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Math Problems
Precalculus
Solve radical equations
Solve for
s
s
s
.
\newline
−
2
s
=
8
s
+
10
\sqrt{-2s} = \sqrt{8s + 10}
−
2
s
=
8
s
+
10
\newline
s
=
s =
s
=
_____
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Soal Latihan Himpunan
\newline
Soal
1
1
1
\newline
Di ketahui :
\newline
A
=
{
x
∣
1
<
x
<
5
A=\{x \mid 1<x<5
A
=
{
x
∣
1
<
x
<
5
, maka
x
x
x
ialah bilangan bulat
}
\}
}
.
\newline
B
=
{
x
∣
x
≤
5
B=\{x \mid x \leq 5
B
=
{
x
∣
x
≤
5
, maka
x
x
x
ialah bilangan prima
}
\}
}
.
\newline
Maka tentukanlah hasil dari
A
∪
B
A \cup B
A
∪
B
?
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y
=
1
cos
x
,
y
=
0
,
x
=
0
,
x
=
π
6
y=\frac{1}{\sqrt{\cos x}}, y=0, x=0, x=\frac{\pi}{6} \quad
y
=
c
o
s
x
1
,
y
=
0
,
x
=
0
,
x
=
6
π
Javob
:
π
2
ln
3
: \frac{\pi}{2} \ln 3
:
2
π
ln
3
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Differentiate
y
=
(
3
x
+
1
)
2
y=(3x+1)^{2}
y
=
(
3
x
+
1
)
2
.
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【例
7
7
7
】设直线
y
=
a
x
y=a x
y
=
a
x
与抛物线
y
=
x
2
y=x^{2}
y
=
x
2
所围成图形的面积为
S
1
S_{1}
S
1
, 它们与直线
x
=
1
x=1
x
=
1
所围成的图形面积为
S
2
S_{2}
S
2
, 并且
a
<
1
a<1
a
<
1
.
\newline
(
1
1
1
) 试确定
a
a
a
的值, 使
S
1
+
S
2
S_{1}+S_{2}
S
1
+
S
2
达到最小, 并求出最小值.
\newline
(
2
2
2
) 求该最小值所对应的平面图形绕
x
x
x
轴旋转一周所得旋转体的体积.
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例
7
7
7
】设直线
y
=
a
x
y=a x
y
=
a
x
与抛物线
y
=
x
2
y=x^{2}
y
=
x
2
所围成图形的面积为
S
1
S_{1}
S
1
, 它们与直线
x
=
1
x=1
x
=
1
所围成的图形面积为
S
2
S_{2}
S
2
, 并且
a
<
1
a<1
a
<
1
.
\newline
(
1
1
1
) 试确定
a
a
a
的值, 使
S
1
+
S
2
S_{1}+S_{2}
S
1
+
S
2
达到最小, 并求出最小值.
\newline
(
2
2
2
) 求该最小值所对应的平面图形绕
x
x
x
轴旋转一周所得旋转体的体积.
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Rotate and find the reference angle for
20
8
∘
208^{\circ}
20
8
∘
.
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Write
7
18
25
7 \frac{18}{25}
7
25
18
as a decimal.
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Progress saved Done
\newline
0
\sqrt{0}
0
\newline
Question
6
6
6
\newline
Write
21
14
\sqrt[14]{21}
14
21
as an expression with a rational exponent.
\newline
21
14
=
\sqrt[14]{21}=
14
21
=
\newline
To get
7
7
(
1
@
)
77^{\left(\frac{1}{@}\right)}
7
7
(
@
1
)
type
7
∧
(
1
/
/
9
)
7^{\wedge}(1//9)
7
∧
(
1//9
)
\newline
Question Help:
\newline
◻ Message instructor
\newline
Submit Question
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Solve for
t
t
t
.
t
2
−
11
t
+
10
=
0
t^2-11t+10=0
t
2
−
11
t
+
10
=
0
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Solve the equation for all values of
x
x
x
.
\newline
−
x
(
x
2
−
1
)
(
49
x
2
−
16
)
=
0
-x(x^{2}-1)(49x^{2}-16) = 0
−
x
(
x
2
−
1
)
(
49
x
2
−
16
)
=
0
\newline
Answer:
x
=
x =
x
=
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Jutia has
32
32
32
sheets of paper remaining in her
200
200
200
page notebook. What percentage of the paper has She used?
