Bookwork code: K27
,Calculator
allowed
A pendulum of length 18 cm is swinging from a fixed point, as shown.
Calculate the distance that the end of the pendulum travels when it swings
through an angle of 87°.
Give your answer in centimetres (cm) to 1 d.p.
87°
18 cm

Answers

Answer 1

The distance that the end of the pendulum travels when it swings is given by the relation D = 27.3 cm

Given data ,

A pendulum of length 18 cm is swinging from a fixed point

Now ,  it swings through an angle of 87°

So , Central Angle = ( s x 360° ) / 2πr

where s is the length of the arc

Now , D = ( θ/360 ) x 2πr

On simplifying , we get

D = ( 87 / 360 ) x 2 ( 3.14 ) ( 18 )

D = ( 0.241667 ) ( 113.04 )

D = 27.3 cm

Hence , the pendulum travels a distance of 27.3 cm

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Related Questions

What is the range of the function y=−7x−5?

Answers

Step-by-step explanation:

"Range'' is the values of 'y' that a graph can have....there are no limits on this one

(-∞,+∞)

Bir saat 4:15 saat ve dört yarım saat kaç şey kaç saat eder

Answers

Answer:

dört yarım saat 2 saattir

Step-by-step explanation:

Enter the number that belongs in the green box

Answers

Answer:

Set your calculator to Degree mode.

10² = 6.78² + 4² - 2(6.78)(4)(cos x)

100 = 61.9684 - 54.24(cos x)

38.0316 = -54.24(cos x)

cos x = -.701173

[tex]x = {cos}^{ - 1} ( - .701173)[/tex]

x = 134.52°

The equation a(s) = 37.5s - 1.5s2 models the function
represented in the table. Fill in the blank to complete the
restricted domain of the function. D = {0 ≤s ≤

Answers

The restricted domain of the function is 0≤s≤25

The equation is a(s) = 37.5s - 1.5s²  models the function represented in the table

a(s) = s(37.5 - 1.5s)

The critical points are s=0 or

37.5 - 1.5s

37.5 = 1.5s

s=25

As area can not be negative, the area should be positive

s< 0 and s>25

Therefore, restricted domain is 0≤s≤25

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The equilateral triangle shown has a perimeter of 30 inches and a height of a inches.
What is the value of a?
O 5 in
O 5√3 in
O10 in
•10√3 in

Answers

The height of the equilateral triangle is a = 5√3 inches

Given data ,

Since the triangle is equilateral, all sides are of equal length.

Let's call the length of one side x.

Therefore, the perimeter of the triangle is 3x, which is given to be 30 inches.

On simplifying , we get

3x = 30

x = 10

Now, we know that the height of an equilateral triangle is given by the formula:

height = √3/2 x

Substituting the value of x, we get:

height = √3/2 x 10

height = 5√3 inches

Hence , the height of triangle is 5√3 inches

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If the Coach chooses the Three-Year Plan, what is the total amount he will spend after 12 months? ANSWER QUICK ILL GIVE BRAINLIST!​

Answers

Answer:

$17,320 after 12 months.

Step-by-step explanation:

f the Coach chooses the Three-Year Plan, the total amount he will spend after 12 months can be calculated as follows:

First, we need to calculate the total amount of monthly payments made in 12 months:

12 months x $610 per month = $7,320

Then, we need to add the down payment made at the time of purchase:

$7,320 + $10,000 = $17,320

Therefore, if the Coach chooses the Three-Year Plan, he will spend a total of $17,320 after 12 months.

Which expression is a function that has zeros at 4 and –3?

Answers

Answer:

[tex]f(x) = (x - 4)(x + 3) [/tex]

[tex]f(x) = {x}^{2} - x - 12[/tex]

Find the sum of -17x,-15x,-2x

Answers

-17x + (-15x) + (-2x) = -17x-15x-2x = -34x

i really need the answer to this, can anyone help me please?

Answers

The value of total area of the shape is,

⇒ 82 cm²

We have to given that;

Figure of shape is shown.

