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Math Problems
Algebra 1
Write inverse variation equations
Given: Triangle
W
T
R
W T R
W
TR
with
W
T
=
13
W T=13
W
T
=
13
and
W
R
=
21
W R=21
W
R
=
21
. Identify possible lengths for
T
R
T R
TR
.
\newline
32
32
32
\newline
50
50
50
\newline
11
11
11
\newline
45
45
45
\newline
25
25
25
\newline
34
34
34
\newline
8
8
8
\newline
6
6
6
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b.
cos
A
=
\cos A=
cos
A
=
\newline
c.
tan
A
=
\tan A=
tan
A
=
\newline
3
3
3
. In the figure below, if
sin
x
=
5
13
\sin x=\frac{5}{13}
sin
x
=
13
5
, what are
cos
x
\cos x
cos
x
and tan
x
x
x
?
cos
x
\cos x
cos
x
and tan
x
x
x
?
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9
9
9
: Solve the equation using inverse operations.
\newline
(
x
+
4
)
2
−
36
=
0
(x+4)^{2}-36=0
(
x
+
4
)
2
−
36
=
0
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If
sin
A
=
p
\sin \mathrm{A}=p
sin
A
=
p
and
cos
A
=
q
\cos \mathrm{A}=q
cos
A
=
q
:
\newline
5
5
5
.
3
3
3
.
1
1
1
Write
tan
A
\tan \mathrm{A}
tan
A
in terms of
p
p
p
and
q
q
q
\newline
5
5
5
.
3
3
3
.
2
2
2
Simplify
p
4
−
q
4
p^{4}-q^{4}
p
4
−
q
4
to a single trigonometric ratio
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A curve
C
C
C
has parametric equations
x
=
3
t
+
3
t
x=3t+\frac{3}{t}
x
=
3
t
+
t
3
,
y
=
3
t
−
3
t
y=3t-\frac{3}{t}
y
=
3
t
−
t
3
. Find the cartesian equation of
C
C
C
.
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Paradigm
\newline
Specialising in O Level Mathematic
\newline
In the diagram,
A
B
C
A B C
A
BC
is a triangle where
M
M
M
is the midpoint of
A
C
A C
A
C
.
\newline
The point
P
P
P
lies on the line
B
M
B M
BM
such that
B
P
=
1
3
B
M
B P=\frac{1}{3} B M
BP
=
3
1
BM
.
\newline
The point
Q
Q
Q
lies on the line
B
C
B C
BC
such that
B
Q
:
Q
C
=
1
:
4
B Q: Q C=1: 4
BQ
:
QC
=
1
:
4
.
\newline
Given that
A
B
undefined
=
b
\overrightarrow{A B}=b
A
B
=
b
and
M
M
M
0
0
0
.
\newline
(a) Express, as simply as possible, in terms of
M
M
M
1
1
1
and or
M
M
M
2
2
2
,
\newline
(i)
M
M
M
3
3
3
,
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Write an equation that describes the following relationship:
y
y
y
varies inversely as the fourth power of
x
x
x
and when
x
=
1
,
y
=
3
x=1, y=3
x
=
1
,
y
=
3
.
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In an inverse variation,
y
=
3
y = 3
y
=
3
when
x
=
12
x = 12
x
=
12
. Write an inverse variation equation that shows the relationship between
x
x
x
and
y
y
y
.
\newline
Write the equation using a decimal or an integer.
\newline
_
_
\_\_
__
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In an inverse variation,
y
=
4
y = 4
y
=
4
when
x
=
8
x = 8
x
=
8
. Write an inverse variation equation that shows the relationship between
x
x
x
and
y
y
y
.
\newline
Write the equation using a decimal or an integer.
\newline
_
_
\_\_
__
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In an inverse variation,
y
=
1
y = 1
y
=
1
when
x
=
6
x = 6
x
=
6
. Write an inverse variation equation that shows the relationship between
x
x
x
and
y
y
y
.
\newline
Write the equation using a decimal or an integer.
\newline
_
_
\_\_
__
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In an inverse variation,
y
=
2
y = 2
y
=
2
when
x
=
9
x = 9
x
=
9
. Write an inverse variation equation that shows the relationship between
x
x
x
and
y
y
y
.
\newline
Write the equation using a decimal or an integer.
