Which fraction is greater than 4/8?

Freddie is at chess practice waiting on his opponent's next move. He notices that the 4-inch-long minute hand is rotating around

ale4655 [162]

Answer:

Part 1: $\frac{2\pi}{3}$ radians

Part 2: The minute hand travels $\frac{8\pi}{3}$ inches.

Part 3: The minute hand travels $\frac{3\pi}{4}$ radians.

Part 4: The coordinate point is $(-\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2})$

Step-by-step explanation:

Part 1:

There are 60 minutes in an hour. 1 hour is 1 revolution (1 circle), which is 360°.

So each minute represents $\frac{360}{60}=6$ degrees

From 3:35 to 3:55 is 20 minutes. Hence, 20 minutes is $6*20=120$ degrees.

To convert from degrees to radians, we multiply the degrees by $\frac{\pi}{180}$

120° is equal to $120*\frac{\pi}{180}=\frac{2\pi}{3}$ radians

Part 2:

We want to find the "arc length" of this.

Formula for arc length is $s=r\theta$

Where,

s is the arc length
r is the radius (here the minute hand was given as 4 inches)
$\theta$ is the angle in radians (we found it to be $\frac{2\pi}{3}$ )

So, $s=r\theta\\s=(4)(\frac{2\pi }{3})=\frac{8\pi}{3}$

The minute hand travels $\frac{8\pi}{3}$ inches.

Part 3:

Here we use the arc length formula where we want to find $\theta$ given that $s=3\pi$ and radius is 4 inches. So we have:

$s=r\theta\\3\pi=(4)(\theta)\\\theta=\frac{3\pi}{4}$

The minute hand travels $\frac{3\pi}{4}$ radians.

Part 4:

The coordinate point associated with a specif radian is given by the formula:

$(x,y)=(cos(\theta)sin(\theta))\\(x,y)=(cos(\frac{3\pi}{4})sin(\frac{3\pi}{4}))\\(x,y)=(-\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2})$

Thus the coordinate point is $(-\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2})$

3 0

4 years ago

Read 2 more answers

Sam bought 4 bags of sugar for his restaurant. Each bag weighed 6.3 kilograms. How many kilograms of sugar did he buy total?

nikklg [1K]

Answer:

25.2

Step-by-step explanation:

4*6.3

3 0

4 years ago

Read 2 more answers

the area of sea horese is 108 cm every day it grows by 2% what will be the sea hores area after 2 days

Vitek1552 [10]

First find 2 percent of 108cm which is 2/100*108=2.16
So the sea hores grows 2.16cm every day. In 2 days, the hores will be 2*2.16=4.32cm

5 0

4 years ago

Whats the sum of 3 fifeens and 4 twos

kap26 [50]

"Sum" is addition.

3(15)+4(2)
First simplify by multiplying 3 by 15 and 4 by 2.

45+8
Now simply add. :)

45+8=53

The answer is 53. :)

7 0

3 years ago

I REALLY NEED HELP please please help me answer all please

Radda [10]

9514 1404 393

Answer:

all are functions except Relation 2

Step-by-step explanation:

If any input value (first of an ordered pair) is used more than once, the relation is not a function. Output values can be used as often as you like.

Only Relation 2 is not a function.

3 0

3 years ago