Answer:
a) 62.5
b) -62.5
Step-by-step explanation:
Given:
x² + y² + z² = 1 is T = 500xyz²
Required:
Locate the highest and lowest temperatures.
Here,
S = (x² + y² + z² = 1)
T = 500 xyz²
Let's take Lagrange multiplier:
∇T = λ∇S
Thus,
500 yz² = λ(2x)........... 1
500 xz² = λ(2y).............2
500 xy² = λ(2z)..............3
Where, x² = y², 2y² = z²
Therefore,
x²+ y²+z² = 1
=> x² + x² + 2x² = 1
Solve for x:
x = ±½ = y
z = ±[tex] \frac{1}{\sqrt{2}} [/tex]
From the above calculations,
x, y, z = ±½, ±½, ±[tex]\frac{1}{\sqrt{2}} [/tex]
Calculate for the highest temperature:
Tmax = T(½, ½, [tex]\frac{1}{\sqrt{2}}) [/tex] = 500 * ½ * ½ * ½ = [tex] \frac{500}{8} = 62.5 [/tex]
Calculate for the lowest temperature:
Tmin = T(-½, ½, [tex]\frac{1}{\sqrt{2}}) [/tex] = 500 * -½ * ½ * ½ = [tex] - \frac{500}{8} = -62.5[/tex]
The highest temperatures is 62.5 and lowest temperatures is -62.5 on the sphere
Given-
The given equation is,
[tex]x^2+y^2+z^2=1[/tex]
The equation for the temperature is,
[tex]T=500(xyz)^2[/tex]
By the Lagrange multiplier
[tex]\bigtriangledown T=\lambda \bigtriangledown S[/tex]
we can rewrite the temperature equation by the above multiplier as,
[tex]500yz^2=\lambda (2x)[/tex]
[tex]500xz^2=\lambda (2y)[/tex]
[tex]500xy^2=\lambda (2z)[/tex]
Here let,
[tex]x^2=y^2[/tex]
[tex]2y^2=z^2[/tex]
therefore,
[tex]2x^2=z^2[/tex]
Put this values in the given equation of the question we get,
[tex]x^2+x^2+2x^2=1[/tex]
[tex]4x^2=1[/tex]
[tex]x^2=\dfrac{1}{4}[/tex]
[tex]x= \pm\dfrac{1}{2}[/tex]
Therefore,
[tex]y= \pm\dfrac{1}{2}[/tex]
[tex]z= \pm\dfrac{1}{\sqrt{2} }[/tex]
Use positive value for the highest temperatures and negative values for the lowest value of temperatures in the temperature equation.
Highest temperature is,
[tex]T=500(xyz)^2[/tex]
[tex]T_h=500(\dfrac{1}{2} \times\dfrac{1}{2}\times\dfrac{1}{2} )[/tex]
[tex]T_h=\dfrac{500}{8}=62.5[/tex]
Lowest temperature is,
[tex]T_l=500(\dfrac{-1}{2} \times\dfrac{-1}{2}\times\dfrac{-1}{2} )[/tex]
[tex]T_l=-62.5[/tex]
Hence, the highest temperatures is 62.5 and lowest temperatures is -62.5 on the sphere
For more about the temperatures follow the link given below-
https://brainly.com/question/15267055
A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let Y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation.
Y
p(x,y), 0 1 2
0 .10 .04 .02
x 1 .08 .20 .06
2 .06 .14 .30
a. What is P(X = 1 and = 1)?
b. Compute P(X land Y 1).
c. Give a word description of the event {X t- 0 and Y 0}, and compute the probability of this event
d. Compute the marginal pmf of X and of Y. Using pX(x), what is P(X 5 1)?
e. Are X and Y independent rv's? Explain.
Answer:
Step-by-step explanation:
Y
p(x,y) 0 1 2
0 0.10 0.04 0.02
x 1 0.08 0.2 0.06
2 0.0 0.14 0.30
a) What is P(X = 1 and = 1)
From the table above we have
P(1,1) = 0.2
b) Compute P(X ≤ 1 and Y ≤ 1).
