All categories

3 years ago

Circle d has a radius of 21 millimeters and central angle, ∠edf, which measures 60°. find the exact length of . mm 7mm 14mm 42mm

2 answers:

8 0

The length of an arc length can be calculated using the formula:
s = ra
where s is the lenght of the arc
and r is the radius of the circle
a is the central angle in radians

first converts degrees to radians
a = 60 ( pi / 180)
a = pi /3 =1.05

s = 21(1.05)
s = 22 mm is the length of the arc

mixer [17]3 years ago

8 0

Answer:

7π mm

Have a good day!

You might be interested in

Amanda created a table to help her represent the sample space of spinning a spinner and flipping a coin.

OlgaM077 [116]

Answer:

$\sf \dfrac{1}{8}$

Step-by-step explanation:

Spinner choices: Red, Green, Yellow, Blue

Coin choices: Heads, Tails

$\large\begin{array}{| c | c | c | c | c |}\cline{1-5} & \sf Red & \sf Green & \sf Yellow & \sf Blue\\\cline{1-5} \sf Heads & RH & GH &YH & BH \\\cline{1-5} \sf Tails &RT & GT& YT& BT\\\cline{1-5}\end{array}$

$\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}$

$\implies \sf P(blue)=\dfrac{1}{4}$

$\implies \sf P(heads)=\dfrac{1}{2}$

$\implies \sf P(blue)\:and\:P(heads)=\dfrac{1}{4} \times \dfrac{1}{2}=\dfrac{1}{8}$

5 0

1 year ago

What product have the same sign as ( -2 3/7 ) (-6/11) ?

motikmotik

Answer:

1. -7/8

2.-9/14

3. 9/14

4. 7/8

2. what is the product of -2/7 and -3/7?

1. -7/8

2.-6/49

3. 6/49

4. 7/8

How do the expressions 72÷ 9 and -72÷ (-9) compare when they are evaluated?

1. They have different values and are different signs.

2. They have different values but are the same sign.

3. They have the same value but are different signs.

4. They have the same value and the same sign.

Step-by-step explanation:

Multiplying fractions: multiply numerators and multiply denominators

1. 3/4 X -6/7 = -18/28 = -9/14

2. -2/7 X -3/7 = 6/49

3. 4 because 72/9 is 8. -72/-9 is 8. Two negatives makes a positive when multiplying and dividing.

7 0

3 years ago

Prove that if sin (2 + y) = 3 sin (x - y), then tan x = 2 tany.

nignag [31]

Answer:

The proof is given below.

Step-by-step explanation:

Given: ( the correct question and ans is as follow )

sin (x + y) = 3sin ( x - y)

To Prove

tan x = 2 tan y

Proof:

$\sin (x+y) = 3\sin (x-y)$

Using the identities

$\sin (A+B) = \sin A.\cos B + \cos A.\sin B\\and\\\sin (A-B) = \sin A.\cos B - \cos A.\sin B\\$

we get

$\sin x.\cos y + \cos x.\sin y = 3(\sin x.\cos y - \cos x.\sin y)\\\sin x.\cos y + \cos x.\sin y = 3\sin x.\cos y - 3\cos x.\sin y$

Now we will take sin x . cos y to the left hand side and cos x . sin y to the right hand side,we get

$3\sin x.\cos y - \sin x.\cos y = 3\cos x.\sin y +\cos x.\sin y\\2\sin x.\cos y =4\cos x.\sin y\\\sin x.\cos y =2\cos x.\sin y \ \textrm{4 divide by 2}\\ \frac{\sin x}{\cos x} =2\times \frac{\sin y}{\cos y} \\\textrm{we know identity }\\\frac{\sin x}{\cos x} = \tan x\\\frac{\sin y}{\cos y} = \tan y\\\therefore \tan x = 2\tan y\ ...............{PROVED}$

7 0

3 years ago

Find the average rate of change for f(x) = x2 + 9x + 18 from x = −10 to x = 10.

igor_vitrenko [27]

The average rate of change formula is
f(b) - f(a)
arc = ----------------
b-a

Here, a= -10 and b = 10

(10)^2 + 9(10) + 18 - [ (-10)^2 + 9(-10) + 18]
Here arc = --------------------------------------------------------------
10 - (-10)

10^2 and -(-10)^2 cancel. 18 - 18 cancel.

90 - (-90) 180
This leaves us with arc = ----------------- = ------------- = 9 (answer)
20 20

7 0

3 years ago

A small business earns a profit of $6500 in January and $17,500 in May. What is the rate of change in profit for this time perio

MAXImum [283]

Rate of change of profit for this period is $2750 per month

Solution:

Given that,

Profit of $6500 in January and $17,500 in May

To find: Rate of change

Since,

January is the first month of the year (1) while May is the fifth month (5)

Therefore, we get two points

(1, 6500) and (5, 17500)

Using these points we can find the rate of change in profit for this time period

The rate of change using the following formula:

$m = \frac{y_2-y_1}{x_2-x_1}$

Here from the points,

$(x_1, y_1) = (1, 6500)\\\\(x_2, y_2) = (5, 17500)$

Therefore, rate of change is given as:

$m = \frac{17500-6500}{5-1}\\\\m = \frac{11000}{4}\\\\m = 2750$

Thus rate of change of profit for this period = $2750 per month

8 0

3 years ago