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Math Problems
Calculus
Find derivatives of using multiple formulae
Evaluate the integral
∫
x
+
4
5
x
+
5
d
x
\int \frac{x+4}{5 x+5} d x
∫
5
x
+
5
x
+
4
d
x
.
\newline
Choose
1
1
1
answer:
\newline
(A)
1
5
x
+
1
5
ln
∣
x
+
1
∣
+
C
\frac{1}{5} x+\frac{1}{5} \ln |x+1|+C
5
1
x
+
5
1
ln
∣
x
+
1∣
+
C
\newline
(B)
1
5
x
+
2
5
ln
∣
x
+
1
∣
+
C
\frac{1}{5} x+\frac{2}{5} \ln |x+1|+C
5
1
x
+
5
2
ln
∣
x
+
1∣
+
C
\newline
(C)
1
5
x
+
3
5
ln
∣
x
+
1
∣
+
C
\frac{1}{5} x+\frac{3}{5} \ln |x+1|+C
5
1
x
+
5
3
ln
∣
x
+
1∣
+
C
\newline
(D)
1
5
x
+
4
5
ln
∣
x
+
1
∣
+
C
\frac{1}{5} x+\frac{4}{5} \ln |x+1|+C
5
1
x
+
5
4
ln
∣
x
+
1∣
+
C
Get tutor help
∫
3
x
3
−
5
x
2
+
10
x
−
3
3
x
+
1
d
x
=
\int \frac{3 x^{3}-5 x^{2}+10 x-3}{3 x+1} d x=
∫
3
x
+
1
3
x
3
−
5
x
2
+
10
x
−
3
d
x
=
\newline
Choose
1
1
1
answer:
\newline
(A)
x
3
3
+
x
2
+
2
x
−
7
ln
∣
3
x
+
1
∣
+
C
\frac{x^{3}}{3}+x^{2}+2 x-7 \ln |3 x+1|+C
3
x
3
+
x
2
+
2
x
−
7
ln
∣3
x
+
1∣
+
C
\newline
(B)
x
3
3
−
x
2
+
2
x
−
7
ln
∣
3
x
+
1
∣
3
+
C
\frac{x^{3}}{3}-x^{2}+2 x-\frac{7 \ln |3 x+1|}{3}+C
3
x
3
−
x
2
+
2
x
−
3
7
l
n
∣3
x
+
1∣
+
C
\newline
(C)
x
3
3
+
x
2
2
+
4
x
−
7
ln
∣
3
x
+
1
∣
3
+
C
\frac{x^{3}}{3}+\frac{x^{2}}{2}+4 x-\frac{7 \ln |3 x+1|}{3}+C
3
x
3
+
2
x
2
+
4
x
−
3
7
l
n
∣3
x
+
1∣
+
C
\newline
(D)
x
3
3
−
x
2
+
4
x
−
7
ln
∣
3
x
+
1
∣
3
+
C
\frac{x^{3}}{3}-x^{2}+4 x-\frac{7 \ln |3 x+1|}{3}+C
3
x
3
−
x
2
+
4
x
−
3
7
l
n
∣3
x
+
1∣
+
C
Get tutor help
Find
∫
1
2
x
2
−
4
x
+
20
d
x
\int \frac{1}{2 x^{2}-4 x+20} d x
∫
2
x
2
−
4
x
+
20
1
d
x
.
\newline
Choose
1
1
1
answer:
\newline
(A)
1
3
arctan
(
x
−
1
3
)
+
C
\frac{1}{3} \arctan \left(\frac{x-1}{3}\right)+C
3
1
arctan
(
3
x
−
1
)
+
C
\newline
(B)
1
6
arcsin
(
x
−
1
3
)
+
C
\frac{1}{6} \arcsin \left(\frac{x-1}{3}\right)+C
6
1
arcsin
(
3
x
−
1
)
+
C
\newline
(C)
1
6
arctan
(
x
−
1
3
)
+
C
\frac{1}{6} \arctan \left(\frac{x-1}{3}\right)+C
6
1
arctan
(
3
x
−
1
)
+
C
\newline
(D)
1
3
arcsin
(
x
−
1
3
)
+
C
\frac{1}{3} \arcsin \left(\frac{x-1}{3}\right)+C
3
1
arcsin
(
3
x
−
1
)
+
C
Get tutor help
Find
∫
1
4
x
2
+
48
x
+
148
d
x
\int \frac{1}{4 x^{2}+48 x+148} d x
∫
4
x
2
+
48
x
+
148
1
d
x
.
