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Let’s check out your problem:
A circle has a circumference of
7
7
7
,
850
850
850
units.
\newline
What is the radius of the circle? Use
3
3
3
.
14
14
14
for
π
\pi
π
and enter your answer as a decimal.
\newline
□
\square
□
units
View step-by-step help
Home
Math Problems
Algebra 2
Pythagorean Theorem and its converse
Full solution
Q.
A circle has a circumference of
7
7
7
,
850
850
850
units.
\newline
What is the radius of the circle? Use
3
3
3
.
14
14
14
for
π
\pi
π
and enter your answer as a decimal.
\newline
□
\square
□
units
Circle
Circumference Formula
:
The formula for the
circumference of a circle
is
C
=
2
×
π
×
r
C = 2 \times \pi \times r
C
=
2
×
π
×
r
, where
C
C
C
is the circumference and
r
r
r
is the radius.
Given Values and Formula:
Given
C
=
7
,
850
C = 7,850
C
=
7
,
850
units and
π
=
3.14
\pi = 3.14
π
=
3.14
, we can solve for
r
r
r
by rearranging the formula:
r
=
C
2
⋅
π
.
r = \frac{C}{2 \cdot \pi}.
r
=
2
⋅
π
C
.
Plug in Values:
Plug in the values:
r
=
7
,
850
2
×
3.14
.
r = \frac{7,850}{2 \times 3.14}.
r
=
2
×
3.14
7
,
850
.
Calculate Radius:
Calculate the radius:
r
=
7
,
850
6.28
r = \frac{7,850}{6.28}
r
=
6.28
7
,
850
.
Division Calculation:
Perform the division:
r
≈
1
,
250
r \approx 1,250
r
≈
1
,
250
.
More problems from Pythagorean Theorem and its converse
Question
Marco's class is painting a mural on the side of their school. The mural covers a
3
1
2
m
3 \frac{1}{2} \mathrm{~m}
3
2
1
m
high, rectangular wall. It has an area of
28
m
2
28 \mathrm{~m}^{2}
28
m
2
.
\newline
What is the length of the mural?
\newline
m
Get tutor help
Posted 10 months ago
Question
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
Get tutor help
Posted 10 months ago
Question
Takumi plants a tree in his backyard and studies how the number of branches grows over time.
\newline
He predicts that the relationship between
N
N
N
, the number of branches on the tree, and
t
t
t
, the elapsed time, in years, since the tree was planted can be modeled by the following equation.
\newline
N
=
5
⋅
1
0
0.3
t
N=5 \cdot 10^{0.3 t}
N
=
5
⋅
1
0
0.3
t
\newline
According to Takumi's model, in how many years will the tree have
100
100
100
branches?
\newline
Give an exact answer expressed as a base
−
10
-10
−
10
logarithm.
\newline
years
Get tutor help
Posted 10 months ago
Question
Let
g
(
x
)
=
2
x
g(x)=2^{x}
g
(
x
)
=
2
x
.
\newline
Can we use the mean value theorem to say the equation
g
′
(
x
)
=
16
g^{\prime}(x)=16
g
′
(
x
)
=
16
has a solution where
3
<
x
<
5
3<x<5
3
<
x
<
5
?
\newline
Choose
1
1
1
answer:
\newline
(A) No, since the function is not differentiable on that interval.
\newline
(B) No, since the average rate of change of
g
g
g
over the interval
3
≤
x
≤
5
3 \leq x \leq 5
3
≤
x
≤
5
isn't equal to
1
6
‾
1 \overline{6}
1
6
.
\newline
(C) Yes, both conditions for using the mean value theorem have been met.
Get tutor help
Posted 9 months ago
Question
d
d
x
(
3
x
2
−
1
x
−
2
)
=
\frac{d}{d x}\left(\frac{3 x^{2}-1}{x-2}\right)=
d
x
d
(
x
−
2
3
x
2
−
1
)
=
Get tutor help
Posted 9 months ago
Question
d
y
d
t
=
2
t
+
3
and
y
(
1
)
=
6
\frac{d y}{d t}=2 t+3 \text { and } y(1)=6
d
t
d
y
=
2
t
+
3
and
y
(
1
)
=
6
\newline
What is
t
t
t
when
y
=
0
y=0
y
=
0
?
\newline
Choose all answers that apply:
\newline
(A)
t
=
−
1
t=-1
t
=
−
1
\newline
(B)
t
=
−
3
t=-3
t
=
−
3
\newline
(C)
t
=
0
t=0
t
=
0
\newline
(D)
t
=
−
4
t=-4
t
=
−
4
\newline
(E)
t
=
1
t=1
t
=
1
\newline
(F)
t
=
−
2
t=-2
t
=
−
2
Get tutor help
Posted 9 months ago
Question
d
d
x
(
x
3
4
)
=
\frac{d}{d x}\left(x^{\frac{3}{4}}\right)=
d
x
d
(
x
4
3
)
=
Get tutor help
Posted 9 months ago
Question
y
=
x
13
y=x^{13}
y
=
x
13
\newline
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
Posted 9 months ago
Question
y
=
x
10
y=x^{10}
y
=
x
10
\newline
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
Posted 9 months ago
Question
d
d
x
[
x
6
]
=
\frac{d}{d x}\left[x^{6}\right]=
d
x
d
[
x
6
]
=
Get tutor help
Posted 9 months ago
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