty}\left(\frac{a-1+\sqrt[n]{b}}{a}\right)^{n}
lim
n
→
∞
(
a
a
−
1
+
n
b
)
n
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Rewrite in simplest terms:
0.4
(
5
y
+
6
z
)
+
7
z
−
0.1
(
8
z
+
10
y
)
0.4(5 y+6 z)+7 z-0.1(8 z+10 y)
0.4
(
5
y
+
6
z
)
+
7
z
−
0.1
(
8
z
+
10
y
)
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(
16
x
8
)
1
2
12
x
\frac{\left(16 x^{8}\right)^{\frac{1}{2}}}{12 x}
12
x
(
16
x
8
)
2
1
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−
25
9
+
2
5
\frac{-25}{9}+\frac{2}{5}
9
−
25
+
5
2
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4
4
4
.) The solution to
x
2
−
4
x
−
6
=
0
x^{2}-4 x-6=0
x
2
−
4
x
−
6
=
0
in simplest surd form is
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sin
(
2
arccos
(
3
7
)
)
\sin \left(2 \arccos (\frac{3}{7})\right)
sin
(
2
arccos
(
7
3
)
)
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e)
−
2
7
4
3
-27^{\frac{4}{3}}
−
2
7
3
4
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Convert in decimals.
\newline
−
(
9
)
/
(
40
)
=
-(9)/(40) =
−
(
9
)
/
(
40
)
=
___
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(iii)
1
12
\frac{1}{\sqrt{12}}
12
1
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x
2
−
log
4
(
x
)
=
π
x^{2-\log _{4}(x)}=\pi
x
2
−
l
o
g
4
(
x
)
=
π
.
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ln
(
8
)
−
ln
(
4
)
\ln (8) - \ln (4)
ln
(
8
)
−
ln
(
4
)
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12
v
6
\sqrt{12 v^{6}}
12
v
6
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Simplify the following fraction:
16
30
\frac{16}{30}
30
16
\newline
Answer:
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Find
4
x
3
\sqrt{4x^{3}}
4
x
3
at
x
=
4
x=4
x
=
4
.
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Which expression is equivalent to
9
h
+
9
h
9h + 9h
9
h
+
9
h
?
\newline
Choices:
\newline
(A)
h
+
18
h + 18
h
+
18
\newline
(B)
h
18
h^{18}
h
18
\newline
(C)
17
h
17h
17
h
\newline
(D)
18
h
18h
18
h
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Which expression is equivalent to the expression below?
\newline
h
+
h
+
h
+
h
+
h
+
k
+
k
+
k
h+h+h+h+h+k+k+k
h
+
h
+
h
+
h
+
h
+
k
+
k
+
k
\newline
8
+
h
+
k
8+h+k
8
+
h
+
k
\newline
h
5
k
3
h^{5} k^{3}
h
5
k
3
\newline
5
h
+
3
k
5 h+3 k
5
h
+
3
k
\newline
h
5
+
k
3
\frac{h}{5}+\frac{k}{3}
5
h
+
3
k
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Differentiate
y
=
(
4
x
+
x
1
5
)
−
1
5
y=(4x+x^{\frac{1}{5}})^{-\frac{1}{5}}
y
=
(
4
x
+
x
5
1
)
−
5
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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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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Find square root.
64
121
\sqrt{\frac{64}{121}}
121
64
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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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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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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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−
2
3
m
=
8
27
-\frac{2}{3} m=\frac{8}{27}
−
3
2
m
=
27
8
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10
−
4
5
6
10-4 \frac{5}{6}
10
−
4
6
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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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
−
4
3
=
16
x
-\frac{4}{3}=\frac{16}{x}
−
3
4
=
x
16
\newline
Answer:
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