\newline
Choose
1
1
1
answer:
\newline
(A)
1
4
arcsin
(
x
+
6
)
+
C
\frac{1}{4} \arcsin (x+6)+C
4
1
arcsin
(
x
+
6
)
+
C
\newline
(B)
1
4
arcsin
(
x
+
6
4
)
+
C
\frac{1}{4} \arcsin \left(\frac{x+6}{4}\right)+C
4
1
arcsin
(
4
x
+
6
)
+
C
\newline
(C)
1
4
arctan
(
x
+
6
)
+
C
\frac{1}{4} \arctan (x+6)+C
4
1
arctan
(
x
+
6
)
+
C
\newline
(D)
1
4
arctan
(
x
+
6
4
)
+
C
\frac{1}{4} \arctan \left(\frac{x+6}{4}\right)+C
4
1
arctan
(
4
x
+
6
)
+
C
Get tutor help
Find
∫
1
5
x
2
−
20
x
+
100
d
x
\int \frac{1}{5 x^{2}-20 x+100} d x
∫
5
x
2
−
20
x
+
100
1
d
x
.
\newline
Choose
1
1
1
answer:
\newline
(A)
arctan
(
x
−
2
4
)
+
C
\arctan \left(\frac{x-2}{4}\right)+C
arctan
(
4
x
−
2
)
+
C
\newline
(B)
arcsin
(
x
−
2
4
)
+
C
\arcsin \left(\frac{x-2}{4}\right)+C
arcsin
(
4
x
−
2
)
+
C
\newline
(c)
1
20
arcsin
(
x
−
2
4
)
+
C
\frac{1}{20} \arcsin \left(\frac{x-2}{4}\right)+C
20
1
arcsin
(
4
x
−
2
)
+
C
\newline
(D)
1
20
arctan
(
x
−
2
4
)
+
C
\frac{1}{20} \arctan \left(\frac{x-2}{4}\right)+C
20
1
arctan
(
4
x
−
2
)
+
C
Get tutor help
Find
∫
1
6
x
2
+
36
x
+
78
d
x
\int \frac{1}{6 x^{2}+36 x+78} d x
∫
6
x
2
+
36
x
+
78
1
d
x
.
\newline
Choose
1
1
1
answer:
\newline
(A)
1
2
arctan
(
x
+
3
2
)
+
C
\frac{1}{2} \arctan \left(\frac{x+3}{2}\right)+C
2
1
arctan
(
2
x
+
3
)
+
C
\newline
(B)
1
2
arcsin
(
x
+
3
2
)
+
C
\frac{1}{2} \arcsin \left(\frac{x+3}{2}\right)+C
2
1
arcsin
(
2
x
+
3
)
+
C
\newline
(C)
1
12
arcsin
(
x
+
3
2
)
+
C
\frac{1}{12} \arcsin \left(\frac{x+3}{2}\right)+C
12
1
arcsin
(
2
x
+
3
)
+
C
\newline
(D)
1
12
arctan
(
x
+
3
2
)
+
C
\frac{1}{12} \arctan \left(\frac{x+3}{2}\right)+C
12
1
arctan
(
2
x
+
3
)
+
C
Get tutor help
Which of the equations are true identities?
\newline
A.
(
5
b
−
2
)
2
+
4
=
25
b
2
−
20
b
(5 b-2)^{2}+4=25 b^{2}-20 b
(
5
b
−
2
)
2
+
4
=
25
b
2
−
20
b
\newline
B.
(
2
x
2
+
y
2
)
(
2
x
2
−
y
2
)
=
4
x
2
−
y
2
\left(2 x^{2}+y^{2}\right)\left(2 x^{2}-y^{2}\right)=4 x^{2}-y^{2}
(
2
x
2
+
y
2
)
(
2
x
2
−
y
2
)
=
4
x
2
−
y
2
\newline
Choose
1
1
1
answer:
\newline
(A) Only A
\newline
(B) Only B
\newline
(C) Both A and B
\newline
(D) Neither
A
\mathrm{A}
A
nor
B
\mathrm{B}
B
Get tutor help
Which of the equations are true identities?
\newline
A.
n
3
+
3
n
2
+
2
n
=
n
(
n
+
1
)
(
n
+
2
)
n^{3}+3 n^{2}+2 n=n(n+1)(n+2)
n
3
+
3
n
2
+
2
n
=
n
(
n
+
1
)
(
n
+
2
)
\newline
B.