\newline
_
_
\_\_
__
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In an inverse variation,
y
=
1
y = 1
y
=
1
when
x
=
9
x = 9
x
=
9
. Write an inverse variation equation that shows the relationship between
x
x
x
and
y
y
y
.
\newline
Write the equation using a decimal or an integer.
\newline
_
_
\_\_
__
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In an inverse variation,
y
=
3
y = 3
y
=
3
when
x
=
4
x = 4
x
=
4
. Write an inverse variation equation that shows the relationship between
x
x
x
and
y
y
y
.
\newline
Write the equation using a decimal or an integer.
\newline
_
_
\_\_
__
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In an inverse variation,
y
=
2
y = 2
y
=
2
when
x
=
8
x = 8
x
=
8
. Write an inverse variation equation that shows the relationship between
x
x
x
and
y
y
y
.
\newline
Write the equation using a decimal or an integer.
\newline
_
_
\_\_
__
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In an inverse variation,
y
=
1
y = 1
y
=
1
when
x
=
16
x = 16
x
=
16
. Write an inverse variation equation that shows the relationship between
x
x
x
and
y
y
y
.
\newline
Write the equation using a decimal or an integer.
\newline
_
_
\_\_
__
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In an inverse variation,
y
=
1
y = 1
y
=
1
when
x
=
8
x = 8
x
=
8
. Write an inverse variation equation that shows the relationship between
x
x
x
and
y
y
y
.
\newline
Write the equation using a decimal or an integer.
\newline
_
_
\_\_
__
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In an inverse variation,
y
=
4
y = 4
y
=
4
when
x
=
4
x = 4
x
=
4
. Write an inverse variation equation that shows the relationship between
x
x
x
and
y
y
y
.
\newline
Write the equation using a decimal or an integer.
\newline
_
_
\_\_
__
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In an inverse variation,
y
=
2
y = 2
y
=
2
when
x
=
4
x = 4
x
=
4
. Write an inverse variation equation that shows the relationship between
x
x
x
and
y
y
y
.
\newline
Write the equation using a decimal or an integer.
\newline
_
_
\_\_
__
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In an inverse variation,
y
=
3
y = 3
y
=
3
when
x
=
3
x = 3
x
=
3
. Write an inverse variation equation that shows the relationship between
x
x
x
and
y
y
y
.
\newline
Write the equation using a decimal or an integer.
\newline
_
_
\_\_
__
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The following table shows a proportional relationship between
x
x
x
and
y
y
y
.
y
y
y
:
2
2
2
5
5
5
8
8
8
x
x
x
:
9
9
9
22.5
22.5
22.5
36
36
36
Write an equation to describe the relationship between
x
x
x
and
y
y
y
.
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Find the constant of proportionality
k
k
k
if
z
=
3600
z = 3600
z
=
3600
when
y
=
3
y = 3
y
=
3
and
x
=
5
x =5
x
=
5
.
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Write a slope-intercept equation for a line with the given characteristics.
\newline
m
=
−
8.5
m=-8.5
m
=
−
8.5
,
y
y
y
-intercept
(
0
,
4
5
)
(0,\frac{4}{5})
(
0
,
5
4
)
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Logarithmic and exponential inverses
\newline
Find the inverse of
\newline
f
(
x
)
=
b
x
f(x)=b^{x}
f
(
x
)
=
b
x
and then prove that they are inverses.
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Write an expression to represent:
4
4
4
less than the product of
1
1
1
and
x
x
x
.
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Write an expression to represent:
4
4
4
times the difference of
x
x
x
and
2
2
2
.
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Write an expression to represent:
10
10
10
minus the product of
4
4
4
and
x
x
x
.
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Write an expression to represent:
\newline
2
2
2
times the difference of
x
x
x
and
3
3
3
.
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Write an expression to represent:
4
4
4
less than the quotient of
x
x
x
and
5
5
5
.
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Write an expression to represent:
\newline
3
3
3
more than the product of
2
2
2
and
x
x
x
.
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Write an expression to represent:
\newline
6
6
6
more than the quotient of
4
4
4
and
x
x
x
.
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Write an expression to represent:
3
3
3
minus the quotient of
x
x
x
and
4
4
4
.
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Write an expression to represent:
\newline
1
1
1
less than the quotient of
4
4
4
and
x
x
x
.
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Write an expression to represent:
3
3
3
minus the product of
2
2
2
and
x
x
x
.
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