All categories

2 years ago

Find the area of the shaded segment of the circle. Please help

Mathematics

1 answer:

natka813 [3]2 years ago

5 0

Answer:

1.4 m²

Step-by-step explanation:

The area of a sector with central angle θ (in radians) is given by the formula

A = (1/2)r²θ

The area of the triangle with central angle θ is given by the formula

A = (1/2)r²sin(θ)

The area of the shaded segment is the difference of these:

A = (1/2)r²(θ -sin(θ))

Your segment has a central angle of 60° = π/3 radians, so its area is ...

A = (1/2)(4 m)²(π/3 -sin(π/3)) = (8 m²)(π/3 -(√3)/2)

A ≈ 1.4 m²

The area of the shaded segment is about 1.4 m².

You might be interested in

The graph below shows the distance, y, in miles, of a bird from its nest for a certain amount of time, x, in minutes:

Montano1993 [528]

Answer:

$0.2$ miles per minute represents the speed of the bird and 3 miles represents the original distance of the bird from its nest.

Step-by-step explanation:

As there is no graph mentioned here but the information are quite sufficient to answer the question.

We have points $(0,3), (5,4),(10,5)...$

From these points we can find the slope of the line .

From point slope formula $y-y_1=m(x-x_1)$

And assigning $(x,y) (0,3)$ and $(x_1,y_1) (5,4)$

$m=\frac{y_1-y}{x_1-x} =\frac{4-3}{5-0} =\frac{1}{5}=0.2$

This slope is also the speed of the bird which is $0.2\ miles\ per\ minute.$

As by plugging the values of any coordinate point we can confirm this.

Lets put $(10,5)$ , y-axis is the distance so in $10$ minutes the the distance covered by the bird must be equal to to y-axis value which is $5$ miles.

$y=0.2(x),y=0.2(10)=5\ miles$

Now as in $t=0$ the bird has started from y-intercept value $3$ so we can say that,the original distance of the bird from its nest is $3\ miles$ .

So the correct choices are: $B$ and $D$

The birds speed is $0.2\ miles$ per minute and is $3\ miles$ away from its nest.

7 0

2 years ago

If q=5 what is the value of 4q + 2q squared

steposvetlana [31]

Answer:

30q or 30

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

Please help me with this problem

sineoko [7]

Answer:

$4$

Step-by-step explanation:

$\frac{ {3x}^{2} -2x + 7}{2x+5} \\ \frac{3( - 1) {}^{2} - 2( - 1) + 7}{2( - 1) + 5 } \\ \frac{3 + 2 + 7}{ - 2 + 5} \\ \frac{12}{3} = 4$

7 0

2 years ago

When x = -3, then y = ?

almond37 [142]

Step-by-step explanation:

the answer is y=-6 when x=-3

7 0

2 years ago

Please help again I need it

Ilya [14]

The two angles are verticals angles so they are congruent, so you can solve for x by writing and solving an equation

6x-82=3x-23

Combine like terms

3x=105

And simplify to get x=35

4 0

2 years ago

Read 2 more answers