(
a
+
3
)
2
−
9
=
a
2
+
6
a
(a+3)^{2}-9=a^{2}+6 a
(
a
+
3
)
2
−
9
=
a
2
+
6
a
\newline
Choose
1
1
1
answer:
\newline
(A) Only A
\newline
(B) Only B
\newline
(C) Both
A
\mathrm{A}
A
and
B
\mathrm{B}
B
\newline
(D) Neither A nor B
Get tutor help
Which of the equations are true identities?
\newline
A.
(
y
+
6
)
(
y
−
7
)
+
42
=
y
2
−
y
(y+6)(y-7)+42=y^{2}-y
(
y
+
6
)
(
y
−
7
)
+
42
=
y
2
−
y
\newline
B.
(
x
+
3
)
(
x
−
8
)
=
x
2
−
5
x
(x+3)(x-8)=x^{2}-5 x
(
x
+
3
)
(
x
−
8
)
=
x
2
−
5
x
\newline
Choose
1
1
1
answer:
\newline
(A) Only A
\newline
(B) Only B
\newline
(C) Both A and B
\newline
(D) Neither
A
\mathrm{A}
A
nor
B
\mathrm{B}
B
Get tutor help
Find
∫
1
x
2
−
8
x
+
65
d
x
\int \frac{1}{x^{2}-8 x+65} d x
∫
x
2
−
8
x
+
65
1
d
x
.
\newline
Choose
1
1
1
answer:
\newline
(A)
1
7
arctan
(
x
−
4
7
)
+
C
\frac{1}{7} \arctan \left(\frac{x-4}{7}\right)+C
7
1
arctan
(
7
x
−
4
)
+
C
\newline
(B)
1
7
arcsin
(
x
−
4
7
)
+
C
\frac{1}{7} \arcsin \left(\frac{x-4}{7}\right)+C
7
1
arcsin
(
7
x
−
4
)
+
C
\newline
(C)
arctan
(
x
−
4
7
)
+
C
\arctan \left(\frac{x-4}{7}\right)+C
arctan
(
7
x
−
4
)
+
C
\newline
(D)
arcsin
(
x
−
4
7
)
+
C
\arcsin \left(\frac{x-4}{7}\right)+C
arcsin
(
7
x
−
4
)
+
C
Get tutor help
Which of the equations are true identities?
\newline
A.
(
9
k
−
8
)
(
9
k
+
8
)
=
81
k
2
+
64
(9 k-8)(9 k+8)=81 k^{2}+64
(
9
k
−
8
)
(
9
k
+
8
)
=
81
k
2
+
64
\newline
B.
(
3
m
+
2
n
)
(
6
m
−
4
n
)
=
18
m
2
−
8
n
2
(3 m+2 n)(6 m-4 n)=18 m^{2}-8 n^{2}
(
3
m
+
2
n
)
(
6
m
−
4
n
)
=
18
m
2
−
8
n
2
\newline
Choose
1
1
1
answer:
\newline
(A) Only A
\newline
(B) Only B
\newline
(C) Both A and B
\newline
(D) Neither
A
\mathrm{A}
A
nor
B
\mathrm{B}
B
Get tutor help
y
=
arccos
(
−
x
3
)
y=\arccos \left(-\frac{x}{3}\right)
y
=
arccos
(
−
3
x
)
\newline
d
y
d
x
=
?
\frac{d y}{d x}=?
d
x
d
y
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
3
1
−
x
2
9
\frac{1}{3 \sqrt{1-\frac{x^{2}}{9}}}
3
1
−
9
x
2
1
\newline
(B)
−
1
3
1
−
x
2
9
\frac{-1}{3 \sqrt{1-\frac{x^{2}}{9}}}
3
1
−
9
x
2
−
1
\newline
(C)
1
3
(
1
−
x
2
9
)
\frac{1}{3\left(1-\frac{x^{2}}{9}\right)}
3
(
1
−
9
x
2
)
1
\newline
(D)
−
1
3
(
1
−
x
2
9
)
\frac{-1}{3\left(1-\frac{x^{2}}{9}\right)}
3
(
1
−
9
x
2
)
−
1
Get tutor help
d
d
x
[
arctan
(
−
5
x
)
]
=
?