Since, Figure is made by three rectangles.

And, Area of rectangle is,

A = length x width

Hence, The area of upper rectangle is,

A = 3 x 8

A = 24 cm²

Area of middle rectangle is,

A = (11 - (3 + 5)) x (8 - 2)

A = 3 × 6

A = 18 cm²

Area of lower rectangle is,

A = 5 x 8

A = 40 cm²

Thus, The value of total area of the shape is,

⇒ 24 + 18 + 40 cm²

⇒ 82 cm²

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y intercepts of f((x)=x^{2}+2x-3

Answers

Answer:

The y-intercept is -3

Written as a point it is (0, -3)

Step-by-step explanation:

To find the y-intercept, let x = 0

(and to find x-intercepts, let y = 0)

So let's let x = 0

f(x) = x^2 + 2x - 3

y = x^2 + 2x - 3

y = 0^2 + 2(0) - 3

y = -3

This means the y-intercept is -3. The graph crosses the y-axis at -3. This is the point (0, -3).

If a town's population doubles every 4 years, how
many people will be in the down 12 years later if the
current population is 28,100? y = ab*

Answers

The population of the town 12 years later will be 224,800 if the current population is 28,100 and the population doubles every 4 years.

Since the population doubles every 4 years, we can use the formula:

P = P0 x [tex]2^{t/4}[/tex]

where P0 is the initial population, t is the time elapsed in years, and P is the population after time t.

In this case, the initial population P0 is 28,100, and we want to know the population after 12 years, so t = 12. Substituting these values into the formula, we get:

P = 28,100  2^(12/4)

  = 28,100 x 2³

  = 28,100 * 8 = 224,800

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Question
Evaluate |—15u| + |3v| + 3 when u
=
3 and v = 3.

Answers

The value of given expression is 57.

We are given that;

|—15u| + |3v| + 3

u=3, v = 3

Now,

To evaluate the expression, you need to substitute the values of u and v and simplify. The absolute value of a number is the distance from zero on the number line, so it is always positive or zero. You can write your solution as:

|—15u| + |3v| + 3 = |—15(3)| + |3(3)| + 3 = |—45| + |9| + 3 = 45 + 9 + 3 = 57

Therefore, by the given expression the answer will be 57.

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Five runners need to be arranged in 5 lanes for a race so that there is a runner in each lane

How many unique ways are there to arrange the numbers in the 5 lanes

Answers

Step-by-step explanation:

5 P 5 = 120 ways = 5!

A random sample of 16 ATM transactions shows the mean transaction time of 2.8 minutes with a standard deviation of 1.2 minutes. Can you show the width of the 90 percent confidence interval for the true mean transaction time?

Answers

The width of the confidence interval is 1.2786.

From the question we are told that

The sample size is n = 16    

The mean time is x = 2.8 minutes

The standard deviation is = 1.2 minutes

Generally, the degree of freedom is mathematically represented as  

df = n-1

df = 15

From the question we are told the confidence level is 95%, hence the level of significance is =

α = 100-95

α = 0.05

Generally, the margin of error is mathematically represented as =

[tex]E = t_{\alpha/2}, 15 \times \sigma/\sqrt{n}[/tex]

E = 2.131 × 1.6 / √16

E = 0.6393

Generally, the width the confidence 95% confidence interval  

W = 2E

W = 1.2786

Hence the width of the confidence interval is 1.2786.

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Solve for x. Round to the nearest tenth of a degree, if necessary.

Answers

Answer: 29.9986-----30.0 degrees

Step-by-step explanation:

x = [tex]tan^-^1(5.6/9.7)\\\\toa[/tex]

[tex]\tan(x )=\cfrac{\stackrel{opposite}{5.6}}{\underset{adjacent}{9.7}} \implies \tan^{-1}(~~\tan( x )~~) \approx \tan^{-1}\left( 0.58 \right) \\\\\\ x \approx\tan^{-1}\left( 0.58 \right)\implies x \approx 30.0^o[/tex]

Please help really urgent

Answers

Answer:

0.0909

Step-by-step explanation:

4 blue + 5 red + 3 black = 12 chips in total.

p=probability

1st draw:

p (blue) = 4/12

there are now 11 chips in the bag, 4-1 =3 are blue.

