A pendulum swings through an angle of 14° each second. If the pendulum is 14 cm in length and the complete swing from right to left last two seconds what area is covered by each complete swing?
Answers
Answer;
\(\text{Area = 47.90 cm}^2\)Explanation;
Firstly, we need a diagrammatic representation to get what is described in the question.
We have this as follows;
Now, from what we have here, the total angle swept by the pendulum moving from left to right is 28 degrees
To get the area, we simply need to find the area of the sector formed by the by pendulum
Mathematically, we have the area of a sector calculated as follows;
\(A\text{ = }\frac{\theta}{360}\times\pi\times R^2\)theta is the angle made by the pendulum in one complete swing which is 28 degrees
pi is 22/7
R is the length of the pendulum which is 14 cm
Substituting these values in the formula above, we have it that;
\(\begin{gathered} A=\frac{28}{360}\times\frac{22}{7}\times14^2 \\ \\ A=47.90cm^2 \end{gathered}\)
Related Questions
When Stretch Gordon signed a contract to play basketball for the Toronto Raptors, he received a one-time $250 000 signing bonus. His contract said that he would also receive $100 000 for each game he plays.
The Raptors are scheduled to play 85 games this season.
Create a table of values that will show some of the possible amounts Stretch might earn throughout the first season. Number of games played is represented by n and money earned by E.
Graph the information to show his earnings for the season. Use a suitable scale. Change the money values in your table to millions of dollars before starting.
i) Write an equation relating Stretch's earnings to the number of games he plays.
ii) Define your variables, including units.
iii) Explain what the numbers in your equation represent for Stretch.
How much money will Stretch make if he plays 44 games this season? Show your work.
Stretch's twin brother, Rory, has been offered a different contract. The following equation defines the offer: E = 95 000n + 450 000
E represents Rory's total earnings in dollars and n represents the number of games Rory plays. Is this a better offer than Stretch's? Give reasons for your answer by comparing the two offers, reporting mathematical details about the comparison.
Answers
Answer:
Here's what I get
Step-by-step explanation:
Stretch
(i) The equation
E = 250 000 + 100 000n
(ii) Variables
n = the number of games played
E = Stretch's total earnings in dollars
(iii) Constants
$250 000 = Stretch's signing bonus
$100 000 = the money earned for each game.
\(\begin{array}{ccc}\textbf{Games played} & \textbf{ Earnings/}\mathbf{\$}&\textbf{Earnings/}\mathbf{\$10^{6}} \\20 & 2 350 000 &2.35\\40 & 4 250 000&4.25 \\60 & 6 150 000 &6.15\\80 & 8 050 000&8.05 \\\end{array}\)
The graph shows how Stretch's total earnings vary with the number of games played.
(iv) Total earnings after 44 games
\(\begin{array}{rcl}E & = & 250000 + 100000n\\& = &250000 + 100000(44)\\& = &250000 + 4400000\\& = & \mathbf{4 650 000}\\\end{array}\)
Rory
E = 95 000n + 450 000
Rory's deal is better than Stretch's if they play fewer than 40 games.
He starts off with a bigger signing bonus, but Stretch earns more money per game.
Stretch closes the gap with each game played.
By 40 games they have the same total earnings.
After 40 games Stretch has more total earnings.
Draw the net and calculate the surface area .
Answers
Hello!
surface area
= 2(4 x 2) + 2(12 x 4) + 2(12 x 2)
= 160cm²
A-Rod Manufacturing Company is trying to calculate its cost of capital for use in making a capital budgeting decision. Mr. Jeter, the vice-president of finance, has given you the following information and has asked you to compute the weighted average cost of capital.
The company currently has outstanding a bond with a 10.9 percent coupon rate and another bond with an 8.5 percent rate. The firm has been informed by its investment banker that bonds of equal risk and credit rating are now selling to yield 11.8 percent. The common stock has a price of $63 and an expected dividend (D1) of $1.83 per share. The historical growth pattern (g) for dividends is as follows:
Answers
The WACC for A-Rod Manufacturing Company is 11.2%.
how to get A-Rod Manufacturing Company's weighted average cost of capital (WACC):
Determine the debt's cost. The yield on the company's outstanding bonds is the cost of debt. In this instance, the company's bond yield is 11.8%.
Determine the preferred stock's price. The dividend yield on the company's preferred stock is the cost of preferred stock. In this instance, the preferred stock of the corporation has a dividend yield of 8.5 percent.
Determine the equity cost. The anticipated return that investors expect on the company's common shares is known as the cost of equity. The dividend discount model is one popular way to determine the cost of equity among the many other approaches. The cost of this model's
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Which Expressions are equivalent to 3/5x +3
Answers
Answer:
A and B
Step-by-step explanation:
B)The top is cut off but if it says 3/5x then that is the answer.... 4/5x-1/5x is 3/5x and the +3 stays the same
the answer for these questions
Answers
The triangles are similar by SSS congruence of triangles.
