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Math Problems
Algebra 2
Write equations of sine and cosine functions using properties
The graph of a sinusoidal function has a maximum point at
(
0
,
7
)
(0,7)
(
0
,
7
)
and then intersects its midline at
(
3
,
3
)
(3,3)
(
3
,
3
)
. Write the formula of the function, where
x
x
x
is entered in radians.
\newline
f
(
x
)
=
f(x)=
f
(
x
)
=
\newline
□
\square
□
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The graph of a sinusoidal function has a maximum point at
\newline
(
0
,
5
)
(0,5)
(
0
,
5
)
and then has a minimum point at
\newline
(
2
π
,
−
5
)
(2\pi,-5)
(
2
π
,
−
5
)
.
\newline
Write the formula of the function, where
\newline
x
x
x
is entered in radians.
\newline
f
(
x
)
=
f(x)=
f
(
x
)
=
\newline
□
\square
□
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The graph of a sinusoidal function intersects its midline at
(
0
,
5
)
(0,5)
(
0
,
5
)
and then has a maximum point at
(
π
,
6
)
(\pi,6)
(
π
,
6
)
.
\newline
Write the formula of the function, where
x
x
x
is entered in radians.
\newline
f
(
x
)
=
f(x)=
f
(
x
)
=
□
\square
□
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For the rotation
84
4
∘
844^{\circ}
84
4
∘
, find the coterminal angle from
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
, the quadrant, and the reference angle.
\newline
The coterminal angle is
□
∘
\square^{\circ}
□
∘
, which lies in Quadrant
□
\square
□
, with a reference angle of
□
∘
\square^{\circ}
□
∘
.
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The graph of a sinusoidal function intersects its midline at
(
0
,
−
2
)
(0,-2)
(
0
,
−
2
)
and then has a minimum point at
(
3
p
i
2
,
−
7
)
(\frac{3pi}{2},-7)
(
2
3
p
i
,
−
7
)
. Write the formula of the function, where
x
x
x
is entered in radians.
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The graph of a sinusoidal function has a minimum point at
(
0
,
3
)
(0,3)
(
0
,
3
)
and then intersects its midline at
(
5
π
,
5
)
(5 \pi, 5)
(
5
π
,
5
)
.
\newline
Write the formula of the function, where
x
x
x
is entered in radians.
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The graph of a sinusoidal function has a maximum point at
(
0
,
10
)
(0,10)
(
0
,
10
)
and then intersects its midline at
(
π
4
,
4
)
\left(\frac{\pi}{4}, 4\right)
(
4
π
,
4
)
.
\newline
Write the formula of the function, where
x
x
x
is entered in radians.
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The graph of a sinusoidal function has a maximum point at
(
0
,
5
)
(0,5)
(
0
,
5
)
and then has a minimum point at
(
2
π
,
−
5
)
(2 \pi,-5)
(
2
π
,
−
5
)
.
\newline
Write the formula of the function, where
x
x
x
is entered in radians.
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The graph of a sinusoidal function has a minimum point at
(
0
,
−
10
)
(0,-10)
(
0
,
−
10
)
and then has a maximum point at
(
2
,
−
4
)
(2,-4)
(
2
,
−
4
)
. Write the formula of the function, where
x
x
x
is entered in radians.
\newline
f
(
x
)
=
□
f(x)=\square
f
(
x
)
=
□
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Find the midpoint
m
m
m
of
z
1
=
(
5
−
6
i
)
z_{1}=(5-6 i)
z
1
=
(
5
−
6
i
)
and
z
2
=
(
16
+
2
i
)
z_{2}=(16+2 i)
z
2
=
(
16
+
2
i
)
.
\newline
Express your answer in rectangular form.
\newline
m
=
m=
m
=
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A complex number
z
1
z_{1}
z
1
has a magnitude
∣
z
1
∣
=
5
\left|z_{1}\right|=5
∣
z
1
∣
=
5
and an angle
θ
1
=
15
0
∘
\theta_{1}=150^{\circ}
θ
1
=
15
0
∘
.