\frac{d}{d x}[\arctan (-5 x)]=?
d
x
d
[
arctan
(
−
5
x
)]
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
5
1
+
25
x
2
\frac{-5}{\sqrt{1+25 x^{2}}}
1
+
25
x
2
−
5
\newline
(B)
−
5
1
−
25
x
2
\frac{-5}{\sqrt{1-25 x^{2}}}
1
−
25
x
2
−
5
\newline
(C)
−
5
1
+
25
x
2
\frac{-5}{1+25 x^{2}}
1
+
25
x
2
−
5
\newline
(D)
−
5
1
−
25
x
2
\frac{-5}{1-25 x^{2}}
1
−
25
x
2
−
5
Get tutor help
(
x
−
3
)
2
+
(
y
−
1
)
2
=
16
(x-3)^{2}+(y-1)^{2}=16
(
x
−
3
)
2
+
(
y
−
1
)
2
=
16
\newline
A circle in the
x
y
x y
x
y
-plane is represented by the given equation. If the circle is shifted
3
3
3
units to the left and
4
4
4
units up, which of the following equations represents the shifted circle?
\newline
Choose
1
1
1
answer:
\newline
(A)
x
2
+
(
y
−
5
)
2
=
16
x^{2}+(y-5)^{2}=16
x
2
+
(
y
−
5
)
2
=
16
\newline
(B)
x
2
+
(
y
+
3
)
2
=
16
x^{2}+(y+3)^{2}=16
x
2
+
(
y
+
3
)
2
=
16
\newline
(C)
(
x
−
6
)
2
+
(
y
−
5
)
2
=
16
(x-6)^{2}+(y-5)^{2}=16
(
x
−
6
)
2
+
(
y
−
5
)
2
=
16
\newline
(D)
(
x
−
6
)
2
+
(
y
+
3
)
2
=
16
(x-6)^{2}+(y+3)^{2}=16
(
x
−
6
)
2
+
(
y
+
3
)
2
=
16
Get tutor help
x
2
−
3
x
y
+
y
2
=
1
x^{2}-3 x y+y^{2}=1
x
2
−
3
x
y
+
y
2
=
1
\newline
Find the value of
d
y
d
x
\frac{d y}{d x}
d
x
d
y
at the point
(
1
,
0
)
(1,0)
(
1
,
0
)
.
\newline
Choose
1
1
1
answer:
\newline
(A)
−
2
3
-\frac{2}{3}
−
3
2
\newline
(B)
2
3
\frac{2}{3}
3
2
\newline
(C)
1
1
1
\newline
(D)
−
1
-1
−
1
Get tutor help
d
d
x
[
arccos
(
x
2
)
]
=
?
\frac{d}{d x}\left[\arccos \left(\frac{x}{2}\right)\right]=?
d
x
d
[
arccos
(
2
x
)
]
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
−
x
2
4
\frac{1}{\sqrt{1-\frac{x^{2}}{4}}}
1
−
4
x
2
1
\newline
(B)
−
1
1
−
x
2
4
\frac{-1}{\sqrt{1-\frac{x^{2}}{4}}}
1
−
4
x
2
−
1
\newline
(c)
1
2
1
−
x
2
4
\frac{1}{2 \sqrt{1-\frac{x^{2}}{4}}}
2
1
−
4
x
2
1
\newline
(D)
−
1
2
1
−
x
2
4
\frac{-1}{2 \sqrt{1-\frac{x^{2}}{4}}}
2
1
−
4
x
2
−
1
Get tutor help
x
3
+
2
y
2
−
x
y
=
2
x^{3}+2 y^{2}-x y=2
x
3
+
2
y
2
−
x
y
=
2
\newline
Find the value of
d
y
d
x
\frac{d y}{d x}
d
x
d
y
at the point
(
0
,
−
1
)
(0,-1)
(
0
,
−
1
)
.
\newline
Choose
1
1
1
answer:
\newline
(A)
4
4
4
\newline
(B)
−
1
4
-\frac{1}{4}
−
4
1
\newline
(C)
1
4
\frac{1}{4}
4
1
\newline
(D)
−
4
-4
−
4
Get tutor help
x
2
−
3
x
y
+
y
2
=
1
x^{2}-3 x y+y^{2}=1
x
2
−
3
x
y
+
y
2
=
1
\newline
Find the value of
d
y
d
x
\frac{d y}{d x}
d
x
d
y
at the point
(
1
,
0
)
(1,0)
(
1
,
0
)
.