What is SSS congruence of triangles?
The two triangles are congruent if the three sides of one triangle are the same as the corresponding three sides (SSS) of the other triangle.
We are given two triangle ABC and PQR.
In order to see whether these are similar or not, we will use the SSS congruence of triangles.
The ratio of sides are:
⇒AB : PQ = 8 : 6
⇒AB : PQ = 4 : 3
Similarly,
⇒BC : QR = 12 : 9
⇒BC : QR = 4 : 3
Similarly,
⇒AC : PR = 12 : 9
⇒AC : PR = 4 : 3
Since, the ratio of all the sides is same so, the triangles are similar.
Hence, the triangles are similar by SSS congruence of triangles.
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Since, there are multiple questions so, the question answered above is attached below
For a camping trip, Jack is preparing water canteens. The canteens each hold 1/3 gallon of water.
How many canteens can Jack fill if he has 14 gallons of water?
Answers
Answer:
42 canteens
Step-by-step explanation:
1 gal = 3 canteens
14*3=42
Kelli had $ 0.55 to buy a sandwich. Gustavo had $ 1.64. They decided to buy a snack together and share it. How much money do they have between the two of them? Use models to solve the problem.
Help me plz
20 points if u do
Answers
Answer:
$1.09 per sandwich
Step-by-step explanation:
$1.64-0.55 = $1.09 per sandwich
Giving a test to a group of students, the grades and gender are summarized below
A B C Total
Male 12 10 17 39
Female 2 19 3 24
Total 14 29 20 63
If one student was chosen at random,
find the probability that the student got a B.
Answers
So we can simply take the total number of students that got B and the total number of students overall. That will be 29/63.
29 divided by 63 is 0.46. Multiply that by 100 and you’ll convert that to a percentage, which is 46%.
If one student was chosen at random, the probability that the student got a B is 46%.
Hope this helped!
HELP PLEASEEEEEEEEEEEEEEE ITS A GRADE
Answers
Answer:
1. b
2. d
3. a
4. A
Step-by-step explanation:
Answer: ITs A
Step-by-step explanation:
Because they are all real numbers and the other options are incorrect
10.8.8 Check Your Understanding
Allison went on a business trip and stayed at a hotel for three nights. She paid a total of $782.07 for the room and to
park her car. Each night, the hotel charged d dollars and $17.20 for parking. Which equation represents the total
amount, in dollars, Allison paid for the three nights?
A) d+3(17.20) = 782.07
(B) 3d+17.20 = 782.07
C) 3(d-17.20) = 782.07
D) 3(d+17.20) = 782.07
Answers
We can see that the correct equation that can depict the problem is 3(d+17.20) = 782.07. Option D
Which equation shows the total charge?We have to look at the problem that we have here. In the case of the question that we have been asked, we can see that for the problem that has been given here, it is clear that; Allison went on a business trip and stayed at a hotel for three nights. She paid a total of $782.07 for the room and to park her car.
If it is known that Each night, the hotel charged d dollars and $17.20 for parking. We can say that let the amount that is charged for the lodging be d and we have the equation as; 3(d+17.20) = 782.07.
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I need Help please!!!
Answers
Step-by-step explanation:
it seems you solved the tricky part yourself already.
just to be sure, let's do the first derivative here again.
the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...
f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =
= 3t⁴ + 18t³ + 24t² + 18t + 21
f'(t) = 12t³ + 54t² + 48t + 18
and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).
we simply put the input number (2) at every place of the input variable (t).
so,
f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =
= 426
Use the image to answer the question. A vertical number line starting at negative 10 on the bottom of the line with tick marks every one unit up to positive 10 at the top. The point negative 4.5 is labeled. What does the absolute value of the point labeled in the image mean if the number line represents temperature change? There was no change in temperature. The temperature equals 4.5 degrees. The temperature decreased 4.5 degrees. The temperature increased 4.5 degrees. HURRY UP
Answers
Since the point negative 4.5 (-4.5) is labeled on this number line representing temperature change, the absolute value of the point labeled in the image means that: B. the temperature equals 4.5 degrees.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).
In conclusion, the absolute value of a number is always positive and it can be used for describing the distance of a number from zero (0) on the number line, without taking its direction into consideration.
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A restaurant bill is $75. You want to leave about a 20% tip. Which is a 20% tip?
Answers
The tip is $15
rewrite -3(5u+5)+10u in simplest form
Answers
Answer:
-5u-15
Step-by-step explanation:
-3(5u+5)+10u
-15u-15+10u
-5u-15
Collect the like term which is -15u and 10u
You get -5u-15 which is your answer
The average rate of change of g(x) between x = 4 and x = 7 is Five-sixths. Which statement must be true?
