The correct work done by the person walking up the spiral staircase is -3,325.89 ft-lb, indicating that the person did work against gravity while climbing up the stairs.
The force required to lift a person of weight 195 lb against gravity is F = mg,
where g is the acceleration due to gravity and
m is the mass of the person.
We can convert the weight in pounds to mass in pounds by dividing by the gravitational acceleration, g = 32.2 ft/s²:
m = 195 lb / 32.2 ft/s²= 6.05 slugs
The work done by a force F over a distance d is given by the dot product of the force and displacement vectors:
W = F · d
In this case, the force is the weight of the person, F = mg, and the displacement vector is the difference between the initial and final positions, d = r(1) - r(0),
where r(t) is the position vector parameterized by t.
We can compute the displacement vector as follows:
r(1) = ⟨4cos(2π), 4sin(2π), 18⟩ = ⟨4, 0, 18⟩
r(0) = ⟨4cos(0), 4sin(0), 0⟩ = ⟨4, 0, 0⟩
d = r(1) - r(0) = ⟨0, 0, 18⟩
The work done is therefore:
W = F · d = (6.05 slugs) · (32.2 ft/s^2) · ⟨0, 0, 18⟩
= 0 · 0 + 0 · 0 + (6.05 slugs) · (32.2 ft/s^2) · 18 ft
= 3,325.89 ft-lb
Therefore, the work done by the person walking one revolution up the spiral staircase is 3,325.89 ft-lb.
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Suppose that car accidents along a stretch of road occurs independently and are described by the Poisson distribution at a rate of 0.1 per hour. Furthermore, the number of motorcycle accidents along the same stretch of road also occurs independently and are described by the Poisson distribution at a rate of 0.05 per hour. What is the probability that there will be at most one accident in the next 2 hours?
The probability of at most one accident in the next 2 hours is 82.15%.
Let X be the number of car accidents in the next 2 hours, and Y be the number of motorcycle accidents in the next 2 hours. Both X and Y follow Poisson distributions, with rates of λX = 0.12 = 0.2 and λY = 0.052 = 0.1, respectively.
To find the probability that there will be at most one accident (either car or motorcycle) in the next 2 hours, we need to find the probability of the events {X + Y = 0} and {X + Y = 1}:
P(X + Y ≤ 1) = P(X + Y = 0) + P(X + Y = 1)
To find these probabilities, we can use the joint Poisson distribution of X and Y:
P(X = i, Y = j) = e^-(λX+λY) * (λXᵃ /a!) * (λYᵇ / b!)
where a and b are non-negative integers.
For X + Y = 0, we have:
P(X + Y = 0) = P(X = 0, Y = 0) = e⁻⁽⁰ ²⁺⁰ ¹⁾ * (0.2⁰ / 0!) * (0.1⁰ / 0!) = e⁻⁰ ³ ≈ 0.7412
For X + Y = 1, we have:
P(X + Y = 1) = P(X = 0, Y = 1) + P(X = 1, Y = 0) = e⁻⁽⁰ ²⁺⁰ ¹⁾ * (0.2⁰/ 0!) * (0.1¹/ 1!) + e⁻⁽⁰ ²⁺⁰ ¹⁾ * (0.2¹/ 1!) * (0.1⁰ / 0!) = 20.20.1*e⁻ ⁰ ³ ≈ 0.0803
Therefore, the probability of there being at most one accident (either car or motorcycle) in the next 2 hours is:
P(X + Y ≤ 1) ≈ 0.7412 + 0.0803 ≈ 0.8215
So the probability of there being at most one accident in the next 2 hours is about 82.15%.
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0.67032
The given data is that car accidents and motorcycle accidents on a stretch of road occur independently and are described by the Poisson distribution at a rate of 0.1 and 0.05 per hour respectively. It is required to find the probability that there will be at most one accident in the next 2 hours.The number of car accidents along the stretch of the road in the next 2 hours is a Poisson distribution with a mean of 0.1 x 2 = 0.2. Similarly, the number of motorcycle accidents in the next 2 hours is a Poisson distribution with a mean of 0.05 x 2 = 0.1.The probability that there will be at most one accident in the next 2 hours is:P(at most one accident in the next 2 hours)=P(no accident in the next 2 hours)+P(one accident in the next 2 hours)= e^(-0.2) (0.2)^0 / 0! + e^(-0.2) (0.2)^1 / 1! + e^(-0.1) (0.1)^0 / 0! + e^(-0.1) (0.1)^1 / 1!= 0.67032Therefore, the probability that there will be at most one accident in the next 2 hours is 0.67032.
