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Math Problems
Algebra 2
Find trigonometric functions using a calculator
Find
d
d
v
(
4
v
5
−
cos
v
)
\frac{d}{d v}\left(4 v^{5}-\cos v\right)
d
v
d
(
4
v
5
−
cos
v
)
\newline
Answer:
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Find
d
d
z
(
3
z
5
+
cos
z
)
\frac{d}{d z}\left(3 z^{5}+\cos z\right)
d
z
d
(
3
z
5
+
cos
z
)
\newline
Answer:
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Find
d
d
z
(
3
z
5
−
2
sin
z
)
\frac{d}{d z}\left(3 z^{5}-2 \sin z\right)
d
z
d
(
3
z
5
−
2
sin
z
)
\newline
Answer:
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Find
d
d
v
(
3
v
3
−
3
sin
v
)
\frac{d}{d v}\left(3 v^{3}-3 \sin v\right)
d
v
d
(
3
v
3
−
3
sin
v
)
\newline
Answer:
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Find
d
d
y
(
3
y
2
−
sin
y
)
\frac{d}{d y}\left(3 y^{2}-\sin y\right)
d
y
d
(
3
y
2
−
sin
y
)
\newline
Answer:
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Find
d
d
z
(
3
z
3
+
4
sin
z
)
\frac{d}{d z}\left(3 z^{3}+4 \sin z\right)
d
z
d
(
3
z
3
+
4
sin
z
)
\newline
Answer:
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Find
d
d
p
(
3
p
2
+
4
cos
p
)
\frac{d}{d p}\left(3 p^{2}+4 \cos p\right)
d
p
d
(
3
p
2
+
4
cos
p
)
\newline
Answer:
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Find
d
d
z
(
2
z
3
+
sin
z
)
\frac{d}{d z}\left(2 z^{3}+\sin z\right)
d
z
d
(
2
z
3
+
sin
z
)
\newline
Answer:
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Find
d
d
z
(
3
z
5
−
4
sin
z
)
\frac{d}{d z}\left(3 z^{5}-4 \sin z\right)
d
z
d
(
3
z
5
−
4
sin
z
)
\newline
Answer:
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5
−
2
x
=
7
−
5
x
5 - 2\sqrt{x} = 7 - 5\sqrt{x}
5
−
2
x
=
7
−
5
x
.Find `x`
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Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth.
\newline
sin
5
1
∘
=
\sin 51^\circ=
sin
5
1
∘
=
\newline
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The angle of elevation to a nearby tree from a point on the ground is measured to be
3
2
∘
32^\circ
3
2
∘
. How tall is the tree if the point on the ground is
71
71
71
feet from the bottom of the tree? Round your answer to the nearest tenth of a foot if necessary.
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The derivative of the function
f
f
f
is defined by
f
′
(
x
)
=
(
x
2
+
4
x
)
cos
(
2
x
)
f^{\prime}(x)=\left(x^{2}+4 x\right) \cos (2 x)
f
′
(
x
)
=
(
x
2
+
4
x
)
cos
(
2
x
)
. If
f
(
3
)
=
9
f(3)=9
f
(
3
)
=
9
, then use a calculator to find the value of
f
(
−
2
)
f(-2)
f
(
−
2
)
to the nearest thousandth.
\newline
Answer:
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The following are all angle measures (in radians, rounded to the nearest hundredth) whose sine is
0
0
0
.
43
43
43
.
\newline
Which is the principal value of
sin
−
1
(
0.43
)
\sin ^{-1}(0.43)
sin
−
1
(
0.43
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
5
-5
−
5
.
84
84
84
\newline
(B)
0
0
0
.
44
44
44
\newline
(C)
6
6
6
.
73
73
73
\newline
(D)
13.01
\mathbf{1 3 . 0 1}
13.01
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A boat is travelling at a speed of
20
k
m
h
20 \frac{\mathrm{km}}{\mathrm{h}}
20
h
km
in a direction that is a
21
0
∘
210^{\circ}
21
0
∘
rotation from east.
\newline
At a certain point it encounters a current at a speed of
12
k
m
h
12 \frac{\mathrm{km}}{\mathrm{h}}
12
h
km
in a direction that is a
4
0
∘
40^{\circ}
4
0
∘
rotation from east.
\newline
What is the boat's speed after it meets the current?
\newline
Round your answer to the nearest tenth. You can round intermediate values to the nearest hundredth.
\newline
k
m
h
\frac{\mathrm{km}}{\mathrm{h}}
h
km
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Two donkeys are tied to the same pole.
\newline
One donkey pulls the pole at a strength of
5
N
5 \mathrm{~N}
5
N
in a direction that is a
5
0
∘
50^{\circ}
5
0
∘
rotation from the east.
\newline
The other donkey pulls the pole at a strength of
4
N
4 \mathrm{~N}
4
N
in a direction that is a
17
0
∘
170^{\circ}
17
0
∘
rotation from the east.
\newline
What is the combined strength of the donkeys' pulls?
\newline
Round your answer to the nearest tenth. You can round intermediate values to the nearest hundredth.
\newline
N
\mathrm{N}
N
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A cup of hot coffee has been left to cool in a room with an ambient temperature of
2
1
∘
C
21^{\circ} \mathrm{C}
2
1
∘
C
.
\newline
The relationship between the elapsed time,
m
m
m
, in minutes, since the coffee was left to cool, and the temperature of the coffee,
T
T
T
, measured in
∘
C
{ }^{\circ} \mathrm{C}
∘
C
, is modeled by the following function.
\newline
T
(
m
)
=
21
+
74
⋅
1
0
−
0.03
m
T(m)=21+74 \cdot 10^{-0.03 m}
T
(
m
)
=
21
+
74
⋅
1
0
−
0.03
m
\newline
What will the temperature of the coffee be after
10
10
10
minutes?
\newline
Round your answer, if necessary, to the nearest hundredth.
\newline
∘
C
{ }^{\circ} C
∘
C
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Solve for
x
x
x
. Enter the solutions from least to greatest.
\newline
Round to two decimal places.
\newline
(
x
+
15
)
2
−
10
=
0
(x+15)^{2}-10=0
(
x
+
15
)
2
−
10
=
0
\newline
lesser
x
=
x=
x
=
\newline
greater
x
=
x=
x
=
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Solve for
x
x
x
. Enter the solutions from least to greatest.
\newline
Round to two decimal places.
\newline
(
x
+
3
)
2
−
3
=
0
(x+3)^{2}-3=0
(
x
+
3
)
2
−
3
=
0
\newline
lesser
x
=
x=
x
=
\newline
greater
x
=
x=
x
=
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Solve for
x
x
x
. Enter the solutions from least to greatest.
\newline
Round to two decimal places.
\newline
(
x
+
8
)
2
−
2
=
0
(x+8)^{2}-2=0
(
x
+
8
)
2
−
2
=
0
\newline
lesser
x
=
x=
x
=
\newline
greater
x
=
x=
x
=
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Solve for
x
x
x
. Enter the solutions from least to greatest.
\newline
Round to two decimal places.
\newline
(
x
+
8
)
2
−
7
=
0
(x+8)^{2}-7=0
(
x
+
8
)
2
−
7
=
0
\newline
lesser
x
=
x=
x
=
\newline
greater
x
=
x=
x
=
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Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth.
\newline
cos
3
5
∘
=
\cos 35^\circ =
cos
3
5
∘
=
__
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