Mathematics College

What is the arc length of an angle of 2π 3 radians formed on the unit circle? A) π 3 B) 2π 3 C) 4π 3 D) 5π 3

Answers

Answer 1
The correct answer is:

2π/3.

Explanation:

An angle formed on the unit circle would be a central angle.

The measure of an intercepted arc is the same as the measure of the central angle; since the angle is 2π/3, the arc length is 2π/3.
Answer 2

The arc length of an angle of 2π/3 radians formed on the unit circle is 2π/3.

To find the arc length of an angle of 2π/3 radians on the unit circle, we can use the formula:

Arc Length = Radius * Angle

Since we are considering the unit circle, the radius is 1. Therefore, the arc length is equal to the measure of the angle.

In this case, the angle is 2π/3 radians. So, the arc length is 2π/3.

The correct option is A) π/3.

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Related Questions

the function f(x)=a^x-4 will never cross the x-axis. true or false

Answers

Answer: False


Solution:

The exponential functions with the form y=a^x never cross the x-axis (x-axis is an asymptote), but in this case we have the exponential function translated 4 units downward, then this function crosses the x-axis.

As it is not given a is positive real number or negative real number.

By supposing a is any real number, we will draw the graph of the curve

[tex]a^x-4[/tex] by taking different values of x.

As i have taken different values of a ,

I found that for a< 0, the graph of the curve [tex]y=a^x-4[/tex]  does not exist.

For any other value of a, the curve cuts the x axis at one point.

For values of 1<a<0, the curve will cut negative side of X axis.

For value of a, a≥1, the curve will cut positive side of X axis.

For , a=0, the curve will not cut the x axis.

So, The function , f(x)=[tex]a^x -4[/tex] will cuts the x axis at one point for a >0 and for negative values of a, and for a< 0 ,it will not cut the x axis.

A recipe for bread calls for 4 1/4 cups of flour. Which expression gives the number of cups of flour needed if you want to make 3 1/2 batches of this recipe?

A. 3 1/2 + 4 1/4
B. 3 1/2 x 4 1/4
C. 4 1/4 ÷ 3 1/2
D. 4 + 1/2 + 3 + 1/2

Answers

the answer to this question is B
the answer is B must multiply

Suppose 60% of the people in a town will get exposed to flu in the next month. if you are exposed and not inoculated then the probability of your getting the flu is 80%, but if you are inoculated that probability drops to 15%. of two executives at beta company, one is inoculated and one is not. what is the probability at least one will not get the flu? assume that the events that determine whether or not they get the flu are independent.

Answers

P(Inoculated getting flu) = 0.6*0.15 = 0.09
P(Non-inoculated getting flu) = 0.6*0.8 = 0.48
P(Both getting flu) = 0.09*0.48 = 0.0432
P(Atleast 1 not getting flu) = 1-0.0432 = 0.9568

a 0.149-kilogram baseball, initially moving at 15 meters per second, is brought to rest in 0.040 seconds by a baseball glove on a catchers hand. the magnitude of the average force exerted on the ball by glove is

Answers

Using the relationship between force and acceleration, the average force exerted on the ball by the glove is :55.875 N

Given the Parameters :

Mass, m = 0.149 kg Velocity, V = 15 m/s Time, t = 0.040 seconds

Recall :

Force = Mass × acceleration

Acceleration = Δv / t

Force = (mΔv ÷ t)

Inputting the Values into the equation :

Force = [0.149 × (15 - 0)] ÷ 0.040

Force = (0.149 × 15) ÷. 0.040

Force = 2.235 ÷ 0.040

Force = 55.875 N

Therefore, the force exerted is 55.875 N

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What is the expression for "the sum of 8 times a number and two"? 8 × 2N 8N + 2 8(N + 2)

Answers

The answer is 8n+2, since it is asking for a sum and the variable is being multiplied by 8.

Answer:

Option B. 8N + 2

Step-by-step explanation:

Expression given in the question is " the sum of 8 times a number and two" will be = (8 times N + 2)

= 8N + 2

Therefore, option B. is the answer.

One side of a triangle is increasing at a rate of 8 cm/s and a second side is decreasing at a rate of 3 cm/s. if the area of the triangle remains constant, at what rate does the angle between the sides change when the first side is 24 cm long, the second side is 35 cm, and the angle is π/6?

