(section 6.1) Find the length of the small arc formed by the intersection of the unit circle a circle centered at the origin with a radius of 1: x2 + y2 = 1 and the line 2 y=1/2​

Answers

Answer 1

Answer:

The length of the arc is approximately 2.0944

Step-by-step explanation:

The given parameters are;

The equation of the circle = x² + y² = 1

The radius of the circle, r = 1

The equation of the line, y = 1/2

Therefore, we point where the line intersects with the circle are given as the points 'y = 1/2' as follows;

When y = 1/2, the equation of the circle becomes;

x² + (1/2)² = 1

x² = 1 - (1/2)² = 3/4

x = ±√3/2

The angle subtended by the arc, θ = 2 × arctan((√3/2)/(1/2)) = 120°

The circumference of the circle, C = 2·π·r

∴ C = 2 × π × 1 = 2·π

The length of the arc, l = (θ/360) × C

∴ l = (120/360) × 2·π = (2/3)·π

The length of the arc, l = (2/3)·π ≈ 2.0944

Answer 2

The length of the arc is approximately 2.09

The intersection of the unit circle a circle

From the question, we have the following parameters

The equation of the circle = x² + y² = 1

The radius of the circle, r = 1

The equation of the line, y = 1/2

The line intersects with the circle are given as the points 'y = 1/2' as follows;

When y = 1/2, the equation of the circle becomes;

x² + (1/2)² = 1

x² = 1 - (1/2)² = 3/4

x = ±√3/2

Determine the subtended angle

The angle subtended by the arc is expressed as:

θ = 2 × arctan((√3/2)/(1/2))

θ = 120°

The circumference of the circle, C = 2·π·r

C = 2 × π × 1 = 2·π

The length of the arc, l = (θ/360) × C

l = (120/360) × 2·π = (2/3)·π

The length of the arc, l = (2/3)·π ≈ 2.09

The length of the arc is approximately 2.09

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Related Questions

PLS HELP (MARKING BRAINLIEST)

Answers

Answer:

there is a fraction calculator you can use

https://www.calculatorsoup.com/calculators/math/fractions.php

Step-by-step explanation:

Bernie can eat 20 oreos in 5 minutes. If Joe can eat oreos at 3/4
of Bernie’s pace, how many oreos can they eat together in half an hour?

a.200
b. 210
c. 220
d. 230

Answers

Answer:

b

Step-by-step explanation:

Please help with B...

Answers

Answer:

B

Step-by-step explanation:

The table tells us that when x=-1, y=5. This shows in graph B because it passes through the point (-1,5). The table also tells us that the curve passes through the origin, (0,0). Curve B is the only one that does.

I hope this helps!

Two geometrically similar jugs have volumes of 1000 cm3and 512 cm3.They have circular bases. The diameter of the base of the larger jug is 9 cm.

Answers

Complete Question

Two geometrically similar jugs have volumes of 1000 cm³and 512 cm³.They have circular bases. The diameter of the base of the larger jug is 9 cm.

Calculate the diameter of the smaller jug.

Answer:

7.2 cm

Step-by-step explanation:

To solve the above question,we have the proportion

Smaller volume/ Larger volume = (Smaller diameter/ Larger diameter)³

We are to find the smaller diameter

Hence our formula is give as

Cube root(Smaller volume/ Larger volume)= Smaller diameter/ Larger diameter

=cube root( 512/1000) = x/9

= 8/10 = x/9

Cross Multiply

10x = 8 × 9

10x = 72

x = 72/10

x = 7.2cm

Therefore, the diameter of the second jug is 7.2 cm

The distance between the points P(–7, 2) and Q(5, –3) is
A. 12 units
B. 13 units
C. 11 units
D. 10 units

Answers

Answer:

B. 13 units

Step-by-step explanation:

Hope this helps

What is 589 divided by 31 with remainder?

Answers

Answer:

19 remainder 0

Step-by-step explanation:

When we divide 589 by 31 we get remainder 0.

Here we have to find the remainder when 589  is divided by 31

In order to this proceed with division,

Since we know that,

When the numerator is equal to or more than the denominator, the fraction is said to be inappropriate. It always has a value of one or higher. Since mixed fractions are simpler to understand, improper fractions are typically expressed in simplified mixed number form.