2nd draw?

p (blue) = 3/11

probability of pulling one blue chip followed by another blue chip is:

(4/12) X (3/11) = (4X3)/12X11)

= (12)/(132)

= 1/11

0.0909

In a certain Integrated Math II class of 29 students, 6 of them play golf and 14 of them play soccer. There are 9 students who play neither. Create a table to find probabilities.
5. What is the probability that a student chosen randomly from the class plays golf or
soccer?
6. What is the probability that a student chosen randomly from the class plays golf and soccer?
I rlly need the help!

Answers

The solution is:

20/29 is the probability that a student chosen randomly from the class plays golf or soccer.

0 is the probability that a student chosen randomly from the class plays golf and soccer.

Here, we have,

given that,

In a certain Integrated Math II class of 29 students, 6 of them play golf and 14 of them play soccer.

There are 9 students who play neither.

Number of students that play = 20

let, students play golf = A

students play soccer = B

so, given that,

n ( A) = 6 and, n ( B) = 14

so, total sample space = 29

now, P(A) = 6/29

P(B) = 14/29

and, P(students who play neither) = 9/29

we get, 6/29 + 14/ 29 + 9/29 = 29/29 = 1

i.e. there are no students who play both golf and soccer = 0

all the events are independent.

so, we have,

the probability that a student chosen randomly from the class plays golf or soccer = P(A) + P(B)

               = 6/29 + 14/ 29

               = 20/29

and, the probability that a student chosen randomly from the class plays golf and soccer = 0.

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(22-26)²+(34-26)²+(30-26)²+(14-26)²+(30-26)[tex]\frac{x}{y}[/tex]5

Answers

Answer:

[tex]20x+240y/y[/tex]

Step-by-step explanation:

1. Subtract the numbers

2. Evaluate the exponents

3. Subtract the numbers, again

4. Have a great day and thx for your inquiry :)

100 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!

Answers

Answer:

Refer to the step-by-step.

Step-by-step explanation:

Verify the given identity.

[tex]E_0\cos^4(\theta)=E_0(\frac{1}{2} +\frac{\cos(2\theta)}{2} )^2[/tex]

Pick the more complex side to manipulate, in this case it is the R.H.S.

(1) - Apply the following double-angle identity

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Double-Angle Identity:}}\\\\\cos(2A)=1-2\sin^2(A)\end{array}\right}[/tex]

[tex]E_0(\frac{1}{2} +\frac{\cos(2\theta)}{2} )^2\\\\\Longrightarrow \boxed{ E_0\Big(\frac{1}{2} +\frac{1-2\sin^2(\theta)}{2}\Big )^2}[/tex]

(2) - Split of the right fraction

[tex]E_0(\frac{1}{2} +\frac{1-2\sin^2(\theta)}{2} )^2\\\\\Longrightarrow E_0(\frac{1}{2} +\frac{1}{2} -\frac{2\sin^2(\theta)}{2})^2\\\\\Longrightarrow \boxed{E_0(1 -sin^2(\theta))^2}[/tex]

Apply the following Pythagorean identity

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Pythagorean Identity:}}\\\\1-\sin^2(A)=\cos^2(A)\end{array}\right}[/tex]

[tex]E_0(1 -sin^2(\theta))^2\\ \\\Longrightarrow E_0(\cos^2(\theta))^2\\\\\therefore \boxed{E_0\cos^4(\theta)=E_0\cos^4(\theta)}[/tex]

Thus, the identity is verified.

It has been proven and verified that [tex]E_0cos^4 \theta = E_0(\frac{1}{2} +\frac{cos2 \theta}{2} )^2[/tex] below.

How to verify the equality of the cosine function?