Answers
- g(7) - g(4) = 5/6
- g(x) is a linear function
- The slope of the tangent line to g(x) at x = 5.5 is 5/6
- The derivative of g(x) at x = 5.5 is 5/6
- The graph of g(x) is concave up on the interval [4, 7]
- The graph of g(x) has a local maximum at x = 5.5 and a local minimum at x = 6.5.
Please help I will give brainliest
Answers
Answer:
D
Step-by-step explanation:
IM RLY SORRY IF THIS IS WRONG IM DOING THIS FORM MEMORY
so I'm pretty sure u the arch equals twice the angle
so pi/2*2 = pi so D
hope it helppsss
trying not to dieT-T
Two alien spaceships start traveling toward each other from space stations that are 710,000 km apart. The first spaceship started an hour before the second spaceship and is traveling at 110,000 km/hr. In how many hours will the two spaceships meet if the second spaceship is traveling at 90,000 km/hr?
Answers
Answer:
They will meet after 4 hours from the departure------------------------
The distance is 710000 km and the first spaceship has travelled 110000 km in the first hour.
The remainder of the distance is reducing by:
110000 + 90000 = 200000 km an hourTime to travel before they meet:
(710000 - 110000)/200000 = 600000/200000 = 3 hoursAdd the first hour to this to get total travel time of 4 hours.
Determine whether the following individual events are independent or dependent. Then find the probability of the combined event.
In a town where 1/4 of the days are sunny and 3/4 are cloudy, the next six days are all sunny.
Answers
The probability of the combined event that the next six days are all sunny is 1/4096
How to determine the probability all days being sunny?From the question, we have the following parameters that can be used in our computation:
Probability that it is sunny = 1/4
Probability that it is cloudy = 3/4
Number of days = 6
The probability for all six days, it is sunny is represented as
Probability = Probability that it is sunny^Number of days
Substitute the known values in the above equation, so, we have the following representation
Probability = (1/4)⁶
Express as decimal
Probability = (0.25)⁶
Evaluate the exponent
Probability = 1/4096
Hence, the probability is 1/4096
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I’m a certain magnetic field the cross-sectional area is 0.5 meter square and the flux is 1500 uwb what is the flux density
Answers
The flux density is 3000 uT.
Flux density (B) is a measure οf the strength οf a magnetic field in a given regiοn.
Hοw tο calculate flux density fοr the given prοblem?It is defined as the amοunt οf magnetic flux () that passes thrοugh a unit area (A) perpendicular tο the magnetic field's directiοn.
The flux density (B) can be calculated using the fοrmula:
B = Φ / A
where 'Φ' is -> flux and A is the -> crοss-sectiοnal area.
Plugging in the values given, we get:
B = 1500 uWb / 0.5 m²
B = 3000 uT (micrοtesla)
Therefοre, the flux density is 3000 uT.
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After collecting eggs from his chickens, Dale puts the eggs into cartons to sell. Dale fills 15 cartons and has 7 eggs leftover. Each carton holds 12 eggs.
Answers
Answer:
Dear User,
Answer to your query is provided below
If you are asking How many eggs collected from chickens then that is 187eggs
Step-by-step explanation:
Dale puts the eggs into cartons to sell. Dale fills 15 cartons and has 7 eggs leftover. Each carton holds 12 eggs.
So, 15x12 = 180
Plus 7 eggs leftover
Total = 180+7 =187
what is the value of g
Answers
Answer:
the value of g is gram .
may this answer is helpful for you
A delivery person has two different delivery routes that he follows. The first route is 20.75 miles long and the second is 33.25 miles long. He travels each route 4 times a week. After 8 weeks, how many total miles has he traveled?
Answers
Answer:
He travelled: 1728 miles
Step-by-step explanation:
20.75 * 4 = 83 (Route A miles a week)
33.25 * 4 = 133 (Route B miles a week)
83 + 133 = 216 (Route A + Route B)
216 * 8 = 1728
Rodrigo made 6/8 of a pound of trail mix. If he puts 1/4 of a pound into each bag, how many bags can Rodrigo fill?
Answers
Answer:
He can fill 3 bags
Step-by-step explanation:
You would first make them have a common denominator so you would have 2/8 instead of 1/4 then you would do 6/8 divided by 2/8 to get 3
1/4 = 2/8
6/8 divided by 2/8 = 3
Answer:3 1/4=2/8 if it's 6/8 then you divide and get three.
Question 5 (5 points)
image
What's the range of this function graph?
Question 5 options:
A)
(–∞,2)
B)
[2,∞)
C)
(–2,∞)
D)
[–2,∞]
Answers
9514 1404 393
Answer:
B) [2,∞)
Step-by-step explanation:
The range is the vertical extent of the graph. Here, the minimum is 2, and it goes up from there. The range is ...