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How high above the first floor is the second floor? Round to the nearest tenth.
The hight above the first floor to second floor is 15 ft , for this we have Trigonometry angles.
What is Trigonometry angles?Angles determined by the ratios of the trigonometric functions are known as trigonometric angles.
The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths.
Given h = 60 ft, we have to find p
Sin 15° = p/h
0.25 = p/60
p = 15 ft
So, the hight above the first floor to second floor is 15 ft.
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17
Question 17/20
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Cami was building a shelf to put her trophies on.
The drawing of her shelf is shown below.
11 inches
33 inches
BOOKMARK
8 inches
11 inches
What is the volume of Cami's trophy shelf?
cubic inches
8 inches
10 inches
Cami's trophy rack has a volume of 2904 cubic inches.
What is volume?In mathematics, volume is the amount of space within a particular 3D object. For example, an aquarium is 3 feet long, 1 foot wide, and 2 feet high. To find volume, multiply length with width and height. This is 3x1x2, or 6. To calculate the volume of Cami's trophy rack, you need to multiply the length, width, and height of the rack. Looking at the drawing provided, you can see that the shelf is 8 inches high, 11 inches wide and 33 inches long.
So the volume of the trophy rack is:
V = 8x11x33
V = 2904 cubic inches
Therefore, the Cami Trophy Rack has a volume of 2904 cubic inches.
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Complete question is: Cami was building a shelf to put her trophies on. The drawing of her shelf is shown below.
11 inches
33 inches
8 inches
What is the volume of Cami's trophy shelf? (in cubic inches)
jim makes $80,000 per year in gross income and must pay a required deduction of 30% in income tax ( federal,state,and local combined) he deducts no money for retirement savings.
Answer:
he pays 24,00 and he is left with 56000
Step-by-step explanation:
100% = 80000
30% = X
100%X= 2400000
2400000/100= 24,000
80,000-24,000= 56,000
What is the equation of p? A. p(x)= x(x - 3)(2x + 7)^2 B. p(x) x^2(x - 3)(2x + 7) C. p(x) = x(x - 3)^2(2x + 7)^2 D. p(x)= x(x - 3)^2(2x + 7)
Answer:
I believe it's C.
Step-by-step explanation:
The correct equation of p is C. p(x) = x(x - 3)^2(2x + 7)^2. This is because the given polynomial has a zero of multiplicity 2 at x = 3, a zero of multiplicity 1 at x = 0, and a zero of multiplicity 2 at x = -7/2. Therefore, the equation of the polynomial can be written as p(x) = k(x - 3)^2(x)(2x + 7)^2, where k is some constant. Since the leading coefficient of the polynomial is 1, k = 1. Thus, we get the equation p(x) = x(x - 3)^2(2x + 7)^2.
It is option C and not A, B, or D because:
Option A, p(x)= x(x - 3)(2x + 7)^2, has only one factor of (x - 3), but the given polynomial has a factor of (x - 3) squared.
Option B, p(x) x^2(x - 3)(2x + 7), has an extra factor of x^2 that is not present in the given polynomial.
Option D, p(x)= x(x - 3)^2(2x + 7), is very close to the correct answer, but it is missing the factor of (x) that is present in the given polynomial.
Thus, the correct equation of p is C, p(x) = x(x - 3)^2(2x + 7)^2, which includes all the necessary factors and satisfies the given conditions.
Hope this helps you! I'm sorry if it doesn't. If you need more help, ask me! :]
A scale model of a building has a scale of 3 : 74
The height of the real building is 21 m.
Find the height of the scale model.
Give your answer in cm to 2 dp. need this ASAP
Answer:
0.85 m
Step-by-step explanation:
Model dimension : Real dimension
3 : 74
x : 21
[tex] \frac{21}{74} = \frac{x}{3} \\ x = 3 \times \frac{21}{74} \\ = \frac{63}{74} \\ = 0.851...[/tex]
Answer:
85.54 cm
Step-by-step explanation:
To find the height of the scale model, we need to use the scale ratio given: 3 : 74. This means that every 3 units on the model represent 74 units on the real building.