\newline
Choose
1
1
1
answer:
\newline
(A)
2
3
\frac{2}{3}
3
2
\newline
(B)
1
1
1
\newline
(C)
−
2
3
-\frac{2}{3}
−
3
2
\newline
(D)
−
1
-1
−
1
Get tutor help
Find
d
d
x
(
ln
(
x
)
e
x
)
\frac{d}{d x}\left(\ln (x) e^{x}\right)
d
x
d
(
ln
(
x
)
e
x
)
.
\newline
Choose
1
1
1
answer:
\newline
(A)
1
x
+
e
x
\frac{1}{x}+e^{x}
x
1
+
e
x
\newline
(B)
e
x
x
+
ln
(
x
)
\frac{e^{x}}{x}+\ln (x)
x
e
x
+
ln
(
x
)
\newline
(C)
e
x
x
\frac{e^{x}}{x}
x
e
x
\newline
(D)
e
x
(
1
x
+
ln
(
x
)
)
e^{x}\left(\frac{1}{x}+\ln (x)\right)
e
x
(
x
1
+
ln
(
x
)
)
Get tutor help
Find
d
d
x
(
ln
(
x
)
e
x
)
\frac{d}{d x}\left(\ln (x) e^{x}\right)
d
x
d
(
ln
(
x
)
e
x
)
.
\newline
Choose
1
1
1
answer:
\newline
(A)
e
x
x
\frac{e^{x}}{x}
x
e
x
\newline
(B)
e
x
x
+
ln
(
x
)
\frac{e^{x}}{x}+\ln (x)
x
e
x
+
ln
(
x
)
\newline
(C)
1
x
+
e
x
\frac{1}{x}+e^{x}
x
1
+
e
x
\newline
(D)
e
x
(
1
x
+
ln
(
x
)
)
e^{x}\left(\frac{1}{x}+\ln (x)\right)
e
x
(
x
1
+
ln
(
x
)
)
Get tutor help
Let
f
(
x
)
=
1
x
e
x
f(x)=\frac{1}{x} e^{x}
f
(
x
)
=
x
1
e
x
.
\newline
Find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
.
\newline
Choose
1
1
1
answer:
\newline
(A)
−
1
x
2
(
1
x
+
e
x
)
-\frac{1}{x^{2}}\left(\frac{1}{x}+e^{x}\right)
−
x
2
1
(
x
1
+
e
x
)
\newline
(B)
e
x
(
1
x
−
1
x
2
)
e^{x}\left(\frac{1}{x}-\frac{1}{x^{2}}\right)
e
x
(
x
1
−
x
2
1
)
\newline
(C)
−
1
x
2
e
x
-\frac{1}{x^{2}} e^{x}
−
x
2
1
e
x
\newline
(D)
1
x
e
x
\frac{1}{x} e^{x}
x
1
e
x
Get tutor help
Let
f
(
x
)
=
1
x
e
x
f(x)=\frac{1}{x} e^{x}
f
(
x
)
=
x
1
e
x
.
\newline
Find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
.
\newline
Choose
1
1
1
answer:
\newline
(A)
−
1
x
2
e
x
-\frac{1}{x^{2}} e^{x}
−
x
2
1
e
x
\newline
(B)
−
1
x
2
(
1
x
+
e
x
)
-\frac{1}{x^{2}}\left(\frac{1}{x}+e^{x}\right)
−
x
2
1
(
x
1
+
e
x
)
\newline
(C)
1
x
e
x
\frac{1}{x} e^{x}
x
1
e
x
\newline
(D)
e
x
(
1
x
−
1
x
2
)
e^{x}\left(\frac{1}{x}-\frac{1}{x^{2}}\right)
e
x
(
x
1
−
x
2
1
)
Get tutor help
Let
f
(
x
)
=
sin
(
x
)
x
−
2
f(x)=\sin (x) x^{-2}
f
(
x
)
=
sin
(
x
)
x
−
2
.
\newline
Find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
.