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z
=
x
2
+
y
2
−
4
+
ln
(
x
y
)
z=\sqrt{x^{2}+y^{2}-4}+\ln(xy)
z
=
x
2
+
y
2
−
4
+
ln
(
x
y
)
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11
11
11
.
P
=
12
+
11
+
12
+
11
P=12+11+12+11
P
=
12
+
11
+
12
+
11
11
11
11
. [ ? ]
\newline
12
12
12
.
P
=
46
P=46
P
=
46
\newline
12
12
12
. Arithmetic
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Solve for
x
\mathrm{x}
x
:
\newline
2
x
+
2
−
18
=
−
14
\sqrt{2 x+2}-18=-14
2
x
+
2
−
18
=
−
14
\newline
Answer:
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Solve for
x
\mathrm{x}
x
:
\newline
6
x
+
43
−
2
=
3
\sqrt{6 x+43}-2=3
6
x
+
43
−
2
=
3
\newline
Answer:
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Solve for
x
\mathrm{x}
x
:
\newline
3
x
+
37
+
16
=
24
\sqrt{3 x+37}+16=24
3
x
+
37
+
16
=
24
\newline
Answer:
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Solve for
x
\mathrm{x}
x
:
\newline
7
x
−
34
+
19
=
20
\sqrt{7 x-34}+19=20
7
x
−
34
+
19
=
20
\newline
Answer:
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Solve for
x
\mathrm{x}
x
:
\newline
4
x
+
68
−
9
=
−
1
\sqrt{4 x+68}-9=-1
4
x
+
68
−
9
=
−
1
\newline
Answer:
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Solve for
x
\mathrm{x}
x
:
\newline
6
x
+
19
−
15
=
−
10
\sqrt{6 x+19}-15=-10
6
x
+
19
−
15
=
−
10
\newline
Answer:
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Solve for
x
\mathrm{x}
x
:
\newline
8
x
+
12
−
16
=
−
10
\sqrt{8 x+12}-16=-10
8
x
+
12
−
16
=
−
10
\newline
Answer:
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Solve for
x
\mathrm{x}
x
:
\newline
3
x
+
19
+
16
=
18
\sqrt{3 x+19}+16=18
3
x
+
19
+
16
=
18
\newline
Answer:
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Solve for
x
\mathrm{x}
x
:
\newline
6
x
+
93
+
20
=
29
\sqrt{6 x+93}+20=29
6
x
+
93
+
20
=
29
\newline
Answer:
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Solve for
x
\mathrm{x}
x
:
\newline
3
x
+
45
−
5
=
1
\sqrt{3 x+45}-5=1
3
x
+
45
−
5
=
1
\newline
Answer:
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Solve for
x
\mathrm{x}
x
:
\newline
2
x
+
34
+
2
=
6
\sqrt{2 x+34}+2=6
2
x
+
34
+
2
=
6
\newline
Answer:
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Solve for
x
\mathrm{x}
x
:
\newline
5
x
+
91
+
12
=
21
\sqrt{5 x+91}+12=21
5
x
+
91
+
12
=
21
\newline
Answer:
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Solve for
x
\mathrm{x}
x
:
\newline
8
x
+
33
−
18
=
−
17
\sqrt{8 x+33}-18=-17
8
x
+
33
−
18
=
−
17
\newline
Answer:
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Solve for
x
\mathrm{x}
x
:
\newline
2
x
+
41
−
17
=
−
12
\sqrt{2 x+41}-17=-12
2
x
+
41
−
17
=
−
12
\newline
Answer:
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Solve for
x
\mathrm{x}
x
:
\newline
6
x
−
47
−
3
=
−
2
\sqrt{6 x-47}-3=-2
6
x
−
47
−
3
=
−
2
\newline
Answer:
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Solve for
x
\mathrm{x}
x
:
\newline
x
+
16
−
19
=
−
16
\sqrt{x+16}-19=-16
x
+
16
−
19
=
−
16
\newline
Answer:
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Solve for
x
\mathrm{x}
x
:
\newline
4
x
+
25
+
10
=
13
\sqrt{4 x+25}+10=13
4
x
+
25
+
10
=
13
\newline
Answer:
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Solve for
x
\mathrm{x}
x
:
\newline
7
x
+
57
+
18
=
24
\sqrt{7 x+57}+18=24
7
x
+
57
+
18
=
24
\newline
Answer:
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Solve for
x
\mathrm{x}
x
:
\newline
x
−
4
−
12
=
−
10
\sqrt{x-4}-12=-10
x
−
4
−
12
=
−
10
\newline
Answer:
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Solve for
x
\mathrm{x}
x
:
\newline
7
x
+
72
+
11
=
15
\sqrt{7 x+72}+11=15
7
x
+
72
+
11
=
15
\newline
Answer:
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Solve for
x
\mathrm{x}
x
:
\newline
5
x
+
11
+
14
=
20
\sqrt{5 x+11}+14=20
5
x
+
11
+
14
=
20
\newline
Answer:
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Algebra Review
\newline
Question
11
11
11
of
35
35
35
(
1
(1
(
1
point) | Question Attempt:
1
1
1
of
1
1
1
\newline
=
1
=1
=
1
\newline
=
2
=2
=
2
\newline
=
3
=3
=
3
\newline
=
4
=4
=
4
\newline
=
5
=5
=
5
\newline
Find the value of
\newline
p
+
6
p+6
p
+
6
when
\newline
p
=
14
p=14
p
=
14
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Determine the value of
y
y
y
, if
x
x
x
is
102
102
102
.
