Resources
Testimonials
Plans
Sign in
Sign up
Resources
Testimonials
Plans
Home
Math Problems
Precalculus
Write equations of sine and cosine functions using properties
Find the average value of the functions on the given interval.
\newline
Average value of
f
(
x
)
=
x
f(x)=x
f
(
x
)
=
x
on
[
5
,
13
]
[5,13]
[
5
,
13
]
Get tutor help
If the sum of three consecutive even integers is
12
12
12
, what is the first of the three even integers? (Hint: If
x
x
x
and
x
+
2
x+2
x
+
2
represent the first two consecutive even integers, then how would the third consecutive even integer be represented?)
\newline
The first of the three even integers is
□
\square
□
Get tutor help
The histogram below shows information about the honey produced by some beehives in one year.
\newline
600
600
600
beehives each produced between
16
k
g
16 \mathrm{~kg}
16
kg
and
18
k
g
18 \mathrm{~kg}
18
kg
of honey.
\newline
Use this information to work out the value of
x
x
x
on the frequency density axis. If your answer is a decimal, give it to
1
1
1
d.p.
Get tutor help
Let
f
f
f
be a differentiable function such that
f
(
2
)
=
1
f(2)=1
f
(
2
)
=
1
and
f
′
(
x
)
=
sin
(
x
2
−
5
)
f^{\prime}(x)=\sin \left(x^{2}-5\right)
f
′
(
x
)
=
sin
(
x
2
−
5
)
.
\newline
What is the value of
f
(
6
)
f(6)
f
(
6
)
? Use a graphing calculator and round your answer to three decimal places.
Get tutor help
Question
\newline
The points
N
,
O
,
P
\mathrm{N}, \mathrm{O}, \mathrm{P}
N
,
O
,
P
and
Q
\mathrm{Q}
Q
all lie on the same line segment, in that order, such that the ratio of
N
O
:
O
P
:
P
Q
N O: O P: P Q
NO
:
OP
:
PQ
is equal to
3
:
3
:
2
3: 3: 2
3
:
3
:
2
. If
N
Q
=
8
N Q=8
NQ
=
8
, find
P
Q
P Q
PQ
.
\newline
Answer Attempt
1
1
1
out of
2
2
2
\newline
P
Q
=
P Q=
PQ
=
Get tutor help
A study of urban density shows that the population density
C
\mathrm{C}
C
(in persons
/
k
m
2
/ \mathrm{km}^{2}
/
km
2
) is related to the distance a (in
k
m
\mathrm{km}
km
) from the city centre by
log
e
C
=
log
e
z
−
v
a
+
t
a
4
\log _{e} \mathrm{C}=\log _{e} \mathrm{z}-\mathrm{va}+\mathrm{ta}^{4}
lo
g
e
C
=
lo
g
e
z
−
va
+
ta
4
, where
z
,
v
\mathrm{z}, \mathrm{v}
z
,
v
, and
t
\mathrm{t}
t
are positive constants. Solve for
C
\mathrm{C}
C
as a function of a.
Get tutor help
3
3
3
. A rhombus is graphed on the set of axes below.
\newline
Which transformation would carry the rhombus onto itsele?
\newline
180
180
180
degree rotation counterclockwise about the origin
\newline
reflection over the line
y
=
1
2
x
+
1
y=\frac{1}{2} x+1
y
=
2
1
x
+
1
\newline
reflection over the line
y
=
0
y=0
y
=
0
\newline
reflection over the line
x
=
0
x=0
x
=
0
Get tutor help
The formula for the perimeter of a rectangle is
P
=
2
l
+
2
w
P=2 l+2 w
P
=
2
l
+
2
w
. Solve the formula for
l
l
l
in terms of
P
P
P
and
w
w
w
.
\newline
Answer:
l
=
l=
l
=
Get tutor help
A formula for converting degrees Celsius
(
C
)
(C)
(
C
)
to degrees Fahrenheit
(
F
)
(F)
(
F
)
is given by the formula
F
=
9
5
C
+
32
F=\frac{9}{5} C+32
F
=
5
9
C
+
32
. Solve the formula for
C
C
C
in terms of
F
F
F
.
\newline
Answer:
C
=
C=
C
=
Get tutor help
A formula to find the period,
T
T
T
, of a cyclic phenomena based on the frequency,
f
f
f
, is
T
=
1
f
T=\frac{1}{f}
T
=
f
1
. Solve the formula for
f
f
f
in terms of
T
T
T
.
\newline
Answer:
f
=
f=
f
=
Get tutor help
The formula for the perimeter of a rectangle is
P
=
2
l
+
2
w
P=2 l+2 w
P
=
2
l
+
2
w
. Solve the formula for
w
w
w
in terms of
P
P
P
and
l
l
l
.
\newline
Answer:
w
=
w=
w
=
Get tutor help