Now

31 ) 589 ( 19

   -  31

 _________

      279

   -  279

 __________

        0

Hence remainder after division is 0.

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Explain what it means for x and y to vary directly​

Answers

Answer:

(Some textbooks describe direct variation by saying " y varies directly as x ", " y varies proportionally as x ", or " y is directly proportional to x . ") This means that as x increases, y increases and as x decreases, y decreases—and that the ratio between them always stays the same.

help!
50 pts and brainiest

Answers

Answer:

303

Step-by-step explanation:

add all of them and you get 303, hope this helps :)

Answer:

Vertical. A vertical is an alignment in which the top is always above the bottom. It is a property of two or more points in which if a point is directly below the ...

Step-by-step explanation:


Find an equation for the line below

Answers

Is this math or algebra??

An antique car sold at auction for $50,000. Its value
appreciates by 10% each year. What is the value of
the car after six years?

Answers

Answer:

80,000

Step-by-step explanation:

Which side lengths form a right triangle?
Choose all answers that apply:
Choose all answers that apply:

(Choice A)
A
2
,
15
,
17
2,15,172, comma, 15, comma, 17

(Choice B)
B
1
,
8
,
65
1,8,
65

1, comma, 8, comma, square root of, 65, end square root

(Choice C)
C
2
,
80
,
9
2,
80

,92

Answers

Laila 15 manhhqManlqhw17

Answer:

B

Step-by-step explanation:

John ran 5,000 meters on Monday. He
ran 6 kilometers on Tuesday. How many
total kilometers did John run?

Answers

Answer:

11 kilometers

Step-by-step explanation:

Since there are 1,000 m in 1 km, John ran 5 km on Monday. Combine that with the 6 km he ran on Tuesday, and you get 11 km in total.

Answer:

11 kilometers

Step-by-step explanation:

1000 meters=1 kilometer

5000÷1000=5

5+6=11

Help me plz 6th grade math

Answers

Answer: 66

Step-by-step explanation:

6+4^3-8÷2

4^3 = 64

6+64-8÷2

70-8÷2

70-4 = 66

Mrs. Humble is filling bags with peanuts to give as gifts. Each bag will contain 1 and 3 over 4 pounds of peanuts. The peanuts cost $5.00 per pound. How much will the peanuts in one bag cost?Mrs. Humble is filling bags with peanuts to give as gifts. Each bag will contain 1\frac{3}{4} pounds of peanuts. The peanuts cost $5.00 per pound. How much will the peanuts in one bag cost?

Answers

Answer:

$8.75

Step-by-step explanation:

STEP TO TAKE TO DETERMINE THE ANSWER

Multiply 13/4 pounds by the cost of one pound of peanut. To do this, convert 13/4 to an improper fraction and then multiply it by $5

[tex]1\frac{3}{4}[/tex] = [tex]\frac{7}{4}[/tex]

[tex]\frac{7}{4}[/tex] × 5 = [tex]\frac{35}{4}[/tex] = [tex]8\frac{3}{4}[/tex] = $8.75

The next math test will contain 50 questions. Some will be worth three points while the rest will be worth six points. If the test is worth 195 points, how many questions are worth three-points and how many worth six-points?

Answers

Explanation is in the file

tinyurl.com/wpazsebu

The no of three-pointer questions is 35 and the no of six-pointer questions is 15.

What is equation?

A formula known as an equation uses the equals sign to denote the equality of two expressions.

Given:

The total no of questions = 50,

The total marks in the test = 195.

According to the question, the equation will be,

3x + 6y = 195 and x + y = 50

Here, x is the no of three mark question and y is the no of six marks question.

Solve the equation by elimination method, and we get,

x = 35 and y = 15

Therefore, the no of three-pointer questions is 35 and the no of six-pointer questions is 15.

To know more about equation:

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Please help me NO LINKS ASAP will give Brainilest

Answers

Answer:

width x height x length=volume so 5 x 14 x 10= 700cm cubed. Volume=700cm^3

Step-by-step explanation:

Pls help me with this

Answers

ANSWER:

the y- intercept would be 0

1. If X+Y=7 and xy = 10 , then x3+ y3​

Answers

I have the same question lol

Answer:

final answer is 21

Step-by-step explanation:

since x+y=7 and xy=10

2+5=7 and 2(5)=10

so,

(5)3=15  

(2)3=6

15+6= 21

A car was purchased for $24,000. Its value is predicted to decay exponentially, decreasing by 13% each year. Write an equation to determine the value of the car.