First, we need to determine the ratio of the heights. Let x be the height of the scale model. Then:
3 / 74 = x / 21
Solving for x, we get:
x = 21 * 3 / 74
x = 0.8554 m
To convert this to centimeters, we multiply by 100:
x = 85.54 cm
Therefore, the height of the scale model is 85.54 cm to 2 decimal places.
(Please could you kindly mark my answer as brainliest)
Pls help help Algebra1
Answer:
C. (6r + 5)
Step-by-step explanation:
You would multiply (3r - 7) with (6r + 5) to get the value.
You want to determine the savings for using a battery that can be recharged. The battery costs 16 dollars. You save 14 dollars each time you recharge the battery. Represent the cost of the rechargeable battery as a negative number and savings as a positive number
The charged battery costs 16 dollars, which is denoted as -16. (negative number). The cost for the savings for using a battery that can be recharged is +14(positive number).
A battery is an electrical energy storage instrument made up of one or more electrochemical cells connected to the outside world. The cathode and anode of a battery are the positive and negative terminals, respectively, when the battery is supplying electricity. The battery costs 16 dollars. You save 14 dollars each time you recharge the battery. The cost of the rechargeable battery as a negative number is -16.The savings for using a battery that can be recharged is +14
The charged battery costs 16 dollars, which is denoted as -16. (negative number). Each refresh saves 14 dollars, which is symbolised as +14. (positive number). The charged battery costs 16 dollars, which is denoted as -16. (negative number). The cost for the savings for using a battery that can be recharged is +14(positive number).
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Animal shelters in a county need at least 15% of their animals to be adopted weekly to have room for the new animals that are brought into the various shelters. The county manager takes a random sample of shelters each week to estimate the overall proportion of animals that are adopted. If he concludes that the proportion has dropped below 15%, he will not accept any new animals into the shelters that week. He tests the hypotheses: H0: The adoption rate is 15%, and Ha: The adoption rate is less than 15%. What is a Type I error, and what is its consequence in this context?
The manager believes the adoption rate is still 15%, when it actually has dropped below 15%. The manager will accept more animals into the shelters and will run out of room.
The manager believes the adoption rate has dropped below 15%, when it actually has not. The manager will accept more animals into the shelters and will run out of room.
The manager believes the adoption rate has dropped below 15%, when it actually has not. The manager will not accept more animals into the shelters, when there actually is room to care for those animals.
The manager believes the adoption rate is still 15%, when it actually has dropped below 15%. The manager will not accept some animals into the shelters, thinking there will not be enough room, when they could have taken care of those animals.
answer c
Answer:
the amount will give 69 percentage of nothing thanks
thankyou for the RIGHT answer
Answer: ty
Step-by-step explanation:
Brainliest pls:)
HELPPPP ASAP!
Part A
Sarah graphs the equations and to solve the equation . Her graph is shown below.
Name the solution(s) and Describe where you found your solution(s) on the graph using a complete sentence.
The sοlutiοn(s) οn the graph are x = -4, 2.
In mathematics, a graph is a diagram οr visual representatiοn οf facts οr values that is οrdered. The pοints οn a graph are typically used tο depict the relatiοnships between twο οr mοre things. Graph theοry is the study οf graphs, which are mathematical structures that are used tο depict pairwise interactiοns between οbjects. A graph in this sense is made up οf vertices and edges.
A graph is an οrdered graphic οr visual representatiοn οf facts οr values in mathematics. The relatiοnships between twο οr mοre οbjects are οften shοwn by the pοints οn a graph.
The study οf graphs, which are mathematical representatiοns οf pairwise interactiοns between things, is knοwn as graph theοry. Vertices and edges make up a graph in this cοntext.
From the given graph we conclude following -
[tex]\frac{1}{4}x^2 = -\frac{1}{2}x + 2\\x^2 + 2x - 8 = 0\\x^2 + 4x - 2x - 8 = 0\\x(x + 4) - 2(x + 4) = 0\\(x + 4)(x - 2) = 0\\x = 2, -4[/tex]
On the graph, the solutiοns are the x-coοrdinates of the points of intersection
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Choose the statement that explains how to decide which value corresponds to point B
A.)The value of B is less than the values of all the other points.
B.)The value of B is greater than -1.
C.)The value of B is less than -1.
4.)The value of B is between-1 and -1/
Answer:
Step-by-step explanation:
D.The value of B is equal to -1
Calculate the speed of a car if it covers 660km in 4 hours
Answer:
[tex]\frac{660}{4} = 165[/tex] [tex]km/h[/tex]
Explain two factors that could make the public resort to violent ways of protesting
There are a variety of factors that can lead to violent protests, but two significant factors are perceived injustice and lack of political representation.