In Mathematics and Geometry, the standard equation of a cosine function is represented or modeled by the following mathematical equation (formula):

y = Acos(Bx - C) + D

Where:

A represents the amplitude.B = 2π/P.P represents the period.C represents the phase shift.D represents the center line (midline).

In this exercise, you are required to prove that the right-hand side of the cosine function is equal to left-hand side of the cosine function;

[tex]E_0cos^4 \theta = E_0(\frac{1}{2} +\frac{cos2 \theta}{2} )^2[/tex]

From the double-angle formulas, we have:

2sin²θ = 1 - cos2θ

cos2θ = 1 - 2sin²θ

Next, we would evaluate the right-hand side of the cosine function by substituting "1 - 2sin²θ" for cos2θ as follows;

[tex]E_0cos^4 \theta = E_0(\frac{1}{2} +\frac{1-2sin^2 \theta}{2} )^2\\\\E_0cos^4 \theta = E_0(\frac{1}{2} +\frac{1}{2} -\frac{2sin^2 \theta}{2})^2\\\\E_0cos^4 \theta = E_0(1 -\frac{2sin^2 \theta}{2})^2\\\\E_0cos^4 \theta = E_0(1 -sin^2 \theta)^2\\\\[/tex]

E₀cos⁴θ = E₀(1² - (sin²θ)²)

E₀cos⁴θ = E₀(1 - sin⁴θ)  ⇒ (Verified).

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The equation y=195(1.10)x can be used to represent growth in the number of Salad Supreme restaurants since 2005. Which is the most reasonable conclusion based on this information? A. Salad Supreme had 110 restaurants in 2005. B. Salad Supreme is increasing the number of restaurants by 10% each year. C. Salad Supreme is increasing the number of restaurants by 195 each year. D. Salad Supreme is increasing the number of restaurants by 110% each year.

Answers

The most reasonable conclusion based on the given information is: Salad Supreme is increasing the number of restaurants by 10% each year. Option B

How to determine the most reasonable conclusion

Based on the given equation y = 195(1.10)^x, where x represents the number of years since 2005 and y represents the number of Salad Supreme restaurants, we can draw the following conclusions:

A. Salad Supreme had 110 restaurants in 2005: This conclusion is not supported by the given equation.

B. Salad Supreme is increasing the number of restaurants by 10% each year: This conclusion is supported by the equation.

C. Salad Supreme is increasing the number of restaurants by 195 each year: This conclusion is not supported by the equation.

D. Salad Supreme is increasing the number of restaurants by 110% each year: This conclusion is not supported by the equation. The growth factor of 1.10 (or 10%) indicates a 10% increase each year, not 110%.

Therefore, the most reasonable conclusion based on the given information is: Salad Supreme is increasing the number of restaurants by 10% each year.

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Which of the following statements are true regarding the reflection of A(1 1/2,-2)? Select all that apply..

Answers

The correct statements are:

A) When this point is reflected across the x-axis, the x-coordinate stays the same and the y-coordinates are opposites.C) When this point is reflected across the y-axis, the x-coordinates are opposites and the y-coordinate stays the same.D) When this point is reflected across the x-axis, the x-coordinates are opposites and the y-coordinate stays the same.

How to explain the statements

When a point is reflected across the x-axis, the x-coordinate remains the same, but the y-coordinate changes sign. Therefore, statement A) is true.

When a point is reflected across the y-axis, the y-coordinate remains the same, but the x-coordinate changes sign. Therefore, statement C) is true.

It should be noted that to represent the reflection of point A (1,-2) across the y-axis, we flip the sign of the x-coordinate to obtain the image point A' (-1,-2). Therefore, statement D) is true.

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In Exercises
frequencies.
9.
Gender
9 and 10, find and interpret the marginal
(See Example 1.)
Male
Female
Set Academic Goals
No
168
142
Yes
64
54
suport
no sas8

Answers

09. The total sample, 118 individuals set academic goals (regardless of gender), while 310 individuals did not set academic goals.

