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Math Problems
Algebra 2
Sin, cos, and tan of special angles
In
△
A
B
C
\triangle ABC
△
A
BC
, right-angled at
C
C
C
find
cos
A
\cos A
cos
A
,
tan
A
\tan A
tan
A
and
cosec
B
\cosec B
cosec
B
if
sin
A
=
24
25
\sin A=\frac{24}{25}
sin
A
=
25
24
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7
7
7
) In a right angled
△
A
B
C
,
∠
B
=
9
0
∘
\triangle \mathrm{ABC}, \angle B=90^{\circ}
△
ABC
,
∠
B
=
9
0
∘
.If
B
C
A
B
=
1
3
\frac{B C}{A B}=\frac{1}{\sqrt{3}}
A
B
BC
=
3
1
, then find
A
B
A
C
\frac{A B}{A C}
A
C
A
B
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the circle shown has a sector with area
1256
π
1256\pi
1256
π
and
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d
y
d
x
\frac{dy}{dx}
d
x
d
y
for
y
=
sin
2
(
cos
3
x
)
y=\sin^2(\cos 3x)
y
=
sin
2
(
cos
3
x
)
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rac{ ext{sec}^
2
2
2
(x)}{ ext{cos}(x)}
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Choosing a Graph Given Values for
h
h
h
and
k
k
k
\newline
Anvee the gateh
d
y
=
(
x
−
3
)
2
+
1
d y=(x-3)^{2}+1
d
y
=
(
x
−
3
)
2
+
1
.
\newline
बलाइa
\newline
Soles
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Simplify.
\newline
Rewrite the expression in the form
9
n
9^{n}
9
n
.
\newline
(
9
2
)
5
=
□
\left(9^{2}\right)^{5}=\square
(
9
2
)
5
=
□
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d
sin
(
x
)
d
x
\frac{d \sin (x)}{d x}
d
x
d
s
i
n
(
x
)
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https://www.chegg.com/homework-help/questions-and-answers/f
4
−
18
4-18
4
−
18
draw the shear and moment diagrams for the beam and indicate the values at the supports and at points where the change of load occurs.
4
4
4
kip
f
t
f
t
\frac{ft}{ft}
f
t
f
t
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2
3
cos
3
0
∘
t
g
4
5
∘
2 \sqrt{3} \cos 30^{\circ} \mathrm{tg} 45^{\circ}
2
3
cos
3
0
∘
tg
4
5
∘
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onsider the diagram below showing an isosceles triangle with its base extended so that
m
∠
A
C
D
=
11
5
∘
\mathrm{m} \angle A C D=115^{\circ}
m
∠
A
C
D
=
11
5
∘
.
\newline
ill in the blanks.
\newline
-
m
∠
A
C
B
=
\mathrm{m} \angle A C B=
m
∠
A
CB
=
□
\square
□
]
∘
^{\circ}
∘
\newline
m
∠
B
A
C
=
\mathrm{m} \angle B A C=
m
∠
B
A
C
=
□
\square
□
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Problem
24
24
24
\newline
Solve the equation
\newline
x
3
−
3
x
=
x
+
2
x^{3}-3 x=\sqrt{x+2}
x
3
−
3
x
=
x
+
2
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Knowiedge Cneck
\newline
Question
7
7
7
\newline
Below is the graph of
y
=
1
x
y=\frac{1}{x}
y
=
x
1
.
\newline
Transform it to make the graph of
y
=
−
1
x
−
4
y=-\frac{1}{x}-4
y
=
−
x
1
−
4
.
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Kromberge Onect
\newline
Antlon?
\newline
Below is the graph of
y
=
1
x
y=\frac{1}{x}
y
=
x
1
.
\newline
Tansformin to make the graph of
y
=
−
1
x
−
4
y=-\frac{1}{x}-4
y
=
−
x
1
−
4
.
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60
60
60
.
tan
22
5
∘
\tan 225^{\circ}
tan
22
5
∘
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∬
0
∞
e
−
t
t
x
d
t
d
x
\iint_{0}^{\infty} e^{-t} t^{x} d t d x
∬
0
∞
e
−
t
t
x
d
t
d
x
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In the figure below,
m
∠
J
K
M
=
10
9
∘
,
m
∠
N
K
M
=
3
5
∘
m \angle J K M=109^{\circ}, m \angle N K M=35^{\circ}
m
∠
J
K
M
=
10
9
∘
,
m
∠
N
K
M
=
3
5
∘
, and
K
N
K N
K
N
bisects
∠
L
K
M
\angle L K M
∠
L
K
M
. Find
m
∠
J
K
L
m \angle J K L
m
∠
J
K
L
.