\newline
Choose
1
1
1
answer:
\newline
(A)
cos
(
x
)
x
2
−
2
sin
(
x
)
x
3
\frac{\cos (x)}{x^{2}}-\frac{2 \sin (x)}{x^{3}}
x
2
c
o
s
(
x
)
−
x
3
2
s
i
n
(
x
)
\newline
(B)
cos
(
x
)
x
2
−
2
sin
(
x
)
x
\frac{\cos (x)}{x^{2}}-\frac{2 \sin (x)}{x}
x
2
c
o
s
(
x
)
−
x
2
s
i
n
(
x
)
\newline
(C)
sin
(
x
)
x
2
−
2
cos
(
x
)
x
\frac{\sin (x)}{x^{2}}-\frac{2 \cos (x)}{x}
x
2
s
i
n
(
x
)
−
x
2
c
o
s
(
x
)
\newline
(D)
sin
(
x
)
x
2
−
2
cos
(
x
)
x
3
\frac{\sin (x)}{x^{2}}-\frac{2 \cos (x)}{x^{3}}
x
2
s
i
n
(
x
)
−
x
3
2
c
o
s
(
x
)
Get tutor help
Write a question that could give an answer of
\newline
(
a
3
b
−
a
)
/
(
c
3
)
(a^{3}b^{-a})/(c^{3})
(
a
3
b
−
a
)
/
(
c
3
)
.
Get tutor help
Diketahui
2
2015
+
2
2014
=
a
b
c
2^{2015}+2^{2014}=a b^{c}
2
2015
+
2
2014
=
a
b
c
maka nilai dari
a
+
b
+
c
=
…
a+b+c=\ldots
a
+
b
+
c
=
…
\newline
A.
2017
2017
2017
\newline
B.
2018
2018
2018
\newline
C.
2019
2019
2019
\newline
D.
2020
2020
2020
\newline
E.
2021
2021
2021
Get tutor help
If
a
=
3
a=3
a
=
3
,
b
=
7
b=7
b
=
7
and
c
=
−
5
c=-5
c
=
−
5
, verify the following property and identify the name of property.
\newline
a
×
(
b
+
c
)
=
a
×
b
+
a
×
c
a \times (b+c) = a \times b + a \times c
a
×
(
b
+
c
)
=
a
×
b
+
a
×
c
Get tutor help
Solve for
h
h
h
:
h
+
5
h
2
−
6
h
\frac{h + 5}{h^2 - 6h}
h
2
−
6
h
h
+
5
−
-
−
3
h
−
6
\frac{3}{h-6}
h
−
6
3
Get tutor help
If
x
=
t
2
−
1
x=t^{2}-1
x
=
t
2
−
1
and
y
=
y =
y
=
l
n
t
lnt
l
n
t
, what is
d
2
y
d
x
2
\frac{d^{2}y}{dx^{2}}
d
x
2
d
2
y
in terms of
t
t
t
?
\newline
a
)
−
1
2
t
4
a) \frac{-1}{2t^{4}}
a
)
2
t
4
−
1
\newline
b
)
1
2
t
4
b) \frac{1}{2t^{4}}
b
)
2
t
4
1
\newline
c
)
−
1
z
3
c) \frac{-1}{z^{3}}
c
)
z
3
−
1
\newline
d
)
−
1
−
2
e
2
d) \frac{-1}{-2e^{2}}
d
)
−
2
e
2
−
1
\newline
e
)
1
2
t
2
e) \frac{1}{2t^{2}}
e
)
2
t
2
1
Get tutor help
Find all real solutions to the equation:
\newline
x
5
−
5
x
4
+
10
x
3
−
10
x
2
+
5
x
−
1
=
0
x^{5}-5x^{4}+10x^{3}-10x^{2}+5x-1=0
x
5
−
5
x
4
+
10
x
3
−
10
x
2
+
5
x
−
1
=
0
Get tutor help
Simplify.