[2, ∞)
Please use the following for the next 6 questions. Suppose that the average weekly earnings for employees in general automotive repair shops is $450, and that the population standard deviation for the earnings for such employees is $50. A sample of 100 such employees is selected at random.
1) What is the probability distribution of the average weekly earnings for employees in general automotive repair shops?
2) Find the probability that the average weekly earnings is less than $445.
3) Find the probability that the average weekly earnings is exactly equal to $445.
4) Find the probability that the average weekly earnings is between $445 and $455.
5) In answering the previous 3 questions, did you have to make any assumptions about the population distribution?
6) Now assume that the weekly earnings for employees in all general automotive repair shops is normally distributed, obtain the probability that a given employee will earn more than $480 in a given week.
Answers
1) The probability distribution of the average weekly earnings for employees in general automotive repair shops is the sampling distribution of the sample mean. According to the Central Limit Theorem, if the sample size is large enough, the sampling distribution of the sample mean is approximately normal, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
2) To find the probability that the average weekly earnings is less than $445, we can standardize the sample mean and use a z-table. The z-score for $445 is calculated as follows: z = (445 - 450) / (50 / sqrt(100)) = -1. Using a z-table, we find that the probability that the average weekly earnings is less than $445 is approximately 0.1587.
3) Since we are dealing with a continuous distribution, the probability that the average weekly earnings is exactly equal to any specific value is zero.
4) To find the probability that the average weekly earnings is between $445 and $455, we can subtract the probability that it is less than $445 from the probability that it is less than $455. The z-score for $455 is calculated as follows: z = (455 - 450) / (50 / sqrt(100)) = 1. Using a z-table, we find that the probability that the average weekly earnings is less than $455 is approximately 0.8413. Therefore, the probability that it is between $445 and $455 is approximately 0.8413 - 0.1587 = 0.6826.
5) In answering questions 2-4, we made an assumption about the population distribution based on the Central Limit Theorem. We assumed that since our sample size was large enough (n=100), our sampling distribution would be approximately normal.
6) If we assume that weekly earnings for employees in all general automotive repair shops are normally distributed with a mean of $450 and a standard deviation of $50, then we can calculate the z-score for an employee earning more than $480 in a given week as follows: z = (480 - 450) / 50 = 0.6. Using a z-table, we find that the probability that an employee will earn more than $480 in a given week is approximately 1 - 0.7257 = 0.2743.
Which set of values could be the side length of a 30 60 90 triangle? A. {5,5v3,10}
Answers
Therefore, the answer is A. {5, 5√3, 10}.
The set of values {5, 5√3, 10} could be the side lengths of a 30-60-90 triangle.
In a 30-60-90 triangle, the sides are in a specific ratio. The ratio is 1 : √3 : 2, where the shortest side (opposite the 30-degree angle) has length x, the side opposite the 60-degree angle has length x√3, and the hypotenuse (opposite the 90-degree angle) has length 2x.
Let's check if the given set of values satisfies this ratio:
If x= 5, then the side opposite the 60-degree angle should be 5√3, and the hypotenuse should be 10. These values match the ratio, so the set {5, 5√3, 10} could be the side lengths of a 30-60-90 triangle.
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i need a equation for 4x + 12 = 64
thanks :)
Answers
Answer: x=13
Step-by-step explanation: i think
if Tom had 78 apples and he gave to the shop for 80% and he put it on sale for another 10% what many apples would Tom get in the end?
Answers
Answer:
he has to many apples
Step-by-step explanation:
Never gonna give you up
Never gonna let you down
Never gonna run around and desert you
Never gonna make you cry
Never gonna say goodbye
Never gonna tell a lie and hurt you
A line through the points (2, -9) and (j, 17) is parallel to the line 2x + 3y = 21. What is the value of j?
Answers
Answer:
j = -37
Step-by-step explanation:
First find the slope of 2x + 3y = 21
Solve for y
Subtract 2x from each side
2x-2x + 3y =-2x+ 21
3y = -2x+21
Divide by 3
3y/3 = -2x /3 + 21/3
y = -2/3 x +7
This is in slope intercept form y = mx+b where m is the slope and b is the y intercept
m = -2/3
The slope of parallel lines are equal
Using the two points
m = (y2-y1)/(x2-x1)
-2/3 = (17 - -9)/(j-2)
-2/3 = (17 +9)/(j-2)
Using cross products
-2(j-2) = 3 ( 17+9)
-2j +4 = 26*3
-2j +4 = 78
Subtract 4 each side
-2j = 78-4
-2j = 74
Divide by -2
-2j/-2 = 74/-2
j = -37
Yall know the answer?
Answers
Answer:
pretty sure its 4
Step-by-step explanation:
hope it helps