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A circle has a circumference of 11,304 units.
What is the diameter of the circle? Use 3.14 for
pi and enter your answer as a decimal.
units

A circle has a circumference of $11$ , $304$ units. $\newline$ What is the diameter of the circle? Use $3$ . $14$ for $\pi$ and enter your answer as a decimal. $\newline$ $\square$ units

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Pythagorean Theorem and its converse

Full solution

Q. A circle has a circumference of

11

,

304

units.

\newline

What is the diameter of the circle? Use

3

.

14

for

\pi

and enter your answer as a decimal.

\newline

\square

units

Circle Circumference Formula: The formula for the circumference of a circle is $C = \pi d$ , where $C$ is the circumference and $d$ is the diameter.
Substitute Values: We know the circumference is $11,304$ units and we're using $3.14$ for $\pi$ . So, we have $11,304 = 3.14d$ .
Calculate Diameter: To find the diameter, we divide the circumference by $\pi$ : $d = \frac{11,304}{3.14}$ .
Final Diameter Calculation: Calculating the diameter: $d = \frac{11,304}{3.14} = 3600$ units.

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 \frac{1}{2} \mathrm{~m}

high, rectangular wall. It has an area of

28 \mathrm{~m}^{2}

\newline

What is the length of the mural?

\newline

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Question

A cup of hot coffee has been left to cool in a room with an ambient temperature of

21^{\circ} \mathrm{C}

\newline

The relationship between the elapsed time,

m

, in minutes, since the coffee was left to cool, and the temperature of the coffee,

T

{ }^{\circ} \mathrm{C}

, is modeled by the following function.

\newline

T(m)=21+74 \cdot 10^{-0.03 m}

\newline

What will the temperature of the coffee be after

10

\newline

Round your answer, if necessary, to the nearest hundredth.

\newline

{ }^{\circ} C

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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

, the number of branches on the tree, and

t

, the elapsed time, in years, since the tree was planted can be modeled by the following equation.

\newline

N=5 \cdot 10^{0.3 t}

\newline

According to Takumi's model, in how many years will the tree have

100

\newline

Give an exact answer expressed as a base

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\newline

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Question

g(x)=2^{x}

\newline

Can we use the mean value theorem to say the equation

g^{\prime}(x)=16

has a solution where

3<x<5

\newline

1

\newline

(A) No, since the function is not differentiable on that interval.

\newline

(B) No, since the average rate of change of

g

over the interval

3 \leq x \leq 5

1 \overline{6}

\newline

(C) Yes, both conditions for using the mean value theorem have been met.

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\frac{d}{d x}\left(\frac{3 x^{2}-1}{x-2}\right)=

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Question

\frac{d y}{d t}=2 t+3 \text { and } y(1)=6

\newline

t

y=0

\newline

Choose all answers that apply:

\newline

t=-1

\newline

t=-3

\newline

t=0

\newline

t=-4

\newline

t=1

\newline

t=-2

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\frac{d}{d x}\left(x^{\frac{3}{4}}\right)=

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y=x^{13}

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\frac{d y}{d x}=

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y=x^{10}

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\frac{d y}{d x}=

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