\newline
(
17
×
2
4
×
5
3
+
1
0
3
÷
5
+
2
3
×
5
+
2
2
×
11
)
×
5
5
×
4
2
×
2
+
2
7
×
5
2
+
64
3
+
2
5
×
5
4
(
5
3
×
2
2
×
4
)
−
{
(
2
4
×
3
÷
2
)
÷
2
}
×
(
2
4
×
5
+
3
)
×
11
\frac{\left(17 \times 2^{4} \times 5^{3}+10^{3} \div 5+2^{3} \times 5+2^{2} \times 11\right) \times 5^{5} \times 4^{2} \times 2+2^{7} \times 5^{2}+\sqrt[3]{64}+2^{5} \times 5^{4}}{\left(5^{3} \times 2^{2} \times \sqrt{4}\right)-\left\{\left(2^{4} \times 3 \div 2\right) \div 2\right\} \times\left(2^{4} \times 5+3\right)} \times 11
(
5
3
×
2
2
×
4
)
−
{
(
2
4
×
3
÷
2
)
÷
2
}
×
(
2
4
×
5
+
3
)
(
17
×
2
4
×
5
3
+
1
0
3
÷
5
+
2
3
×
5
+
2
2
×
11
)
×
5
5
×
4
2
×
2
+
2
7
×
5
2
+
3
64
+
2
5
×
5
4
×
11
Get tutor help
Factorize the following polynomial expression:
\newline
2
x
6
−
8
x
5
+
12
x
4
−
16
x
3
+
24
x
2
−
32
x
2x^{6}-8x^{5}+12x^{4}-16x^{3}+24x^{2}-32x
2
x
6
−
8
x
5
+
12
x
4
−
16
x
3
+
24
x
2
−
32
x
Get tutor help
6
p
4
s
t
5
9
p
3
s
2
\frac{6 p^{4} s t^{5}}{9 p^{3} s^{2}}
9
p
3
s
2
6
p
4
s
t
5
Get tutor help
(
a
1
2
+
b
1
2
)
3
⋅
(
a
1
2
−
b
1
2
)
3
(a^{\frac{1}{2}}+b^{\frac{1}{2}})^3 \cdot (a^{\frac{1}{2}} - b^{\frac{1}{2}})^3
(
a
2
1
+
b
2
1
)
3
⋅
(
a
2
1
−
b
2
1
)
3
Get tutor help
Simplify.
\newline
(
−
y
2
z
4
)
2
(
3
x
2
y
3
z
)
\left(-y^{2} z^{4}\right)^{2}\left(3 x^{2} y^{3} z\right)
(
−
y
2
z
4
)
2
(
3
x
2
y
3
z
)
Get tutor help
5
c
2
d
(
9
c
2
d
2
−
4
c
3
d
−
2
)
5 c^{2} d\left(9 c^{2} d^{2}-4 c^{3} d-2\right)
5
c
2
d
(
9
c
2
d
2
−
4
c
3
d
−
2
)
Get tutor help
The area of an equilateral triangle with side
6
3
c
m
6 \sqrt{3} \mathrm{~cm}
6
3
cm
is
\newline
(a)
27
c
m
2
27 \mathrm{~cm}^{2}
27
cm
2
\newline
(b)
27
3
c
m
2
27 \sqrt{3} \mathrm{~cm}^{2}
27
3
cm
2
\newline
(c)
18
3
c
m
2
18 \sqrt{3} \mathrm{~cm}^{2}
18
3
cm
2
\newline
(d)
54
3
c
m
2
54 \sqrt{3} \mathrm{~cm}^{2}
54
3
cm
2
Get tutor help
Find
k
′
(
x
)
k^{\prime}(x)
k
′
(
x
)
if
k
(
x
)
=
e
(
−
x
1
/
2
+
1
5
x
−
3
/
5
)
k(x)=e^{\left(-x^{1 / 2}+\frac{1}{5} x^{-3 / 5}\right)}
k
(
x
)
=
e
(
−
x
1/2
+
5
1
x
−
3/5
)
Get tutor help
Given the function
f
(
x
)
=
−
x
3
−
4
5
f(x)=-x^{3}-\frac{4}{5}
f
(
x
)
=
−
x
3
−
5
4
, then what is
f
(
−
2
x
)
f(-2 x)
f
(
−
2
x
)
as a simplified polynomial?
\newline
Answer:
Get tutor help
The equation is
\newline
z
2
−
4
z
+
4
+
2
i
=
0
z^{2}-4 z+4+2 i=0
z
2
−
4
z
+
4
+
2
i
=
0
\newline
I know that i am supposed to use
\newline
(
a
+
b
i
)
2
=
a
2
+
2
a
b
i
+
b
i
2
(a+b i)^{2}=a^{2}+2 a b i+b i^{2}
(
a
+
bi
)
2
=
a
2
+
2
abi
+
b
i
2
\newline
to solve the equation but i am stuck on how to expand the equation.
\newline
Can you help out with which term to expand?
Get tutor help
The function
f
f
f
is given by
f
(
x
)
=
x
2
+
1
f(x)=x^{2}+1
f
(
x
)
=
x
2
+
1
, and the function
g
g
g
is given by
g
(
x
)
=
(
x
−
3
)
x
g(x)=\frac{(x-3)}{x}
g
(
x
)
=
x
(
x
−
3
)
. Which of the following is an expression for
f
(
g
(
x
)
)
f(g(x))
f
(
g
(
x
))
?
