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Nikolay [14]
3 years ago
13

Find the area of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximati

ons).

Mathematics
2 answers:
Alik [6]3 years ago
5 0

Answer:

The area of the shaded region is 36π - 72 cm²

Step-by-step explanation:

Given

The radius of the circle segment, r = 12cm

The angle subtended at the centre of the circle is right angled, so

θ = 90°

Convert to radians

θ = 90π/180

θ = ½π

The shaded region is a segment;

To calculate the area of the segment, we make use of the following formula;

A = ½r²(πθ/180 - sinθ) in radians

By substituton,

A = ½ * 12² * (π/2 - sin90)

A = ½ * 144(π/2 - 1)

A = 72(π/2 - 1)

A = 36π - 72 cm²

Area of the shaded region is 36π - 72 cm²

Lera25 [3.4K]3 years ago
4 0

Answer:

  (36π -72) cm²

Step-by-step explanation:

The area of a segment that subtends arc α (in radians) is given by ...

  A = (1/2)r²·(α - sin(α))

Here, you have r = 12 cm and α = π/2 radians, so the area of the segment is ...

  A = (1/2)(12 cm)²·(π/2 -1) = (36π -72) cm²

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Identify the type of observational study​ (cross-sectional, retrospective, or​ prospective) described below. A research company
Sindrei [870]

Answer:

Prospective study

Step-by-step explanation:

<em>A cross-sectional study, also known as transverse study, is a type of observational study that analyzes data from a population at a specific point in time.</em> This kind of observation is used if cases cannot be identified a priori or if the prevalence of the disease or condition needs to be determined.

Cohort studies are when two or more groups of subjects are followed over time to see if they develop some disease or if some event occurs, there are two type of cohort studies, prospective and retrospective. <em>Prospective studies (or follow-up studies) follow subjects with different exposures until some point in time where something happens or the study ends</em>, r<em>etrospective studies use historical data</em> to make comparisons based on risk factors or exposures that occurred before the events.

Considering the information given and the observational study exposed to the question, we can conclude that we are talking about a prospective study because data is collected over the next 10 years.

I hope you find this information useful and interesting! Good luck!

7 0
2 years ago
The table shows the breakdown of the points scored in last week's basketball game.
o-na [289]

Answer:

a. Total field goal points scored in the first two quarters, in simplest linear expression form is: 3x - 4.

b. The total points scored in the game, in simplest linear expression form is: 6x - 1.

a. The goal points scored in the first two quarters are expressed in linear forms as: 2x - 6 and x + 2.

The total field goal points in the first two quarters = 2x - 6 + x + 2

Add like terms

3x - 4

b. The total points scored in the game = 2x - 6 + x + 2 + 2x + x - 6 + 9

Add like terms and simplify the expression

2x - 6 + x + 2 + 2x + x - 6 + 9

6x - 1

Step-by-step explanation:

3 0
2 years ago
Freddy is on a nature hike. He hikes west 4 miles, and then he turns due north and hikes for 2 miles. It is getting dark and Fre
melomori [17]

The direct path back forms a right triangle. Use the Pythagorean theorem:

X = sqrt(4^2 + 2^2)

X = sqrt(16 + 4)

X = sqrt(20) = 2sqrt(5)

X = 4.472

Round the answer as needed.

7 0
2 years ago
Solve the systems of equation by graphing (Picture provided)
11Alexandr11 [23.1K]

Answer:

Option b

Step-by-step explanation:

The following system of linear equations is shown

x + y = 8\\2x + y = 3

These are two different slope lines.

We find the cut points of both lines with the axes.

x + y = 8

Cut with the x axis. (y = 0)

x = 8

Cut with the y axis. (x = 0)

y = 8

...................................................................

2x + y = 3

Cut with the x axis. (y = 0)

2x = 3\\x = 1.5

Cut with the y axis. (x = 0)

y = 3

The solution to this system will be a point for which it is fulfilled that:

x + y - 8 = 2x + y-3

In the image, different graphs with intersections are shown.

Locate among the options, one that shows the two lines of the system of equations according to their intersections with the x and y axes.

Option b is the only one that shows the graph of the lines

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Then, The point of intersection of both lines in the graph is:

(-5, 13)

Therefore the solution of the system of equations is: (-5, 13)

You can verify this by replacing the point in the relationship

x + y - 8 = 2x + y-3\\\\(-5) +13 -8 = 2 (-5) +13 -3\\\\0 = 0

Equality is satisfied

Finally the answer is the option b

8 0
3 years ago
Suppose 10 and 6 are common factors of two numbers. What other
kvasek [131]

Answer: 2

Step-by-step explanation:

We can list out their factors

10:1,2,5,10

6:1,2,3,6

Both have the same factors of 2.

5 0
2 years ago
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