All categories

4 years ago

PLEASE HELP

Mathematics

2 answers:

konstantin123 [22]4 years ago

7 0

The length of the minor arc AB is 6.3cm

kipiarov [429]4 years ago

3 0

Answer:

D. 6.3 cm

Step-by-step explanation:

First we find the circumference of the circle. The formula for circumference is

C = 2πr

Using 3.14 for π and our value for 5, we have

C = 2(3.14)(5) = 31.4 cm

Next we find the portion of the circle represented by this sector. The angle is 72 out of 360 total degrees:

72/360 = 36/180 = 6/30 = 1/5

Multiply the circumference by this fraction:

1/5(31.4) = 6.28 ≈ 6.3 cm

You might be interested in

A ship sails 250km due North qnd then 150km on a bearing of 075°.1)How far North is the ship now? 2)How far East is the ship now

olga_2 [115]

Answer:

1) 288.8 km due North

2) 144.9 km due East

3) 323.1 km

4) 207°

Step-by-step explanation:

Bearing: The angle (in degrees) measured clockwise from north.

Trigonometric ratios

$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$

where:

$\theta$ is the angle
O is the side opposite the angle
A is the side adjacent the angle
H is the hypotenuse (the side opposite the right angle)

Cosine rule

$c^2=a^2+b^2-2ab \cos C$

where a, b and c are the sides and C is the angle opposite side c

-----------------------------------------------------------------------------------------------

Draw a diagram using the given information (see attached).

Create a right triangle (blue on attached diagram).

This right triangle can be used to calculate the additional vertical and horizontal distance the ship sailed after sailing north for 250 km.

Question 1

To find how far North the ship is now, find the measure of the short leg of the right triangle (labelled y on the attached diagram):

$\implies \sf \cos(75^{\circ})=\dfrac{y}{150}$

$\implies \sf y=150\cos(75^{\circ})$

$\implies \sf y=38.92285677$

Then add it to the first portion of the journey:

⇒ 250 + 38.92285677... = 288.8 km

Therefore, the ship is now 288.8 km due North.

Question 2

To find how far East the ship is now, find the measure of the long leg of the right triangle (labelled x on the attached diagram):

$\implies \sf \sin(75^{\circ})=\dfrac{x}{150}$

$\implies \sf x=150\sin(75^{\circ})$

$\implies \sf x=144.8888739$

Therefore, the ship is now 144.9 km due East.

Question 3

To find how far the ship is from its starting point (labelled in red as d on the attached diagram), use the cosine rule:

$\sf \implies d^2=250^2+150^2-2(250)(150) \cos (180-75)$

$\implies \sf d=\sqrt{250^2+150^2-2(250)(150) \cos (180-75)}$

$\implies \sf d=323.1275729$

Therefore, the ship is 323.1 km from its starting point.

Question 4

To find the bearing that the ship is now from its original position, find the angle labelled green on the attached diagram.

Use the answers from part 1 and 2 to find the angle that needs to be added to 180°:

$\implies \sf Bearing=180^{\circ}+\tan^{-1}\left(\dfrac{Total\:Eastern\:distance}{Total\:Northern\:distance}\right)$

$\implies \sf Bearing=180^{\circ}+\tan^{-1}\left(\dfrac{150\sin(75^{\circ})}{250+150\cos(75^{\circ})}\right)$

$\implies \sf Bearing=180^{\circ}+26.64077...^{\circ}$

$\implies \sf Bearing=207^{\circ}$

Therefore, as bearings are usually given as a three-figure bearings, the bearing of the ship from its original position is 207°

8 0

2 years ago

Read 2 more answers

A basketball with a diameter of 9.5 in. is placed in a cubic box with sides 12 in. long. How many cubic inches of packing foam a

elena55 [62]

Answer:

1279.3 cubic inches (Rounded to the nearest tenth)

Step-by-step explanation:

Side of a cubic box = 12 inches

volume of cubic box = $side^3$ (since side is equal to 12 inches)

= $12^3$ = 1,728 cubic inches

It means that box can be filled with 1,728 cubic inches of any material

____________________________________________________

But, it is given that it has one basketball placed in it.

hence we need to find the volume of basketball .

Since basket ball is spherical in shape

formula to calculate its volume will be same as that of formula to calculate volume of sphere

volume of sphere = $(4/3 ) \pi r^3\\$ where r is the radius of sphere

radius of basketball = diameter/2 = 9.5/2 in = 4.75 inches

therefore volume of basket ball is given by

volume of basketball = $(4/3 ) \pi r^3\\\\\\=>(4/3 ) \3.14* 4.75^3\\\\\\= 448.693 \ cubic \ inches$

___________________________________________

In box with volume 1,728 cubic inches,, 448.693 cubic inches is occupied by basketball.

It means rest is empty which can be filled with foam.

To calculate the empty space, we subtract volume of basket ball from volume of box

volume of empty space = volume of box - volume of basket

= 1728 - 448.693 = 1279.307 cubic inches

1279.307 cubic inches in nearest tenth will be 1279.3 cubic inches.

Hence, 1279.3 cubic inches of foam are needed to fill the rest of the box

7 0

4 years ago

Please help meeeeeeeeeeeeeeeee

S_A_V [24]

Answer:

1436.8 in³

Step-by-step explanation:

Volume of sphere = (4/3)πr³

r = 7

---> (4/3)π(7)³ = 1436.8 in³

Have a great day :)

5 0

3 years ago

Read 2 more answers

A train travels 500 miles in 8 hours. Assuming that the train continues to travel at a constant rate, write an equation that rep

Ne4ueva [31]

The answer is D. y=125/2x

3 0

4 years ago

Read 2 more answers

Round each addend to the nearest hundred and then the sum 403+179

maks197457 [2]

582

Add: 403
Then: 179

8 0

3 years ago