10. The total sample, 290 individuals have cats, while 306 individuals do not have cats. Furthermore, 312 individuals have dogs, while 284 individuals do not have dogs.

In order to find the marginal frequencies, we need to calculate the totals for each category separately.

For question 9:

The marginal frequency for "Set Academic Goals - yes" is 64 + 54 = 118. This represents the total number of individuals who answered "yes" to setting academic goals.

The marginal frequency for "Set Academic Goals - no" is 168 + 142 = 310. This represents the total number of individuals who answered "no" to setting academic goals.

The marginal frequency for "Male" is 64 + 168 = 232. This represents the total number of males.

The marginal frequency for "Female" is 54 + 142 = 196. This represents the total number of females.

Interpretation:

The marginal frequencies provide us with the total counts for each category in a contingency table. In this case, we can see that out of the total sample, 118 individuals set academic goals (regardless of gender), while 310 individuals did not set academic goals. Additionally, there were 232 males and 196 females in the sample.

For question 10:

The marginal frequency for "Cat - yes" is 104 + 186 = 290. This represents the total number of individuals who have cats.

The marginal frequency for "Cat - no" is 208 + 98 = 306. This represents the total number of individuals who do not have cats.

The marginal frequency for "Dog - yes" is 104 + 208 = 312. This represents the total number of individuals who have dogs.

The marginal frequency for "Dog - no" is 186 + 98 = 284. This represents the total number of individuals who do not have dogs.

Interpretation:

The marginal frequencies reveal the total counts for each category in the contingency table. In this case, we can observe that out of the total sample, 290 individuals have cats, while 306 individuals do not have cats. Furthermore, 312 individuals have dogs, while 284 individuals do not have dogs.

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1,3,5,7,9…. What is the next number

Answers

Answer: 11

Step-by-step explanation:

this is a sequence of odd numbers.

it goes;

1,3,5,7,9,11,13,15,17,19,21,23....

John collected data to determine how many minutes his teammates spend practicing basketball each night. Identify the outlier in his data.

Question 1 options:

10 minutes


40 minutes


30 minutes


5 minutes

Answers

Answer:

Step-by-step explanation:

5 minutes is the outlier. It sticks out from the rest.

QUESTION 8 1 POINT
.
Find the GCF of the following three monomials:
21x³y5
63x5y²
45x¹y³

Answers

The greatest common factor (GCF) of the three monomial, 21x³y⁵, 63x⁵y² and 45x¹y³ is 3xy²

How do i determine the greatest common factor (GCF)?

The greatest common factor (GCF) of the three monomials, 21x³y5, 63x5y² and 45x¹y³ can be obtained as follow:

First, we shall determine the factors of each monomials. This is illustrated below:

21x³y⁵ = 3 × 7 × x × x × x × y × y × y × y × y

63x⁵y² = 3 × 3 × 7 × x × x × x × x × x × y × y

45x¹y³ = 3 × 3 × 5 × x × y × y × y

Finally, we shall determine the greatest common factor (GCF) from the factors listed above. This is shown below:

3 × x × y × y = 3xy²

Thus, we can conlude that the greatest common factor (GCF) of the three monomials is 3xy²

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convert 500 cm to m?​

Answers

Hello!

m     dm    cm    mm

5   ,   0        0

500cm = 5m

HELP! Whoever answers first to get marked as brainliest!

Answers

Pick the first option.

f(x) is dependent on x.

the 2nd option is wrong; the dependent variable is the output, the independent variable is the input.

3rd option is wrong, dependent determines the range.

4th is wrong, x is independent variable.

Evaluate the following question given below

Answers

The solution is, simplification of the expression is; 71.19.