Answers

A = (1/2)ab*sin(θ)
A' = (a'*b*sin(θ) +a*b'*sin(θ) +a*b*cos(θ)*θ')/2
0 = (8 cm/s)*(35 cm)*sin(π/6) +(24 cm)*(-3 cm/s)*sin(π/6) +(35 cm)*(24 cm)*cos(π/6)*θ'
0 = 140 cm^2/s -36 cm^2/s +420√3 cm^2*θ'
θ' = -104/(420√3) . . . . rad/s
.. = -26(√3)/315 . . . . . . rad/s
.. ≈ -8.19°/s

_____
The figure offers a sort of sanity check on the numbers.

i dont get this. can you explain

Answers

The rightmost column is the product shown in the middle column. From top-to-bottom, those numbers will be 83.1, 831 (given), 8310.

The middle column is a re-write of the first column and is equal to the third column. You can figure the numbers there from either direction. In the center row, you need 8.31 × ___ = 831. It should not be difficult for you to figure out the number in the blank is 100. (It is also the power of 10 between 10 in the first row and 1000 in the third row.)

The divisor in the first column is the inverse of the multiplier in the second column. 0.1 = 1/10, 0.01 = 1/100, and in the third row, 0.001 = 1/1000. The missing number in the first column is 0.001.

_____
The four missing numbers are 83.1, 100, 0.001, 8310. (top to bottom, left to right)

The lifetimes of batteries produced by the juicy battery company are normally distributed with a mean of 100 hours and a standard deviation of 10 hours. find the number of hours where at least 90% of the batteries will continue to operate at.

Answers

The z-score associated with 90% is:
P(0.9)=1.28
sup[pose the number of hours whereby at least 90% of the batteries will continue to operate is x.
the z-score is given by:
z=(x-μ)/σ
where:
μ is the mean
σ is the standard deviation
substituting the values we shall have:
1.28=(x-100)/10
solving for x we get:
x=112.8 hours

 

Johnson Certified bought a fiber optic cable for $975,000. The estimated life of the cable is 20 years, after which its salvage value is estimated to be $5,000. Using the straight-line method, what is the annual depreciation to the nearest cent?

Answers

Remember that straight line depreciation can be calculated using the formula:
[tex]D_{a}= \frac{C-R}{U} [/tex]
where
[tex]D_{a}[/tex] is the annual depreciation 
[tex]C[/tex] is cost
[tex]R[/tex] is the salvage value 
[tex]U[/tex] is the estimated life in years.

For our problem we know that [tex]C=975000[/tex], [tex]R=5000[/tex], and [tex]U=5000[/tex]. Lets replace those values in our formula to find [tex]D_{a}[/tex]:
[tex]D_{a}= \frac{975000-5000}{20} [/tex]
[tex]D_{a}= \frac{970000}{20} [/tex]
[tex]D_{a}=48500[/tex]

We can conclude that the annual depreciation of the optic fiber cable is $45,000

Suppose that after he makes his first shot, he shoots exactly 5 more shots. what is the probability that, out of these 5 attempts, he makes an even number of shots?

Answers

The probability of making 2 of 5 shots is 0.31250. The probability of making 4 of 5 shots is 0.15625. So, the probability of making an even number of shots is
.. 0.31250 +0.15625 = 0.46875

_____
p(2 of 5) = (5C2)/2^5 = 10/32
p(4 of 5) = (5C4)/2^5 = 5/32

For the above, we have assumed the probability of success is 1/2.

2) Suppose 3x + 4y = 52 and 5x + y = 30. What is the value of 8x − 2y?

Answers

Try this solution, note, the suggested option is not the shortest way.

Answer:

c

Step-by-step explanation:

If f(x) = 0.5x and g(x) = 0.25x. Which statement is true?

Answers

I FOUND YOUR COMPLETE QUESTION IN OTHER SOURCES.
 PLEASE SEE ATTACHED IMAGE.

 First, we rewrite both functions correctly:
 f (x) = 0.5 ^ x
 g (x) = 0.25 ^ x
 We observe that they are exponential functions, where, rewriting:
 f (x) = (1/2) ^ x
 g (x) = (1/4) ^ x
 We observe that both graphs present an exponential decay where, f (x)> g(x), since, the rate of change of f (x) (1/2) is greater than the rate of change of g (x) ( 1/4).
 Answer: 
 as -> infinity, f (x)> g (x) *

what is the answer to this word problem??

Answers

Let’s use m for months
So,
1st service
10m + 20

1. 10 + 20 =30
2. 10x2=20+20=40
3.10x3=30+20=50
4.10x4=40+20=60
5.10x5=50+20=70

2nd service
11m + 15

1. 11+15=26
2. 11x2=22+15=37
3 11x3=33+15=48
4.11x4=44+15=59
5.11x5=55+15=70

So, the 5th month the services cost the same

Hope this helps! ;)

P= s-c/s        solve for c

Answers

Therefore, the solution for c in terms of P and s is c = s(1 - P).