\newline
Express
z
1
z_{1}
z
1
in rectangular form, as
z
1
=
a
+
b
i
z_{1}=a+b i
z
1
=
a
+
bi
.
\newline
Express
a
+
b
i
a+b i
a
+
bi
in exact terms.
\newline
z
1
=
□
z_{1}=\square
z
1
=
□
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Apolline is mowing lawns for a summer job. For every mowing job, she charges an initial fee plus a constant fee for each hour of work. Her fee for a
5
5
5
-hour job, for instance, is
$
42
\$ 42
$42
. Her fee for a
3
3
3
hour job is
$
28
\$ 28
$28
.
\newline
Let
y
y
y
represent Apolline's fee (in dollars) for a single job that took
x
x
x
hours for her to complete.
\newline
Which of the following information about the graph of the relationship is given?
\newline
Choose
1
1
1
answer:
\newline
(A) Slope and
x
x
x
-intercept
\newline
(B) Slope and
y
y
y
-intercept
\newline
(C) Slope and a point that is not an intercept
\newline
(D)
x
x
x
-intercept and
y
y
y
intercept
\newline
(E)
y
y
y
-intercept and a point that is not an intercept
\newline
(F) Two points that are not intercepts
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V
=
π
r
2
h
V=\pi r^{2} h
V
=
π
r
2
h
\newline
The formula gives the volume
V
V
V
of a right circular cylinder with radius
r
r
r
and height
h
h
h
. What is the volume, in cubic inches, of a right circular cylinder with a radius of
3
3
3
inches and a height of
2
2
2
inches?
\newline
Choose
1
1
1
answer:
\newline
(A)
5
π
5 \pi
5
π
\newline
(B)
6
π
6 \pi
6
π
\newline
(C)
12
π
12 \pi
12
π
\newline
(D)
18
π
18 \pi
18
π
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V
=
π
r
2
h
V=\pi r^{2} h
V
=
π
r
2
h
\newline
The formula gives the volume
V
V
V
of a right circular cylinder with radius
r
r
r
and height
h
h
h
. What is the volume, in cubic centimeters, of a right circular cylinder with a radius of
2
2
2
centimeters and a height of
20
20
20
centimeters?
\newline
Choose
1
1
1
answer:
\newline
(A)
40
π
40 \pi
40
π
\newline
(B)
80
π
80 \pi
80
π
\newline
(C)
400
π
400 \pi
400
π
\newline
(D)
800
π
800 \pi
800
π
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Franklin Middle School is having a canned food drive. In Mr. Lao's class, Mr. Lao brought
10
10
10
cans of food, and each student brought
2
2
2
cans. In Ms. Roger's class, Ms. Rogers did not bring any cans, but each student brought
3
3
3
cans of food. Write two equations in slope-intercept form to represent the number of cans of food for each class
y
y
y
in terms of the number of students
x
x
x
.
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Franklin Middle School is having a canned food drive. In Mr. Lao's class, Mr. Lao brought
10
10
10
cans of food, and each student brought
2
2
2
cans. In Ms. Roger's class, Ms. Rogers did not bring any cans, but each student brought
3
3
3
cans of food. Write two equations in slope-intercept form to represent the number of cans of food for each class
y
y
y
in terms of the number of students
x
x
x
.
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Find an equation for a sinusoidal function that has period
2
π
2\pi
2
π
, amplitude
1
1
1
, and contains the point
(
π
,
−
1
)
\left(\pi, -1\right)
(
π
,
−
1
)
.
\newline
Write your answer in the form
f
(
x
)
=
A
cos
(
B
x
+
C
)
+
D
f(x)=A\cos(Bx+C)+D
f
(
x
)
=
A
cos
(
B
x
+
C
)
+
D
, where
A
A
A
,
B
B
B
,
C
C
C
, and
D
D
D
are real numbers.
\newline
f
(
x
)
=
f(x)=
f
(
x
)
=
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