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Math Problems
Algebra 1
Write and solve inverse variation equations
If
p
p
p
is inversely proportional to the square of
q
q
q
, and
p
p
p
is
16
16
16
when
q
q
q
is
10
10
10
, determine
p
p
p
when
q
q
q
is equal to
2
2
2
.
\newline
Answer:
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If
p
p
p
and
q
q
q
vary inversely and
p
p
p
is
24
24
24
when
q
q
q
is
3
3
3
, determine
q
q
q
when
p
p
p
is equal to
6
6
6
.
\newline
Answer:
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If
p
p
p
is inversely proportional to the square of
q
q
q
, and
p
p
p
is
27
27
27
when
q
q
q
is
11
11
11
, determine
p
p
p
when
q
q
q
is equal to
3
3
3
.
\newline
Answer:
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If
p
p
p
and
q
q
q
vary inversely and
p
p
p
is
6
6
6
when
q
q
q
is
2
2
2
, determine
q
q
q
when
p
p
p
is equal to
3
3
3
.
\newline
Answer:
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If
p
p
p
is inversely proportional to the square of
q
q
q
, and
p
p
p
is
4
4
4
when
q
q
q
is
5
5
5
, determine
p
p
p
when
q
q
q
is equal to
2
2
2
.
\newline
Answer:
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If
p
p
p
and
q
q
q
vary inversely and
p
p
p
is
23
23
23
when
q
q
q
is
27
27
27
, determine
q
q
q
when
p
p
p
is equal to
3
3
3
.
\newline
Answer:
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If
p
p
p
is inversely proportional to the square of
q
q
q
, and
p
p
p
is
25
25
25
when
q
q
q
is
12
12
12
, determine
p
p
p
when
q
q
q
is equal to
5
5
5
.
\newline
Answer:
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If
p
p
p
is inversely proportional to the square of
q
q
q
, and
p
p
p
is
20
20
20
when
q
q
q
is
10
10
10
, determine
p
p
p
when
q
q
q
is equal to
2
2
2
.
\newline
Answer:
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If
p
p
p
and
q
q
q
vary inversely and
p
p
p
is
9
9
9
when
q
q
q
is
5
5
5
, determine
q
q
q
when
p
p
p
is equal to
3
3
3
.
\newline
Answer:
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If
p
p
p
is inversely proportional to the square of
q
q
q
, and
p
p
p
is
20
20
20
when
q
q
q
is
5
5
5
, determine
p
p
p
when
q
q
q
is equal to
2
2
2
.
\newline
Answer:
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If
p
p
p
and
q
q
q
vary inversely and
p
p
p
is
29
29
29
when
q
q
q
is
25
25
25
, determine
q
q
q
when
p
p
p
is equal to
145
145
145
.
\newline
Answer:
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If
p
p
p
and
q
q
q
vary inversely and
p
p
p
is
7
7
7
when
q
q
q
is
22
22
22
, determine
q
q
q
when
p
p
p
is equal to
11
11
11
.
\newline
Answer:
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If
p
p
p
and
q
q
q
vary inversely and
p
p
p
is
25
25
25
when
q
q
q
is
29
29
29
, determine
q
q
q
when
p
p
p
is equal to
5
5
5
.
\newline
Answer:
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Given that
f
(
x
)
=
5
x
,
g
(
x
)
=
x
−
2
f(x)=5 x, \quad g(x)=x-2
f
(
x
)
=
5
x
,
g
(
x
)
=
x
−
2
and
h
(
x
)
=
−
2
f
(
x
+
3
)
−
3
g
(
x
)
h(x)=-2 f(x+3)-3 g(x)
h
(
x
)
=
−
2
f
(
x
+
3
)
−
3
g
(
x
)
, then what is the value of
h
(
6
)
h(6)
h
(
6
)
?
\newline
Answer:
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Given that
f
(
x
)
=
x
+
4
,
g
(
x
)
=
4
x
f(x)=x+4, \quad g(x)=4 x
f
(
x
)
=
x
+
4
,
g
(
x
)
=
4
x
and
h
(
x
)
=
2
f
(
x
−
1
)
+
3
g
(
x
)
h(x)=2 f(x-1)+3 g(x)
h
(
x
)
=
2
f
(
x
−
1
)
+
3
g
(
x
)
, then what is the value of
h
(
1
)
h(1)
h
(
1
)
?
\newline
Answer:
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Given that
f
(
x
)
=
5
x
,
g
(
x
)
=
x
+
1
f(x)=5 x, \quad g(x)=x+1
f
(
x
)
=
5
x
,
g
(
x
)
=
x
+
1
and
h
(
x
)
=
f
(
x
+
1
)
−
2
g
(
x
−
2
)
h(x)=f(x+1)-2 g(x-2)
h
(
x
)
=
f
(
x
+
1
)
−
2
g
(
x
−
2
)
, then what is the value of
h
(
1
)
h(1)
h
(
1
)
?
\newline
Answer:
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Given that
f
(
x
)
=
5
x
,
g
(
x
)
=
x
−
1
f(x)=5 x, \quad g(x)=x-1
f
(
x
)
=
5
x
,
g
(
x
)
=
x
−
1
and
h
(
x
)
=
−
3
f
(
x
+
2
)
+
2
g
(
x
)
h(x)=-3 f(x+2)+2 g(x)
h
(
x
)
=
−
3
f
(
x
+
2
)
+
2
g
(
x
)
, then what is the value of
h
(
3
)
h(3)
h
(
3
)
?