To solve for c in the equation P = (s - c) / s, you want to isolate c on one side. Here's the step-by-step:

Multiply both sides by s to eliminate the denominator: P × s = s - c.

Distribute P within s: Ps = s - c.

Now, get all terms containing c on one side: c = s - Ps.

So, the solution for c in terms of P and s is c = s - Ps, or c = s(1 - P).

During the two hours of the morning rush from 8
a.m. to 10
a.m., 100 customers per hour arrive at the coffee shop. the coffee shop has a capacity of 80 customers per hour. what is the number of customers waiting at 10
a.m.

Answers

80 customers per hour

A snail traveled 3 over 8, of an inch in 3 minutes. How many inches can the snail travel in 9 minutes? Express the answer as a decimal

Answers

So, first of all, let's convert the fraction [tex] \frac{3}{8} [/tex] into a decimal, which would be 0.375 (3 divided by 8)

The snail travels this far in 3 minutes. To find out how far it travels in nine minutes, we have to find out how many times 3 goes into 9.

9 / 3 = 3

Now. we simply multiply our decimal by three in order to get our answer!

0.375 x 3 = 1.125 inches

The answer is 1.125 inches!

find the area of the right triangle with the base length 30 inches and height 3 feet

Answers

A = (1/2)bh
.. = (1/2)(2.5 ft)*(3 ft) . . . . . . 30 inches = 2.5 feet
.. = 3.75 ft^2

Trigonometric Identities and Applications plz help

Answers

[tex]\bf \textit{Sum and Difference Identities} \\\\ sin(\alpha + \beta)=sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta)\\\\ -------------------------------\\\\ sin(A+B)=(0.35)(0.81)~~+~~(0.94)(0.58) \\\\\\ sin(A+B)=0.2835+0.5452[/tex]

Help with this algebra math question please

Answers

The answer is the 3rd one
For this case, the first thing you should know is that the cotangent is the inverse function of the tangent.
 We have then:
 cot (x) = 1 / (tan (x))
 Rewriting we have:
 cot (x) = 1 / ((sin (x)) / (cos (x)))
 We do double c:
 cot (x) = cos (x) / sin (x)
 Answer:
 cot (x) = cos (x) / sin (x)
 option 3

On a standardized test raw answer the first 22 questions in 5 minutes there are 77 questions on the test if he continues to answer questions at the same rate how long will it take him to complete the test from start to finish

Answers

Hello!

If you answered 22 questions on the test in 5 minutes, there will be an unequal time amount. 22 x 3 = 15 minutes (66 questions) 22 x 4 = 20 minutes (88 questions).
Therefore, it would take you 17.5 minutes to finish all the questions on your test.
Enjoy.

Answer:

Step-by-step explanation:

17.5

The relationship between the number of hours a plumber works and the total work fee she charges is proportional. Her fee for 5 hours of work is $350. Which of the following could be combinations of values for the plumber's work hours and total work fee she charges?

Answers

Answer: I saw someone else answer this and it doesn't match up with the choices so I decided to do this my self and for anyone else who might need this in the future. For those on Khan academy the answers are B, C, AND D.

Step-by-step explanation: I found the unit rate of 350 and 5, because we can use a calculator (as stated on top) I just punched in 350 divided by 5 and got 70. Now i know this may not sound that "professional", but nothing needs to always be professional as long as its efficient and most importantly gets you the right answer. I then took the time to multiply each number, (the ones on the left : 3, 3.5, 6, 7.25, and 8) by 70. If the answer you got on the calculator match up to the number on the right, (240, 420, 507.50, and 490) its correct, if it doesn't match up, you can tell that its most likely not the answer. You should end up with three answers that all end up having the unit rate of 70. Hope this helps anyone who needed it.

ANSWERS ARE B, C, AND D.

Following could be combinations of values for the plumber's work hours and total work fee she charges : 8 hours and $490, 7.25 hours and $500, 270 for 3 hours work. So, the correct choice of options for the image are B, C, and D.

Since the relationship between the number of hours a plumber works and the total work fee he charges is proportional, we can use the following equation to calculate the total work fee:

Total work fee = Number of hours worked * Hourly rate

Therefore, the following combinations of values for the plumber's work hours and total work fee are proportional:

8 hours and $490 (the hourly rate is $490/8 hours = $61.25)

7.25 hours and $500 (the hourly rate is $500/7.25 hours = $68.75)

6 hours and $420 (the hourly rate is $420/6 hours = $70)

The other two options, A and E, are not proportional.