Here, we have,

the given expression is:

(5/2)^4/2 * (3/2)^6

=(5/2)^2 * (3/2)^6

as we know that, 4/2 = 2.

now, we have,

(5/2)^2 * (3/2)^6

=5²/2² ^ 3⁶/2⁶

= 5² * 3⁶ / 2² * 2⁶

=5² * 3⁶  / 2 ^ (2+6)

=5² * 3⁶  / 2 ^8

=25 * 729/ 256

=18225/ 256

=71.19

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Help please im not that good in math

Answers

Answer: the awnser is b

Step-by-step explanation:

PLEASE HELP ME
Which of these triangles are definitely right triangles?
(Note that not all triangles are drawn to scale.)
(Select all that apply.)
A
B
C
D
E

Answers

Answer:

I'd like to explain more but I have limited comment

chat me up

A

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The waste material that is cleared away during surface mining in order to access *a mineral deposit. Includes rocks, soil, and vegetation):O OverburdenO WastificationClear CuttingONuisance ClearingBackSubmitPage 2 of 2Clear form On January 1, 2026, Bonita Inc. granted stock options to officers and key employees for the purchase of 18,000 shares of the company's $10 par common stock at $27 per share. The options were exercisable within a 5-year period beginning January 1,2028 , by grantees still in the employ of the company, and expiring December 31,2032. The service period for this award is 2 years. Assume that the fair value option-pricing model determines total compensation expense to be $379,600. On April 1, 2027, 1,800 options were terminated when the employees resigned from the company. The market price of the common stock was $35 per share on this date. On March 31, 2028, 10,800 options were exercised when the market price of the common stock was $39 per share. Prepare journal entries to record issuance of the stock options, termination of the stock options, exercise of the stock options, and charges to compensation expense, for the years ended December 31, 2026, 2027, and 2028. (List all debit entries before credit entries. Credit account titles are automatically indented when amount is entered. Do not indent manually. If no entry is required, select "No Entry" for the account titles and enter 0 for the amounts. Record entries in the order displayed in the problem statement i found ______ who could do the calculation. may be the question was tough. A. no one B. someone C. anyone D. everyone through which mechanism does bronchiolitis cause the destruction of alveoli? is emphysema genetic? can environmental factors increase the risk of emphysema? why or why not PLEASE HELP ME FAST////////////// How many intersections are there between the graphs of f(x) = Ix^2-4I and g(x)+2^x? what events led to the hunter games and what purpose are the game meant to serve? cite specific textual evidence from paragraph 8 of chapter 1 to support your answer unlike victims of other crimes, hate crime victims are unable to: A stainless steel patio heater is a square pyramid. The length of one side of the base is 25.2 in. The slant height of the pyramid is 93.7 in. What is the height of the pyramid? an oscilloscope is set in the 2volt per division scale. the signal measures three whole divisions. what is the value of voltage? Which major actor is at the center of the foreign exchange market?A) corporations B) central banks C) commercial banks D) non-bank financial institutions E) individual firms an adult female client is about to undergo a physical assessment conducted by a nurse practitioner at the gynecology clinic. the nurse is preparing the room for a complete head-to-toe examination, along with a genitalia and rectal assessment and screening through the papanicolaou test. what should the nurse do next before proceeding? individuals and groups will develop formal alliances that are informally structured and organizationally determined please i need help on this how does the ability to product differentiate benefit a monopolistically competitive firm? product differentiation increases the costs of production. allows monopolistically competitive firms to compete on quantity. affects perfectly competitive firms, not monopolistically competitive firms. allows monopolistically competitive firms to compete on price and quality. what is the reactance of an inductor with an inductance of 2.60 h at a frequency of 82.0 hz ? express your answer in ohms. question 7 you have just finished analyzing data for a marketing project. before moving forward, you share your results with members of the marketing team to see if they might have additional insights into the business problem. what process does this support? which one of the following is a diprotic acid? view available hint(s) for part c sulfuric acid barium hydroxide nitric acid chloric acid Find the solutions of the quadratic equation x2 + 7x + 10 = 0.OA) X=-7, -3B) x=2,5OC) x = 7,3OD) x = -2, -5 Which of the following is not a valid arithmetic operator? O a (division Db (exponentation Omultiplication d. (addition) modulas division Ostraction