\newline
(A)
x
3
−
3
x
2
+
x
−
3
x
\frac{x^{3}-3 x^{2}+x-3}{x}
x
x
3
−
3
x
2
+
x
−
3
\newline
(B)
x
2
−
2
x
2
+
1
\frac{x^{2}-2}{x^{2}+1}
x
2
+
1
x
2
−
2
\newline
(C)
x
2
−
6
x
+
9
x
2
+
1
\frac{x^{2}-6 x+9}{x^{2}}+1
x
2
x
2
−
6
x
+
9
+
1
\newline
(D)
x
2
−
8
x
2
\frac{x^{2}-8}{x^{2}}
x
2
x
2
−
8
Get tutor help
Simplify the expression.
\newline
10
m
6
n
3
5
m
2
n
7
\frac{10 m^{6} n^{3}}{5 m^{2} n^{7}}
5
m
2
n
7
10
m
6
n
3
Get tutor help
x
4
y
+
x
2
y
4
x^{4} y+x^{2} y^{4}
x
4
y
+
x
2
y
4
=
Get tutor help
Find the value of
⋄
\diamond
⋄
:
\newline
(
y
5
y
−
3
)
⋄
=
y
24
\left(\frac{y^{5}}{y^{-3}}\right)^{\diamond}=y^{24}
(
y
−
3
y
5
)
⋄
=
y
24
Get tutor help
Find the value of
⋄
\diamond
⋄
:
\newline
(
n
2
n
−
6
n
⋄
)
8
=
n
24
\left(n^{2} n^{-6} n^{\diamond}\right)^{8}=n^{24}
(
n
2
n
−
6
n
⋄
)
8
=
n
24
Get tutor help
Simplify:
(
2
a
4
b
)
2
\left(2 a^{4} b\right)^{2}
(
2
a
4
b
)
2
Get tutor help
2
x
2
(
x
3
−
x
)
−
3
x
(
x
4
+
2
x
)
−
2
(
x
4
−
3
x
2
)
2 x^{2}\left(x^{3}-x\right)-3 x\left(x^{4}+2 x\right)-2\left(x^{4}-3 x^{2}\right)
2
x
2
(
x
3
−
x
)
−
3
x
(
x
4
+
2
x
)
−
2
(
x
4
−
3
x
2
)
Get tutor help
Which expression is equivalent to
(
3
2
p
+
1
)
(
1
2
p
+
3
)
\left(\frac{3}{2} p+1\right)\left(\frac{1}{2} p+3\right)
(
2
3
p
+
1
)
(
2
1
p
+
3
)
?
\newline
A
2
p
2
+
3
2 p^{2}+3
2
p
2
+
3
\newline
B
4
p
2
+
3
4 p^{2}+3
4
p
2
+
3
\newline
C
3
4
p
2
+
5
p
+
3
\frac{3}{4} p^{2}+5 p+3
4
3
p
2
+
5
p
+
3
\newline
D
3
4
p
2
+
10
p
+
3
\frac{3}{4} p^{2}+10 p+3
4
3
p
2
+
10
p
+
3
Get tutor help
2
2
2
.) A triangle has angle measures of
8
2
∘
,
5
3
∘
82^{\circ}, 53^{\circ}
8
2
∘
,
5
3
∘
, and
4
5
∘
45^{\circ}
4
5
∘
. Classify the triangle by its angles.
\newline
(A) acute
\newline
(B) equiangular
\newline
(C) obtuse
\newline
(D) right
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Find the values of
x
x
x
.
\newline
4
x
2
−
3
x
−
1
4
x
+
1
+
x
3
+
1
x
2
−
x
+
1
=
2
\frac{4 x^{2}-3 x-1}{4 x+1}+\frac{x^{3}+1}{x^{2}-x+1}=2
4
x
+
1
4
x
2
−
3
x
−
1
+
x
2
−
x
+
1
x
3
+
1
=
2
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x
=
−
5
±
(
5
)
2
−
4
(
1
)
(
6
)
2
(
1
)
x=\frac{-5 \pm \sqrt{(5)^{2}-4(1)(6)}}{2(1)}
x
=
2
(
1
)
−
5
±
(
5
)
2
−
4
(
1
)
(
6
)
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