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3 years ago

The circumference of a circle is 28π inches. What is the length of the radius of this circle?

Mathematics

2 answers:

nlexa [21]3 years ago

7 0

Answer:

Step-by-step explanation:

took the quiz

devlian [24]3 years ago

6 0

Answer:

The radius of the circle is 14 inches.

Step-by-step explanation:

How is the circumference of a circle related to its radius?

$\displaystyle \text{Circumference} = \pi\times \text{Diameter} = \pi\;(2\times \text{Radius})$ .

In brief,

$\text{Circumference} = 2\pi\times \text{Radius}$ .

For this question,

$\text{Circumference} = 28\pi$ , and
$\text{Radius}$ needs to be found.

Divide both sides of the equation by $2\pi$ :

$\displaystyle \frac{\text{Circumference}}{2\pi} = \text{Radius}$ .

$\displaystyle \text{Radius} = \frac{\text{Circumference}}{2\pi} = \frac{28\pi}{2\pi} = 14$ .

In other words, the radius of this circle is 14 inches.

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Step-by-step explanation:

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3 years ago

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vesna_86 [32]

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2 years ago

Express angle 37 in radian

Snezhnost [94]

Answer:

0.646 radians to the nearest thousandth.

Step-by-step explanation:

To convert degrees to radians we multiply by π/180

= 37 * π/180

= 0.20556π radians

= 0.646 radians to the nearest thousandth.

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2 years ago

The eastbound train travels 10 miles per hour faster than the westbound train. After 2 hours, they are 232 miles apart. At what

patriot [66]

Answer:

48,58

Step-by-step explanation:

Let The speed of the west bound train be x

Let the east bound train be x+10

The speeds can be calculated as follows

2(2x+10)= 232

4x + 40= 232

4x= 232-40

4x= 192

x= 192/4

= 48

Hence the speedof the west bound train is 48

The speed of the east bound train is 48+10

= 58

8 0

2 years ago

The radius of a cone is increasing at a constant rate of 7 meters per minute, and the volume is decreasing at a rate of 236 cubi

storchak [24]

Answer:

The rate of change of the height is 0.021 meters per minute

Step-by-step explanation:

From the formula

$V = \frac{1}{3}\pi r^{2}h$

Differentiate the equation with respect to time t, such that

$\frac{d}{dt} (V) = \frac{d}{dt} (\frac{1}{3}\pi r^{2}h)$

$\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (r^{2}h)$

To differentiate the product,

Let r² = u, so that

$\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (uh)$

Then, using product rule

$\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h\frac{du}{dt}]$

Since $u = r^{2}$

Then, $\frac{du}{dr} = 2r$

Using the Chain's rule

$\frac{du}{dt} = \frac{du}{dr} \times \frac{dr}{dt}$

∴ $\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h(\frac{du}{dr} \times \frac{dr}{dt})]$

Then,

$\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]$

Now,

From the question

$\frac{dr}{dt} = 7 m/min$

$\frac{dV}{dt} = 236 m^{3}/min$

At the instant when $r = 99 m$

and $V = 180 m^{3}$

We will determine the value of h, using

$V = \frac{1}{3}\pi r^{2}h$

$180 = \frac{1}{3}\pi (99)^{2}h$

$180 \times 3 = 9801\pi h$

$h =\frac{540}{9801\pi }$

$h =\frac{20}{363\pi }$

Now, Putting the parameters into the equation

$\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]$

$236 = \frac{1}{3}\pi [(99)^{2} \frac{dh}{dt} + (\frac{20}{363\pi }) (2(99)) (7)]$

$236 \times 3 = \pi [9801 \frac{dh}{dt} + (\frac{20}{363\pi }) 1386]$

$708 = 9801\pi \frac{dh}{dt} + \frac{27720}{363}$

$708 = 30790.75 \frac{dh}{dt} + 76.36$

$708 - 76.36 = 30790.75\frac{dh}{dt}$

$631.64 = 30790.75\frac{dh}{dt}$

$\frac{dh}{dt}= \frac{631.64}{30790.75}$

$\frac{dh}{dt} = 0.021 m/min$

Hence, the rate of change of the height is 0.021 meters per minute.

3 0

2 years ago