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Math Problems
Calculus
Product rule
1
6
x
2
+
y
+
1
6
x
+
y
2
16^{x^2}+y+16^x+y^2
1
6
x
2
+
y
+
1
6
x
+
y
2
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solve the followimg equation
3
x
+
5
y
=
52
3^x+5^y=52
3
x
+
5
y
=
52
,
3
x
−
5
y
=
2
3^x-5^y=2
3
x
−
5
y
=
2
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In the following equation, what is the value of
z
z
z
?
\newline
6
2
=
6
z
6
3
6^2 = \frac{6^z}{6^3}
6
2
=
6
3
6
z
\newline
z
=
z =
z
=
____
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Select all the expressions that are equivalent to
6
4
3
4
\frac{6^4}{3^4}
3
4
6
4
.
\newline
Multi-select Choices:
\newline
(A)
1
2
−
4
\frac{1}{2^{-4}}
2
−
4
1
\newline
(B)
2
0
2^0
2
0
\newline
(C)
2
2
2
\newline
(D)
1
2
4
\frac{1}{2^4}
2
4
1
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Select all the expressions that are equivalent to
6
4
3
4
\frac{6^4}{3^4}
3
4
6
4
.
\newline
Multi-select Choices:
\newline
(A)
1
2
4
\frac{1}{2^4}
2
4
1
\newline
(B)
2
2
2
\newline
(C)
2
4
2^4
2
4
\newline
(D)
1
2
−
4
\frac{1}{2^{-4}}
2
−
4
1
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2
x
+
17
=
3
x
−
2
2^x + 17 = 3^x - 2
2
x
+
17
=
3
x
−
2
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How does
f
(
t
)
=
2
t
f(t) = 2^t
f
(
t
)
=
2
t
change over the interval from
t
=
1
t = 1
t
=
1
to
t
=
2
t = 2
t
=
2
?
\newline
Choices:
\newline
(A)
f
(
t
)
f(t)
f
(
t
)
decreases by
2
%
2\%
2%
\newline
(B)
f
(
t
)
f(t)
f
(
t
)
increases by
200
%
200\%
200%
\newline
(C)
f
(
t
)
f(t)
f
(
t
)
increases by a factor of
2
2
2
\newline
(D)
f
(
t
)
f(t)
f
(
t
)
increases by
2
2
2
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Q
T
‾
\overline{\mathrm{QT}}
QT
is a tangent to circle
R
⋅
R
Q
=
6.
Q
T
=
8
\mathrm{R} \cdot \mathrm{RQ}=6 . \mathrm{QT}=8
R
⋅
RQ
=
6.
QT
=
8
. Find
R
T
\mathrm{RT}
RT
.
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find the argument of
z
=
−
4
−
4
3
i
z=-4-4^3i
z
=
−
4
−
4
3
i
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8.
2
2
+
x
2
=
y
2
8.2^{2}+x^{2}=y^{2}
8.
2
2
+
x
2
=
y
2
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Construct the truth table.
\newline
\begin{tabular}{|c|c|c|c|c|}
\newline
\hline
p
p
p
&
q
q
q
&
r
r
r
&
(
r
∧
q
)
∨
p
(r \wedge q) \vee p
(
r
∧
q
)
∨
p
&
(
q
∨
p
)
∧
r
(q \vee p) \wedge r
(
q
∨
p
)
∧
r
\\
\newline
\hline
T
T
T
&
T
T
T
&
T
T
T
&
T
T
T
&
T
T
T
\\
\newline
\hline
T
T
T
&
T
T
T
&
q
q
q
2
2
2
&
T
T
T
&
q
q
q
4
4
4
\\
\newline
\hline
T
T
T
&
q
q
q
2
2
2
&
T
T
T
&
q
q
q
2
2
2
&
q
q
q
4
4
4
\\
\newline
\hline
T
T
T
&
q
q
q
2
2
2
&
q
q
q
2
2
2
&
q
q
q
2
2
2
&
q
q
q
4
4
4
\\
\newline
\hline
q
q
q
2
2
2
&
T
T
T
&
T
T
T
&
T
T
T
&
q
q
q
4
4
4
\\
\newline
\hline
\newline
\end{tabular}
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Show that there exist irrational numbers
x
,
y
x,y
x
,
y
for which
x
y
x^y
x
y
is rational
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Given:
m
∠
D
A
C
=
m
∠
D
B
C
m \angle D A C=m \angle D B C
m
∠
D
A
C
=
m
∠
D
BC
;
\newline
A
B
‾
\overline{A B}
A
B
bisects
∠
D
A
C
\angle D A C
∠
D
A
C
;
\newline
A
B
‾
\overline{A B}
A
B
bisects
∠
D
B
C
\angle D B C
∠
D
BC
.
\newline
Prove:
m
∠
1
=
m
∠
2
m \angle 1=m \angle 2
m
∠1
=
m
∠2
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4
2
+
4
2
+
4
2
+
4
2
=
2
n
4^2+4^2+4^2+4^2=2^n
4
2
+
4
2
+
4
2
+
4
2
=
2
n
what is the value of
n
n
n
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Suppose that the functions
\newline
f
f
f
and
\newline
g
g
g
are defined as follows.
\newline
f
(
x
)
=
9
x
g
(
x
)
=
4
x
+
3
f(x)=\frac{9}{x}\quad g(x)=\frac{4}{x+3}
f
(
x
)
=
x
9
g
(
x
)
=
x
+
3
4
\newline
Find
\newline
g
f
\frac{g}{f}
f
g
. Then, give its domain using an interval or union of intervals.
\newline
Simplify your answers.
\newline
(
g
f
)
(
x
)
=
∏
\left(\frac{g}{f}\right)(x)=\prod
(
f
g
)
(
x
)
=
∏
\newline
Domain of
\newline
g
f
\frac{g}{f}
f
g
:
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Draw
f
(
x
,
y
)
=
x
2
⋅
y
2
f(x,y) = x^2 \cdot y^2
f
(
x
,
y
)
=
x
2
⋅
y
2
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Solve for
x
x
x
:
x
2
+
3
x
−
10
=
0
x^{2} + 3x - 10 = 0
x
2
+
3
x
−
10
=
0
a
=
1
a=1
a
=
1
,
b
=
3
b=3
b
=
3
, and
c
=
−
10
c=-10
c
=
−
10
.
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Find the derivative of
f
(
x
)
f(x)
f
(
x
)
.
\newline
f
(
x
)
=
x
e
x
f(x) = x e^x
f
(
x
)
=
x
e
x
\newline
f
′
(
x
)
=
f'\left(x\right) =
f
′
(
x
)
=
______
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