\newline
y
=
x
+
19
y=\sqrt{x+19}
y
=
x
+
19
\newline
Answer:
y
=
y=
y
=
Get tutor help
41
−
8
a
+
7
=
a
\sqrt{41-8a}+7=a
41
−
8
a
+
7
=
a
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y
=
ln
(
1
+
sin
x
1
−
sin
x
)
y=\ln \sqrt{\left(\frac{1+\sin x}{1-\sin x}\right)}
y
=
ln
(
1
−
s
i
n
x
1
+
s
i
n
x
)
Get tutor help
The cumulative cost of purchasing and maintaining Julia's computer is increasing at a rate of
r
(
t
)
r(t)
r
(
t
)
dollars per year (where
t
t
t
is the time in years). At
t
=
1
t=1
t
=
1
, Julia had spent a total of
$
420
\$ 420
$420
on her computer.
\newline
What does
420
+
∫
1
5
r
(
t
)
d
t
=
570
420+\int_{1}^{5} r(t) d t=570
420
+
∫
1
5
r
(
t
)
d
t
=
570
mean?
\newline
Choose
1
1
1
answer:
\newline
(A) Julia spent
$
570
\$ 570
$570
on her computer in the fifth year.
\newline
(B) By the end of the fifth year, Julia had spent a total of
$
570
\$ 570
$570
purchasing and maintaining her computer.
\newline
(C) Julia spent an additional
$
570
\$ 570
$570
on her computer between years
1
1
1
and
5
5
5
.
\newline
(D) Julia spent an average of
$
570
\$ 570
$570
per year purchasing and maintaining her computer.
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The cumulative cost of purchasing and maintaining Julia's computer is increasing at a rate of
r
(
t
)
r(t)
r
(
t
)
dollars per year (where
t
t
t
is the time in years). At
t
=
1
t=1
t
=
1
, Julia had spent a total of
$
420
\$ 420
$420
on her computer.
\newline
What does
420
+
∫
1
5
r
(
t
)
d
t
=
570
420+\int_{1}^{5} r(t) d t=570
420
+
∫
1
5
r
(
t
)
d
t
=
570
mean?
\newline
Choose
1
1
1
answer:
\newline
(A) Julia spent an additional
$
570
\$ 570
$570
on her computer between years
1
1
1
and
5
5
5
.
\newline
(B) Julia spent
$
570
\$ 570
$570
on her computer in the fifth year.
\newline
(C) Julia spent an average of
$
570
\$ 570
$570
per year purchasing and maintaining her computer.
\newline
(D) By the end of the fifth year, Julia had spent a total of
$
570
\$ 570
$570
purchasing and maintaining her computer.
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lim
x
→
2
6
x
+
13
=
\lim _{x \rightarrow 2} \sqrt{6 x+13}=
lim
x
→
2
6
x
+
13
=
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Solve the following equation for
z
z
z
.
\newline
53
+
5
z
7
=
2
\sqrt{\frac{53+5 z}{7}}=2
7
53
+
5
z
=
2
\newline
z
=
z=
z
=
Get tutor help
Solve the following equation for
x
x
x
.
\newline
2
x
+
1
=
x
+
2
2 x+1=\sqrt{x+2}
2
x
+
1
=
x
+
2
\newline
x
=
x=
x
=
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