The difference between 3 1/2 and 1 4/5 a 2 4/5 b 2 7/10 c 1 4/5 d 1 7/10

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

The mean (rounded to the nearest tenth if needed) of the following data set is: 30, 29, 40, 51, 39, 33, 24, 60, 40, 35, 58

bekas [8.4K]

Mean is just the average so to calculate the average just add up all the data and divide it by the number of data.
so it's gonna be
(30+29+40+51+39+33+24+60+40+35+58) / 11
= 39.9 (corrected to the nearest tenth)

5 0

3 years ago

Andrew is showing his work in simplifying −4.5 + 4.2 + 5.6 − 7.3. Identify any errors in his work or in his reasoning. Write fee

Vinil7 [7]

Solving the expression $-4.5 + 4.2 + 5.6 -7.3$ we get -2.

Comparing the solution with the one given, you can find the errors.

Step-by-step explanation:

We need to simplify $-4.5 + 4.2 + 5.6 -7.3$ and identify errors.

Since the steps are not shown, so we cannot identify errors but I can solve the expression and you can compare to find errors.

Simplifying:

$-4.5 + 4.2 + 5.6 -7.3$

Using algebraic rule: if one digit has positive (+) sign and other digit has negative (-) sign then we will perform subtraction. and after subtraction, the sign of bigger value will be the sign of result.

Using the rule and solving:

$=(-4.5 + 4.2) + 5.6 -7.3$