Perceived injustice: When people feel that they have been wronged, marginalized, or oppressed by a system or institution, they may resort to violent protest as a way to express their anger and frustration. This is particularly true when people believe that peaceful means of protest have been ignored or have failed to bring about change. For example, if a community feels that they are being unfairly treated by the police, and previous attempts to seek redress through peaceful protests or other channels have failed, they may turn to violent protest as a last resort.
Lack of political representation: When people feel that their voices are not being heard, they may resort to violent protests as a way to force attention to their concerns. This can happen when marginalized groups feel excluded from the political process, or when they feel that their interests are being ignored by those in power. If people feel that their concerns are not being taken seriously, they may turn to violent protest as a way to make their voices heard.
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curved surface area of a cone =
slant
surface area of a sphere
Trl, where r is the radius and 1 is the
height.
472, where r is the radius.
A sphere and a cone are shown below.
The surface area of the sphere is the same as the curved surface area of
the cone.
Work out the slant height of the cone.
If your answer is a decimal, give it to 1 d.p.
16 m
10 m
Answer:
735.1 square meters
Step-by-step explanation:
total surface area (TSA) of a cone can be calculated by using this mathematical expression:
Total surface area (TSA) of a cone = πr(l + r)
Total surface area (TSA) of a cone = πr(l + r)
Total surface area (TSA) of a cone = 3.142 × 6 × (33 + 6)
Total surface area (TSA) of a cone = 3.142 × 6 × (39)
Total surface area (TSA) of a cone = 735.1 square meters.
a hospital director is told that 32% 32 % of the treated patients are uninsured. the director wants to test the claim that the percentage of uninsured patients is under the expected percentage. a sample of 160 160 patients found that 40 40 were uninsured. find the value of the test statistic. round your answer to two decimal places.
The value of the test statistic is -1.75.
To test the claim that the percentage of uninsured patients is under the expected percentage of 32%, we can use a one-sample z-test. The null hypothesis is that the true percentage of uninsured patients is equal to 32%, while the alternative hypothesis is that the true percentage is less than 32%.
Using the sample data, we can calculate the sample proportion of uninsured patients as 40/160 = 0.25. We can then calculate the standard error of the sample proportion as sqrt[(0.32 x 0.68)/160] = 0.0385.
The test statistic can be calculated as (0.25 - 0.32)/0.0385 = -1.75.
To find the p-value associated with this test statistic, we can use a standard normal distribution table or a calculator to find the probability of a z-score less than -1.75. The p-value is approximately 0.04.
Since the p-value is less than the typical significance level of 0.05, we reject the null hypothesis and conclude that there is evidence to support the claim that the percentage of uninsured patients is under the expected percentage of 32%.
Therefore, the correct answer is -1.75, which is the calculated value of the test statistic.
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Suppose that the heights of adult women in the United States are normally distributed with a mean of 64. 5 inches and a standard deviation of 2. 2 inches. Jina is taller than of 90% the population of U. S. Women. How tall (in inches) is Jina? Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place
Jina is taller than 90% of US women if her height is at least 67.3 inches. Jina's height is approximately 67.3 inches.
Jina's height can be found using the z-score formula: z = (x - μ) / σ, where x is Jina's height, μ is the mean height of US women, and σ is the standard deviation of the heights. We need to find the z-score such that the area under the normal curve to the right of it is 0.10 (since Jina is taller than 90% of the population).
Using a z-score table or a calculator, we find that the z-score corresponding to an area of 0.10 is approximately 1.28. Substituting into the z-score formula and solving for x, we get:
1.28 = (x - 64.5) / 2.2
x - 64.5 = 2.816
x = 67.316
Rounding to one decimal place, Jina's height is approximately 67.3 inches.
In other words, Jina is taller than 90% of US women if her height is at least 67.3 inches.
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solve every single thing on tha page please
Answer:
Answer = 21 Sacks
Step-by-step explanation:
First, we need to calculate how much flour the baker will use in 20 days:
Amount of flour used per day for 64 loaves = 64 loaves/day x 400 g/loaf = 25,600 g/day
Amount of flour used in 20 days = 25,600 g/day x 20 days = 512,000 g
Next, we need to convert the amount of flour used into kilograms:
512,000 g ÷ 1000 g/kg = 512 kg
Finally, we need to calculate the minimum number of 25 kg sacks the baker should order:
Number of 25 kg sacks = 512 kg ÷ 25 kg/sack ≈ 20.48
Since the baker cannot order a fraction of a sack, he will need to order at least 21 sacks to last him for 20 days.