\newline
m
∠
J
K
L
=
7
2
∘
m \angle J K L=72^{\circ}
m
∠
J
K
L
=
7
2
∘
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Simplify fully, WITHOLIT the use of a calculator
\newline
sin
30
tan
2
3
0
∘
cos
cos
3
0
∘
cot
cot
4
5
∘
\frac{\sin 30 \tan ^{2} 30^{\circ}}{\cos \cos 30^{\circ} \cot \cot 45^{\circ}}
cos
cos
3
0
∘
cot
cot
4
5
∘
sin
30
tan
2
3
0
∘
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Given the function
y
=
x
4
−
x
4
y=\frac{x}{4-x^{4}}
y
=
4
−
x
4
x
, find
d
y
d
x
\frac{dy}{dx}
d
x
d
y
in simplified form.
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∫
x
2
sin
x
d
x
\int x^{2} \sin x d x
∫
x
2
sin
x
d
x
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If
f
(
x
)
=
cos
(
4
x
)
f(x)=\cos (4 x)
f
(
x
)
=
cos
(
4
x
)
, find
f
′
(
π
12
)
f^{\prime}\left(\frac{\pi}{12}\right)
f
′
(
12
π
)
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Simplify:
sec
2
θ
sec
2
θ
−
1
=
csc
2
θ
\frac{\sec^{2}\theta}{\sec^{2}\theta-1}=\csc^{2}\theta
s
e
c
2
θ
−
1
s
e
c
2
θ
=
csc
2
θ
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cosec
A
−
1
cosec
A
+
1
=
(
cos
A
1
+
sin
A
)
2
\frac{\operatorname{cosec} A-1}{\operatorname{cosec} A+1}=\left(\frac{\cos A}{1+\sin A}\right)^{2}
cosec
A
+
1
cosec
A
−
1
=
(
1
+
s
i
n
A
c
o
s
A
)
2
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What could be the value of
x
x
x
in the following equation? Select all that apply.
\newline
x
2
=
49
x^2 = 49
x
2
=
49
\newline
Multi-select Choices:
\newline
(A)
7
7
7
\newline
(B)
−
7
-7
−
7
\newline
(C)
49
\sqrt{49}
49
\newline
(D)
−
49
-\sqrt{49}
−
49
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Which equation has both
1
4
\frac{1}{4}
4
1
and
−
1
4
-\frac{1}{4}
−
4
1
as possible values of
x
x
x
? Select all that apply.
\newline
Multi-select Choices:
\newline
(A)
x
2
=
1
2
x^2 = \frac{1}{2}
x
2
=
2
1
\newline
(B)
x
3
=
1
2
x^3 = \frac{1}{2}
x
3
=
2
1
\newline
(C)
x
2
=
1
16
x^2 = \frac{1}{16}
x
2
=
16
1
\newline
(D)
x
3
=
1
16
x^3 = \frac{1}{16}
x
3
=
16
1
\newline
(E)
x
2
=
1
64
x^2 = \frac{1}{64}
x
2
=
64
1
\newline
(F)
x
3
=
1
64
x^3 = \frac{1}{64}
x
3
=
64
1
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y
=
x
tan
x
y=\frac{x}{\tan x}
y
=
t
a
n
x
x
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y
=
(
5
x
−
3
)
3
y=(5 x-3)^{3}
y
=
(
5
x
−
3
)
3
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∫
x
x
d
x
\int x^{x} d x
∫
x
x
d
x
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2
2
2
. Ray
B
D
\mathrm{BD}
BD
bisects
∠
A
B
C
\angle \mathrm{ABC}
∠
ABC
. If
m
∠
A
B
D
=
(
7
x
−
9
)
∘
\mathrm{m} \angle \mathrm{ABD}=(7 \mathrm{x}-9)^{\circ}
m
∠
ABD
=
(
7
x
−
9
)
∘
and
m
∠
C
B
D
=
(
2
x
+
36
)
∘
\mathrm{m} \angle \mathrm{CBD}=(2 \mathrm{x}+36)^{\circ}
m
∠
CBD
=
(
2
x
+
36
)
∘
, what is the
m
∠
A
B
C
\mathrm{m} \angle \mathrm{ABC}
m
∠
ABC
?
\newline
A.
5
4
∘
54^{\circ}
5
4
∘
\newline
B.
13
2
∘
132^{\circ}
13
2
∘
\newline
C.
8
6
∘
86^{\circ}
8
6
∘
\newline
D.
10
8
∘
108^{\circ}
10
8
∘
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p
=
10
,
000
9
+
4
e
−
0.2
t
p=\frac{10,000}{9+4 e^{-0.2 t}}
p
=
9
+
4
e
−
0.2
t
10
,
000
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Q
(
x
,
y
)
=
x
0
,
2
y
0
,
9
Q(x, y) = x^{0,2}y^{0,9}
Q
(
x
,
y
)
=
x
0
,
2
y
0
,
9
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Find
x
x
x
any
y
y
y
and draw a grap of
y
=
(
x
−
1
)
2
+
3
y=(x-1)^{2} +3
y
=
(
x
−
1
)
2
+
3
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Solve for
u
u
u
.
