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3 years ago

What is the length of arc S shown below?

Mathematics

1 answer:

natka813 [3]3 years ago

5 0

An angle in radians marks out the same number of radiuses on the circle. That's one thing that often makes radians so neat to work with.

The angle in the middle of this circle is 2 radians. So the arc ' S ' is 2 times the length of the circle's radius.

In my head, I get S = 14 units , but you should check it out.

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Hi!

Elina [12.6K]

Answer:

404.09x cm³ (to 5 s.f.),

where x is the unknown height of the shape.

Step-by-step explanation:

Volume of the shape

= base area × height

= (large semicircle- small semicircle) × thickness of shape

Area of circle= $\pi {r}^{2}$

Area of semicircle= $\frac{1}{2} (\pi)( {r}^{2} )$

Diameter of small circle= 14

Radius= diameter ÷2

radius= 14 ÷2

radius = 7 cm

Area of small semicircle

$= \frac{1}{2} (\pi)( {7}^{2} ) \\ = \frac{49}{2} \pi$

Radius of large semicircle

= 35 ÷2

= 17.5 cm

Area of large semicircle

$= \frac{1}{2} (\pi)( {17.5}^{2} ) \\ = \frac{1225}{8} \pi$

Base area of shape

$= \frac{1225}{8}\pi - \frac{49}{2} \pi \\ = \frac{1029}{8} \pi$

Since the height if the shape is not given, I'm afraid I cant help you find the volume.

Let the height of the shape be x cm.

Volume of shape= $\frac{1029x}{8} \pi \: cm^{3}$

3 0

3 years ago

HURRYYY !!!! A bacteria population doubles in size every 5 hours. After 5 hours, the sample contains 2,000 bacteria. Which equat

Ainat [17]

Equation of y, the population size after x hours is y = 1000 (1.15)ˣ

<h3>Further explanation</h3>

Firstly , let us learn about types of sequence in mathematics.

Arithmetic Progression is a sequence of numbers in which each of adjacent numbers have a constant difference.

$\boxed{T_n = a + (n-1)d}$

$\boxed{S_n = \frac{1}{2}n ( 2a + (n-1)d )}$

<em>Tn = n-th term of the sequence</em>

<em>Sn = sum of the first n numbers of the sequence</em>

<em>a = the initial term of the sequence</em>

<em>d = common difference between adjacent numbers</em>

<em />

Geometric Progression is a sequence of numbers in which each of adjacent numbers have a constant ration.

$\boxed{T_n = a ~ r^{n-1}}$

$\boxed{S_n = \frac{a( 1 - r^n ) }{1 - r}}$

<em>Tn = n-th term of the sequence</em>

<em>Sn = sum of the first n numbers of the sequence</em>

<em>a = the initial term of the sequence</em>

<em>r = common ratio between adjacent numbers</em>

Let us now tackle the problem!

Let :

Initial number of population = a

After 5 hours → Population = y = a × 2 = 2000

2a = 2000

a = 2000 ÷ 2

a = 1000

After 10 hours → Population = y = a × 2 × 2 = a × 2² = 1000 × 2²

After 15 hours → Population = y = a × 2 × 2 × 2 = a × 2³ = 1000 × 2³

After x hours ↓

Population = y = $1000 \times 2^{\frac{x}{5}}$

Population = y = $1000 \times (2^{\frac{1}{5}})^x$

Population = y = $\large{ \boxed {1000 \times (1.15)^x} }$

Let's prove the equation above :

After 5 hours :

Population = y = $1000 \times (1.15)^5$ = 2011 ≈ 2000 ✔

After 10 hours :

Population = y = $1000 \times (1.15)^{10}$ = 4046 ≈ 4000 ✔

After 15 hours :

Population = y = $1000 \times (1.15)^{15}$ = 8137 ≈ 8000 ✔

<h3>Learn more</h3>

Geometric Series : brainly.com/question/4520950
Arithmetic Progression : brainly.com/question/2966265
Geometric Sequence : brainly.com/question/2166405

<h3>Answer details</h3>

Grade: Middle School

Subject: Mathematics

Chapter: Arithmetic and Geometric Series

Keywords: Arithmetic , Geometric , Series , Sequence , Difference , Term

4 0

4 years ago

Read 2 more answers

14285714/1000000000 simplified

Advocard [28]

Is this a joke or do u actually want us to answer it

4 0

3 years ago

The radius of dinner table is 6 meters. what is the area of the table

Elina [12.6K]

Answer:

Is there a picture of the table?

3 0

3 years ago

Select the correct answer. Simplify. square root of 72 A. 2 square root of 6 B. 36 square root of 2 C. 12 square root of 6 D. 6

rusak2 [61]

Answer:

it's B 36 square root of 2

8 0

2 years ago