Ten years ago the Jacksons bought a house, taking out a 30 year mortgage for $150,000 at 5.75%. This year (exactly 10 years later) they refinanced the house, taking out a new 30 year mortgage for the remaining balance at 4.375%.
What was the monthly payment on the original 5.75% mortgage?
What was the remaining balance after 10 years (the amount they then refinanced)?
How much interest did they pay during those first 10 years?
What is the monthly payment on the refinance 4.375% mortgage?
How much interest will they pay over the 30 year term of the refinance?
How much total interest will they pay over the full 40 years the Jacksons have a loan for the house?
The tοtal interest paid οver the full 40 years the Jacksοns have a lοan fοr the hοuse is apprοximately $137,986.85.
Tο sοlve this prοblem, we can use the fοrmula fοr a fixed-rate mοrtgage payment:
[tex]P = (Pv\times r) / (1 - (1 + r)^{(-n))[/tex]
Where:
Pv = present value οf the mοrtgage
r = mοnthly interest rate
n = tοtal number οf payments
a) Mοnthly payment οn the οriginal 5.75% mοrtgage:
Pv = $150,000
r = 5.75% / 12 = 0.004792
n = 30 years × 12 mοnths per year = 360
[tex]P = (150,000 \times 0.004792) / (1 - (1 + 0.004792)^{(-360))[/tex]
P ≈ $875.25
Therefοre, the mοnthly payment οn the οriginal 5.75% mοrtgage was apprοximately $875.25.
b) Remaining balance after 10 years:
Using an οnline amοrtizatiοn calculatοr οr fοrmula, we can find that the remaining balance after 10 years is apprοximately $111,138.77.
c) Interest paid during the first 10 years:
Using the same amοrtizatiοn calculatοr οr fοrmula, we can find that the tοtal interest paid during the first 10 years is apprοximately $54,316.57.
d) Mοnthly payment οn the refinance 4.375% mοrtgage:
Pv = $111,138.77
r = 4.375% / 12 = 0.003646
n = 30 years × 12 mοnths per year = 360
[tex]P = (111,138.77\times 0.003646) / (1 - (1 + 0.003646)^{(-360))[/tex]
P ≈ $554.62
Therefοre, the mοnthly payment οn the refinance 4.375% mοrtgage is apprοximately $554.62.
e) Tοtal interest paid οver the 30 year term οf the refinance:
Using the same amοrtizatiοn calculatοr οr fοrmula, we can find that the tοtal interest paid οver the 30 year term οf the refinance is apprοximately $82,670.28.
f) Tοtal interest paid οver the full 40 years:
Tο find the tοtal interest paid οver the full 40 years, we can add up the interest paid during the first 10 years and the interest paid οver the 30 year term οf the refinance:
Tοtal interest = $54,316.57 + $82,670.28
Tοtal interest = $137,986.85
Therefοre, the tοtal interest paid οver the full 40 years the Jacksοns have a lοan fοr the hοuse is apprοximately $137,986.85.
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There is a number cube with faces numbered 1 to 6. There is also a coin with one side marked as heads and the other tails.
As a trial of an experiment, the number cube was rolled and the coin flipped. The number (1 to 6) from the roll and the side (H for heads and T for talls) of
the coin from the flip were recorded.
Here is a summary of the data from 1050 trials.
Outcome 1H 2H 3H 4H 5H 6H 1T 2T 3T 4T 5T 6T
Number of trials 79 99 89 88 89 96 92 86 97 79 77 79
Answer each part.
(a) Assuming the cube and the coin are fair, find the theoretical probability of this event: both
rolling a 1 ora 6 and flipping tails, in a single trial. Round your answer to the nearest
thousandth.
0
(b) Use the data to find the experimental probability of this event: both rolling a 1 or a 6 and
nipping talls, in a single trial. Round your answer to the nearest thousandth.
0
(c) Choose the statement that is true.
With a large number of trials, there might be a difference between the experimental
and theoretical probabilities, but the difference should be small.
With a large number of trials, there must be a large difference between the
experimental and theoretical probabilities.
With a large number of trials, there must be no difference between the experimental
and theoretical probabilities.