\newline
4
u
2
=
−
12
u
−
9
4 u^{2}=-12 u-9
4
u
2
=
−
12
u
−
9
\newline
If there is more than one solution, separate them with commas. If there is no solution, click on
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y
(
y
+
2
)
=
y
2
−
6
y(y+2)=y^{2}-6
y
(
y
+
2
)
=
y
2
−
6
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1
+
sec
A
sec
A
=
sin
2
A
1
−
cos
A
\frac{1+\sec A}{\sec A}=\frac{\sin ^{2} A}{1-\cos A}
s
e
c
A
1
+
s
e
c
A
=
1
−
c
o
s
A
s
i
n
2
A
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Prove the identities with all angles acute
\newline
i.
1
+
sec
A
sec
A
=
sin
2
A
1
−
cos
A
\frac{1+\sec A}{\sec A}=\frac{\sin ^{2} A}{1-\cos A}
s
e
c
A
1
+
s
e
c
A
=
1
−
c
o
s
A
s
i
n
2
A
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Graph the function.
\newline
g
(
x
)
=
−
3
2
(
x
−
2
)
2
g(x)=-\frac{3}{2}(x-2)^{2}
g
(
x
)
=
−
2
3
(
x
−
2
)
2
\newline
Show Calculator
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Find
B
D
B D
B
D
.
\newline
Write your answer in simplified, rationalized form. Do not round.
\newline
B
D
=
B D=
B
D
=
\newline
□
\square
□
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10
10
10
. Solve for
x
x
x
,
\newline
(
23
x
−
3
)
∘
(23 x-3)^{\circ}
(
23
x
−
3
)
∘
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Give one pair of supplementary angles and one pair of vertical angles shown in the figure below.
\newline
(a) Supplementary angles:
\newline
∏
\prod
∏
and
∠
\angle
∠
□
\square
□
\newline
(b) Vertical angles:
\newline
∠
\angle
∠
□
\square
□
and
∠
\angle
∠
□
\square
□
\newline
Check
\newline
Q.
2024
2024
2024
McGraw Hill LLC. All Rights Roser
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d
x
d
t
+
x
t
2
=
1
t
2
\frac{d x}{d t}+\frac{x}{t^{2}}=\frac{1}{t^{2}}
d
t
d
x
+
t
2
x
=
t
2
1
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Evaluate the integral
\newline
∫
cos
3
(
x
)
sin
(
x
)
d
x
=
\int \cos^{3}(x)\sin(x)dx =
∫
cos
3
(
x
)
sin
(
x
)
d
x
=
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What is the measure of angle
J
\mathrm{J}
J
in the triangle below? Drawing is not to scale.
\newline
(
1
1
1
point)
\newline
9
7
∘
97^{\circ}
9
7
∘
\newline
8
3
∘
83^{\circ}
8
3
∘
\newline
3
5
∘
35^{\circ}
3
5
∘
\newline
7
∘
7^{\circ}
7
∘
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P
Q
2
=
208
3
P Q^{2}=208 \sqrt{3}
P
Q
2
=
208
3
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7
7
7
−
21
-21
−
21
. Evaluate each expression below for
a
a
a
when
a
=
2
/
3
a=2 / 3
a
=
2/3
, if possible.
\newline
enter
\newline
b.
3
a
3 \mathrm{a}
3
a
\newline
c.
a
0
\frac{a}{0}
0
a
\newline
d.
0
a
\frac{0}{a}
a
0
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Evaluate the following expression.
\newline
6
6
6
⋅
\cdot
⋅
2
2
2
+
6
4
=
+6^{4}=
+
6
4
=
□
\square
□
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∠
a
\angle a
∠
a
and
∠
b
\angle b
∠
b
are complementary angles.
∠
a
\angle a
∠
a
measures
2
8
∘
28^{\circ}
2
8
∘
.
\newline
What is the measure of
∠
b
\angle b
∠
b
?
\newline
□
\square
□
\newline
Related content
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a
2
+
1
=
0
a^{2}+1=0
a
2
+
1
=
0
\newline
How many distinct real solutions does the given equation have?
\newline
□
\square
□
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Solve for the minimg angle
\newline
A.
8
0
∘
80^{\circ}
8
0
∘
\newline
B.
24
5
∘
245^{\circ}
24
5
∘
\newline
C.
6
5
∘
65^{\circ}
6
5
∘
\newline
D.
10
0
∘
100^{\circ}
10
0
∘
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lowing functions.
\newline
3
3
3
.
g
(
x
)
=
x
3
1
−
x
4
g(x)=\frac{x^{3}}{\sqrt{1-x^{4}}}
g
(
x
)
=
1
−
x
4
x
3
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1
2
3
...
4
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