For example, if the plumber works for 3 hours and charges $245, the hourly rate would be $245/3 hours = $81.67.

However, if the plumber works for 3.5 hours and charges $270, the hourly rate would be $270/3.5 hours = $77.14.

This shows that the hourly rate is not constant, so the relationship between the number of hours worked and the total work fee is not proportional.

The correct choice of options for the image are B, C, and D.

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Please help asap!!!
Which expression is equivalent to -9x^-1y^-9/-15^5y^-3
A.3/5x^5y^3
B.3/5x^6y^6
C.5/3x^5y^3
D.5/3x^6y^6

Answers

The answer is [tex]\frac{3}{5x^6y^6}[/tex].

Our original expression was
[tex]\frac{-9x^{-1}y^{-9}}{-15x^5y^{-3}}[/tex]

Negative exponents tell us to switch sides of the fraction; therefore they get moved as such:

[tex]\frac{-9y^3}{-15x^5x^1y^9}[/tex]

We can reduce the fraction we have:
[tex]\frac{3y^3}{5x^5x^1y^9}[/tex]

Using the product property of exponents we can combine the exponents on the denominator:
[tex]\frac{3y^3}{5x^6y^9}[/tex]

Using the division property of exponents, we subtract the exponents of y and get:
[tex]\frac{3}{5x^6y^6}[/tex]

You can rake a 20 square meter lawn in 10 minutes. If your mother asks you to rake your own lawn, which is 30 square meters, how long will it take you to do this?

Answers

20 square meter lawn..............................10 min
10 square meter lawn...............................5 min
30 square meter lawn in.........................5*3=15 min

A rectangular prism has a length of 5 centimeters, a width of 5 centimeters, and a height of 10 centimeters. The surface area of this prism is 250 square centimeters.

True or False

Answers

that is true because if you use the surface area formula, 2(wl+hl+hw), you'll get 250.

Edgar has a bird bath that holds 2 gallons of water. He only want to fill it 3/4 full. How much water in gallons should Edgar put in the bird bath?

Answers

In order to solve this problem, we need to multiply the total gallons the bath can hold with the amount he wants it full.

2 × 3/4 = 6/4 = 1 1/2

Edgar should put 1 1/2 gallons of water in the bath.

Hope this helps!

Rachel jogged along a trail that was 1/4 (fraction) of a mile long. She jogged along the trail 8 times. How many miles did Rachel jog in all??

Answers

1/4+1/4+1/4+1/4+1/4+1/4+1/4+1/4 = 8 Miles

1/4+1/4 = 1/2 Mile

1/2+1/2 = 1 Mile

1+1 = 2 Miles
2 miles because 8 divided by 1/4 is 2

Help! I’ve been stuck for like minuteeesss!!!

Answers

a. For each mile, you use 14.5/348=0.0417 gallons of gas. If you drive 2163 miles, you will use 0.0417*2163=90.2 gallons.

b. For each gallon, you can drive 348/14.5=24 miles. If you have 132 gallons, you can drive 132*24=3168 miles.

Bella Sandino failed to pay her cell phone bill in the amount of $85.14 by the due date of March 4. Calculate the amount Bella must pay on March 20 if the company charges 20% interest on late payments. Assume a 365-day year.

Answers

 $85.14/ 100= 0.8514 x 20= 17.028 + 85.14 = $102.168
85.14*(1 +0.20*16/365) = 85.89

There were three trains made of the cars with exactly the same number of passenger's seats. The first train had 418 seats, the second 456, and the third 494. How many cars were in each train, if it is known that each train had not more than 50 cars?

1 train=?

2 train=?

3 train=?

Answers

1 train=418  2 train=456  3train=494 add them all together and divide by 3      418+456+494=1368/3=456 i hope this helps you and each train has more than 50 cars
You apparently need to find the greatest common divisor of (418, 456, 494). You can start by looking at the differences between these numbers. They are
.. 456 -418 = 38
.. 494 -456 = 38
So, if 38 divides these numbers evenly, that is the number of seats in each car. (It does).

train 1 had 418/38 = 11 cars
train 2 had 456/38 = 12 cars
train 3 had 494/38 = 13 cars

_____
The number of seats in each car could be a sub-multiple of 38, say 19. In that case, the number of cars in each train would be twice the number shown above. It is slightly unusual for a train car to have an odd number of seats, but is not unheard of.

At a grocery store a four-pack of yogurt costs $3.95. How much does each container of yogurt cost

Answers

99 cents if you round up the 7.
about 99 cents or exactly 0.9875
Other Questions
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