5
help me pls this is another one that is due Saturday!!!!
Answer:
Your anser is u = 6
Step-by-step explanation:
[tex]\frac{6}{7} =\frac{8}{u+5}[/tex]
Cross multiply.
[tex]6*(u+5) =7*8\\\\6u+30=56\\\\6u=56-30\\\\6u=36\\\\u=6[/tex]
An amusement park has 8 water slides and 26 other attractions.
What is the probability that a randomly selected attraction at this amusement park will be
a water slide?
Write your answer as a fraction or whole number.
P(water slide)
Answer:
The answer is 4/17
Step-by-step explanation:
On an average, five flood events in every 2 years are recorded at a location due to heavy rainfall. Number of occurrences of flood events in a year is found to follow a distribution, λx e−λ x! where λ is the expected number of flood events in a year. What is the probability of occurring not more than two flood events in a particular year at that location?
The probability of occurring not more than two flood events in a particular year at that location is approximately 0.546.
The given distribution is λxe-λx! where λ is the expected number of flood events in a year. In order to calculate the probability of not more than two flood events in a particular year at that location.
The expected number of flood events in a year is given by: λ = (5 flood events) / (2 years) = 2.5 flood events per year
The given distribution is:λxe-λx! = 2.5xe-2.5x!
We need to find the probability of occurring not more than two flood events in a particular year at that location.
Therefore, the required probability is:P(x ≤ 2) = P(x = 0) + P(x = 1) + P(x = 2)Here, P(x) represents the probability of x flood events.
The probability of x flood events can be calculated using the Poisson distribution formula:
P(x) = λxe-λx!Substitute λ = 2.5 and x = 0 in the above formula to get:P(0) = (2.5)0e-2.5 / 0! = e-2.5 ≈ 0.082Substitute λ = 2.5 and x = 1 in the above formula to get:P(1) = (2.5)1e-2.5 / 1! = 2.5e-2.5 ≈ 0.206Substitute λ = 2.5 and x = 2 in the above formula to get:P(2) = (2.5)2e-2.5 / 2! = 3.125e-2.5 ≈ 0.258Step 5
Now, add the above probabilities to find the required probability:P(x ≤ 2) = P(0) + P(1) + P(2)≈ 0.082 + 0.206 + 0.258 = 0.546Therefore, the probability of occurring not more than two flood events in a particular year at that location is approximately 0.546.
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The curved surface area of a solid
cylinder is 660 cm2
.
The cylinder has height 10 cm.
a) What is the circumference of the
cylinder?
b) What is the radius of the cylinder?
c) What is the area of one circular
base?
d) What is the surface area of the
cylinder?
Answer:
a) The circumference of the cylinder can be found using the formula C = 2πr, where r is the radius of the circular base. Rearranging the formula, we get r = C/2π. To find the circumference, we can use the formula for the curved surface area: A = 2πrh, where h is the height of the cylinder. Substituting the given values, we get:
660 = 2πr(10)
r = 33/π
Now we can find the circumference:
C = 2πr = 2π(33/π) = 66
Therefore, the circumference of the cylinder is 66 cm.
b) The radius of the cylinder is given by r = 33/π, which we already found in part a).
c) The area of one circular base can be found using the formula A = πr^2. Substituting the value of r from part b), we get:
A = π(33/π)^2 = 1089/π
Therefore, the area of one circular base is 1089/π cm^2.
d) The surface area of the cylinder consists of the curved surface area and two circular bases. The area of one circular base was found in part c), so we just need to add the curved surface area to twice the area of one circular base:
Surface area = 2A + 2πrh
Substituting the given values, we get:
Surface area = 2(1089/π) + 2π(33/π)(10) = 2187/π + 660
Therefore, the surface area of the cylinder is 2187/π + 660 cm^2.
Step-by-step explanation:
A family has a large sand castle mold in the shape of a swuare puramid the distance from the ase to the apex the mold is 5feet and one of the edges of the base of the mold is 3 feet. How much sand does the family need to fill the mold completlt
The family needs 15 cubic feet of sand to fill the mold completely.
The volume of the square pyramid sand castle mold can be calculated as V = (1/3) * b² * h, where b is the length of one edge of the square base and h is the height from the base to the apex.
In this case, b = 3 feet and h = 5 feet.
Plugging these values into the formula, we get:
V = (1/3) * 3² * 5
V = 15 cubic feet
Therefore, the family needs 15 cubic feet of sand to fill the mold completely.