\newline
Answer:
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Given that
f
(
x
)
=
4
x
,
g
(
x
)
=
x
+
5
f(x)=4 x, \quad g(x)=x+5
f
(
x
)
=
4
x
,
g
(
x
)
=
x
+
5
and
h
(
x
)
=
−
2
f
(
x
−
2
)
−
2
g
(
x
+
3
)
h(x)=-2 f(x-2)-2 g(x+3)
h
(
x
)
=
−
2
f
(
x
−
2
)
−
2
g
(
x
+
3
)
, then what is the value of
h
(
2
)
h(2)
h
(
2
)
?
\newline
Answer:
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If
3
r
=
18
3r=18
3
r
=
18
, what is the value of
6
r
+
3
6r+3
6
r
+
3
?
\newline
A)
6
6
6
\newline
B)
27
27
27
\newline
C)
36
36
36
\newline
D)
39
39
39
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Given the substitutions
ln
2
=
a
,
ln
3
=
b
\ln 2=a, \ln 3=b
ln
2
=
a
,
ln
3
=
b
, and
ln
5
=
c
\ln 5=c
ln
5
=
c
, find the value of
ln
(
200
)
\ln (200)
ln
(
200
)
in terms of
a
,
b
a, b
a
,
b
, and
c
c
c
.
\newline
Answer:
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Given the substitutions
ln
2
=
a
,
ln
3
=
b
\ln 2=a, \ln 3=b
ln
2
=
a
,
ln
3
=
b
, and
ln
5
=
c
\ln 5=c
ln
5
=
c
, find the value of
ln
(
10
)
\ln (10)
ln
(
10
)
in terms of
a
,
b
a, b
a
,
b
, and
c
c
c
.
\newline
Answer:
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Given the substitutions
ln
2
=
a
,
ln
3
=
b
\ln 2=a, \ln 3=b
ln
2
=
a
,
ln
3
=
b
, and
ln
5
=
c
\ln 5=c
ln
5
=
c
, find the value of
ln
(
16
27
)
\ln \left(\frac{16}{27}\right)
ln
(
27
16
)
in terms of
a
,
b
a, b
a
,
b
, and
c
c
c
.
\newline
Answer:
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Given the substitutions
ln
2
=
a
,
ln
3
=
b
\ln 2=a, \ln 3=b
ln
2
=
a
,
ln
3
=
b
, and
ln
5
=
c
\ln 5=c
ln
5
=
c
, find the value of
ln
(
50
)
\ln (50)
ln
(
50
)
in terms of
a
,
b
a, b
a
,
b
, and
c
c
c
.
\newline
Answer:
Get tutor help
Given the substitutions
ln
2
=
a
,
ln
3
=
b
\ln 2=a, \ln 3=b
ln
2
=
a
,
ln
3
=
b
, and
ln
5
=
c
\ln 5=c
ln
5
=
c
, find the value of
ln
(
25
27
)
\ln \left(\frac{25}{27}\right)
ln
(
27
25
)
in terms of
a
,
b
a, b
a
,
b
, and
c
c
c
.
\newline
Answer:
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Let
h
(
x
)
=
x
−
5
h(x)=x^{-5}
h
(
x
)
=
x
−
5
.
\newline
h
′
(
2
)
=
h^{\prime}(2)=
h
′
(
2
)
=
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h
(
x
)
=
1
−
cos
(
x
)
2
sin
2
(
x
)
h(x)=\frac{1-\cos (x)}{2 \sin ^{2}(x)}
h
(
x
)
=
2
sin
2
(
x
)
1
−
cos
(
x
)
\newline
We want to find
lim
x
→
0
h
(
x
)
\lim _{x \rightarrow 0} h(x)
lim
x
→
0
h
(
x
)
.
\newline
What happens when we use direct substitution?
\newline
Choose
1
1
1
answer:
\newline
(A) The limit exists, and we found it!
\newline
(B) The limit doesn't exist (probably an asymptote).
\newline
(C) The result is indeterminate.
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h
(
x
)
=
7
−
4
x
3
+
9
x
−
2
h(x)=\frac{7-4 x}{3+\sqrt{9 x-2}}
h
(
x
)
=
3
+
9
x
−
2
7
−
4
x
\newline
We want to find
lim
x
→
3
h
(
x
)
\lim _{x \rightarrow 3} h(x)
lim
x
→
3
h
(
x
)
.
\newline
What happens when we use direct substitution?
\newline
Choose
1
1
1
answer:
\newline
(A) The limit exists, and we found it!
\newline
(B) The limit doesn't exist (probably an asymptote).
\newline
(C) The result is indeterminate.
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h
(
x
)
=
x
2
−
6
x
+
10
x
−
1
h(x)=\frac{x^{2}-6 x+10}{x-1}
h
(
x
)
=
x
−
1
x
2
−
6
x
+
10
\newline
We want to find
lim
x
→
2
h
(
x
)
\lim _{x \rightarrow 2} h(x)
lim
x
→
2
h
(
x
)
.
\newline
What happens when we use direct substitution?
\newline
Choose
1
1
1
answer:
\newline
(A) The limit exists, and we found it!
\newline
(B) The limit doesn't exist (probably an asymptote).
\newline
(C) The result is indeterminate.
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y
=
29
8
x
−
2
3
y=\frac{29}{8} x-\frac{2}{3}
y
=
8
29
x
−
3
2
\newline
The given equation is graphed in the
x
y
x y
x
y
-plane. What is the slope of the line?
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Assume that
y
y
y
varies inversely with
x
x
x
. If
y
=
1
y = 1
y
=
1
when
x
=
4
x = 4
x
=
4
, find
y
y
y
when
x
=
2
x = 2
x
=
2
.
\newline
Write and solve an inverse variation equation to find the answer.
\newline
y
=
y =
y
=
_____
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