Answers

Answer:

y= P(0.87)^t

Step-by-step explanation:

Given data

Price P=  $24,000

Rate of decay in price= 13%

The expression in terms of y, p and t  is

y=P(1-r)^t

y= P(1-0.13)t

y= P(0.87)^t

please help ASAP... here is a question WRITE 894 290 000 IN SCIENTIFIC NOTATION​

Answers

Answer:

hey there, the answer is 8.9429 × 10^8

Answer:

8.9429 × 10^8

Step-by-step explanation:

ya the answer is 8.9429 × 10^8

A culture of bacteria has an initial population of 330 bacteria
and doubles every 8 hours.
what is the population of bacteria in the culture after 17 hours,
to the nearest whole number?

Answers

Answer:

1439.4702≈1439

which of the following decimal has highest value is a 0.5 b 0.12 c 0.17 d 0.8​

Answers

Answer:

d 80 cents or 0.8

Step-by-step explanation:

Change them all to money. Then look at it again.

0.5 = 50 cents

0.12 = 12 cents

0.17 = 17 cents

0.8 = 80 cents.

You get each of them by starting with a dollar. A dollar has 100 cents.

So 0.5 of a dollar is 1/2 a dollar.

1/2 a dollar is 0.5 * 100 = 50 cents

0.17 * 100 = 17 cents

0.12 * 100 = 12 cents

0.8 * 100 = 80 cents

The largest one is 8

Answer d) 0.8

Step-by-step explanation: Here is a tip, when you see a decimal like 0.5 compared to a bigger looking one like 0.12 add a 0 to the end. It will still have the same value and you won't be as confused.

0.80> 0.50> 0.17> 0.12

What type of real numbers are these.

Answers

They are all integers

could someone help me on this pleaseeee :)​

Answers

Answer:

the slope is 1, y-intercept is (0,5) hope this helps!

Step-by-step explanation:

A circular swimming pool has a radius of 20 feet. A fence is going to be built so that there is a 4-foot space around the entire pool. What is the length of the fence? Sunitha solved the problem as shown. A circle with radius 20 feet. A larger circle is 4 feet larger than the smaller circle. Radius = 24 feet. Circumference = 24 pi. What was her error? She should have used 12 in the formula, not 24. She forgot to multiply the radius by 2 in the formula. She did not add the additional fence length to the pool’s radius. She should have used 4 ft in the formula.

Answers

Answer:

she forgot to multiply the radius by 2 in the formula (B)

Step-by-step explanation:

i got it right :)

Answer:

B.

Step-by-step explanation:

What is the multiplier?

A. 0.1

B. 0.01

C. 10

D. 100​

Answers

Answer:

c

Step-by-step explanation:

0.6*10=6

6*10=60

Answer:

B or A

Step-by-step explanation:

Given the definitions of f(x) and g(x) below, find the value of g(f(5)).
f(x) = 2x – 10
g(x) = x^2 + 6x – 8

I don’t need work I am just looking for the answer !

Answers

gf(x) = g(x^-1) = x^2 + 6x - 8

f(x) = 2x - 10

gf(x) = 6 ( 2x - 10) - 8

gf(x) = 12x- 60 - 8

gf(x) = 12x -68

gf(5) = gf(x) = 12x - 68

gf(5) = 12(5) - 68

gf(5) = 60 - 68

gf(5) = -8

The equation of the line through (3, - 4) with slope 2/3

Answers

Y = mx + b
m = slope, b = y intercept
Plug in point
Y = 2/3x + b
-4 = 2/3(3) + b
-4 = 2 + b, b = -6
Y = 2/3x - 6

What is the sale price of $160 airpods with an 18% discount?

Answers

Answer:

$131.20

Step-by-step explanation:

$160 is the full price, so it is 100% of the full price.

With a discount of 18%, you pay 100% - 18% = 82% of the full price.

82% of $160 =

= 0.82 * $160

= $131.20

Answer: $131.20

Answer ASAP pls pls ASAP

Answers

Answer:

it 5

Step-by-step explanation:

15-10= 5 so r=5

Answer:

The value of r will be 5.

Step-by-step explanation:

15=r+10

15-10=r

5=r

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