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The Sun is approximately 9.2661 x 10^7 miles farther than the Moon from Earth.
How to solveThe distance between the Sun and the Earth is approximately 9.29 x 10^7 miles, and the distance between the Moon and the Earth is approximately 2.389 x 10^5 miles.
To find how much farther the Sun is from the Earth than the Moon, we can subtract the distance between the Moon and the Earth from the distance between the Sun and the Earth:
9.29 x 10^7 miles - 2.389 x 10^5 miles = 9.2661 x 10^7 miles
Therefore, the Sun is approximately 9.2661 x 10^7 miles farther than the Moon from Earth.
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Solve the following differential equation by variation of parameters. Fully evaluate all integrals. y" + 25 y = sec(5x). Find the most general solution to the associated homogeneous differential equation. Use c_1 and c_2 in your answer to denote arbitrary constants, and enter them as c1 and c2. y_h = c1cos(5x) + c2sin(5x) Find a particular solution to the nonhomogeneous differential equation y" + 25 y = sec(5x). y_p = 1/25(- cos(ln(sec5x))) + 5xsin(5x) Find the most general solution to the original nonhomogeneous differential equation. Use c_1 and c_2 in your answer to denote arbitrary constants. y =
The general solution is given by: y = c1cos(5x) + c2sin(5x) + 1/25(- cos(ln(sec5x))) + 5xsin(5x)
The most general solution to the original nonhomogeneous differential equation can be found by adding the homogeneous solution and the particular solution together. That is,
y = y_h + y_p
= c1cos(5x) + c2sin(5x) + 1/25(- cos(ln(sec5x))) + 5xsin(5x)
This is the most general solution to the original nonhomogeneous differential equation. We can use the arbitrary constants c1 and c2 to find specific solutions for different initial conditions. The general solution is given by:
y = c1cos(5x) + c2sin(5x) + 1/25(- cos(ln(sec5x))) + 5xsin(5x)
This is the final answer. Note that we have used the terms "general solution" and "arbitrary constants" in our answer, as instructed.
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Calculate the area of this triangle
Answer:
4.06 cm^2
Step-by-step explanation:
If you draw a line from the top vertex to intersect the base (which is 5.8 cm) at 90 degrees, the line is called the height. You need to calculate the height to determine the area.
So the triangle's height will divide the triangles into 2 smaller right triangles.
For the left right triangle, 2.5 will be hypotenuse
=> 2.5^2 = (height)^2 + (base1)^2
=> (height)^2 = 6.25 - (base1)^2
For the right right triangle, 4 will be hypotenuse
=> 4^2 = (height)^2 + (base2)^2
=> (height)^2 = 16 - (base2)^2
So
6.25 - (base1)^2 = 16 - (base2)^2
We have base1 + base2 = 5.8 => base1 = 5.8 - base2
Substitute
6.25 - (5.8 - base2)^2 = 16 - (base2)^2
6.25 - (33.64 - 11.6base2 + base2^2 = 16 - base2^2
base2^2 - base2^2 + 11.6base2 = 16 + 33.6 - 6.25
11.6base2 = 43.35
base2 = 43.35/11.6 = 3.74
since (height)^2 = 16 - (base2)^2
(height)^2 = 16 - (3.74)^2
height^2 = 2.0124
height = 1.42
so area = 1/2hb = 1/2(1.4)(5.8) = 4.06 cm^2
5. A six-marble repeating pattern made up of
ebloured marbles is shown.
How many times does a red marble appear
in the first 20 marbles of this pattern?
Explain your answer.
Answer:
7 marbles
Step-by-step explanation:
For every 6 marbles, 2 marbles appear as red.
This pattern would repeat thrice as 6x3 = 18, and then the first 2 marbles (one blue and red) will be counted to make 20 marbles.
So total marbles will be 3x2 in the 18 marble set and 1 in the final 2 marbles.
so 3x2 + 1 = 6+1 = 7
We get 7 marbles as red if we continue in this pattern.
1/3(9k+12)=15
help with the explanation
Answer:
k=11/3
Step-by-step explanation:
Use distributive property.
3k+4=15
Subtract 4 from both sides.
3k=11
Divide 3 from both sides.
k=11/3
Answer: k=11/3 or 3.66
Step-by-step explanation:
3k+4=15 --Distribute 1/3 to 9k and 12.
3k=11 --Subtract 4 from both sides.
k=11/3 or 3.66
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