[tex]=p(0,0)+p(0,1)+p(1,0)+p(1,1)\\\\=0.1+0.04+0.08+0.2\\\\=0.42[/tex]
C)
Let A ={X ≠ 0 and Y ≠ 0}
p{X ≠ 0 , Y ≠ 0}
= p(1,1) + p(1,2) + p(2,1) + p(2,2)
= 0.20 + 0.06 + 0.14 + 0.30
=0.7
d) The possible X values are in the figure 0,1,2
[tex]p_x(0)=p(0,0)+p(0,1)+p(0,2)\\\\=0.1+0.04+0.02\\\\=0.16\\\\p_x(1)=p(1,0)+p(1,1)+p(1,2)\\\\=0.08+0.2+0.06\\\\=0.34\\\\p_x(2)=p(2,0)+p(2,1)+p(2,2)\\\\=0.06+0.14+0.3\\\\=0.5[/tex]
The possible Y values are in the figure 0,1,2
[tex]p_y(0)=p(0,0)+p(1,0)+p(2,0)\\\\=0.1+0.08+0.06\\\\=0.24\\\\p_y(1)=p(0,1)+p(1,1)+p(2,1)\\\\=0.04+0.2+0.14\\\\=0.38\\\\p_y(2)=p(0,2)+p(1,2)+p(2,2)\\\\=0.02+0.06+0.3\\\\=0.38[/tex]
So the probability of x ≤ 1 is
[tex]p(x\leq 1)=p_x(0)+p_x(1)\\\\=0.34+0.16\\\\=0.50[/tex]
e) From the table
[tex]p_x(x=1,y=1)=p(1,1)\\\\=0.2\\\\p_x(1)=0.34\\\\p_y(1)=0.38[/tex]
we multiply both together
0.34 x 0.38
=0.1292
Therefore p(1,1) is not equal px(1), py(1)
Hence x and y are not independent it is not equal
HELP HELP HELP PLEASE!!!!!
A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 3 tables is $31. The total cost to rent 6 chairs and 5 tables is $59
What is the cost to rent each chair and each table?
Answer:
The rental of each chair is $2.75
The rental of each table is $8.5
Step-by-step explanation:
Let's name the unknowns "c" for the cost of each chair rental, and "t" for the cost of each table rental.
Now we can create the equations that represent the statements:
a) "The total cost to rent 2 chairs and 3 tables is $31."
2 c + 3 t = 31
b) "The total cost to rent 6 chairs and 5 tables is $59."
6 c + 5 t = 59
now we have a system of two equations and two unknowns that we proceed to solve via the elimination method by multiplying the first equation we got by "-3" so by adding it term by term to the second equation, we eliminate the variable "c" and solve for "t":
(-3) 2 c + (-3) 3 t = (-3) 31
-6 c - 9 t = -93
6 c + 5 t = 59
both these equations added give:
0 - 4 t = -34
t = 34/4 = 8.5
So each table rental is $8.5
now we find the rental price of a chair by using any of the equations:
2 c + 3 t = 31
2 c + 3 (8.5) = 31
2 c + 25.5 = 31
2 c = 5.5
c = 5.5/2
c = $2.75
Vitamin D is important for the metabolism of calcium and exposure to sunshine is an important source of vitamin D. A researcher wanted to determine whether osteoperosis was associated with a lack of exposure to sunshine. He selected a sample of 250 women with osteoperosis and an equal number of women without osteoperosis. The two groups were matched - in other words they were similar in terms of age, diet, occupation, and exercise levels. Histories on exposure to sunshine over the previous twenty years were obtained for all women. The total number of hours that each woman had been exposed to sunshine in the previous twenty years was estimated. The amount of exposure to sunshine was compared for the two groups. Group of answer choices
Answer:
The type of observational study describer here is retrospective study.
Step-by-step explanation:
The complete question is:
Vitamin D is important for the metabolism of calcium and exposure to sunshine is an important source of vitamin D. A researcher wanted to determine whether osteoperosis was associated with a lack of exposure to sunshine. He selected a sample of 250 women with osteoperosis and an equal number of women without osteoperosis. The two groups were matched - in other words they were similar in terms of age, diet, occupation, and exercise levels. Histories on exposure to sunshine over the previous twenty years were obtained for all women. The total number of hours that each woman had been exposed to sunshine in the previous twenty years was estimated. The amount of exposure to sunshine was compared for the two groups. Determine what type of observational study is described. Explain.
Solution:
In retrospective study design, the concerned outcome has previously taken place in each participant by the phase he or she is signed up for the study, and the information are gathered either from past data or by requesting the participants to recall exposures.
It is also known as a historic cohort study.
A retrospective study is completed as posterior experiment, using data on events that have already taken place in the history. In most cases some or most of the data has already been collected and stowed in the archive.
In the provided scenario, the researcher collect the past data for the exposure to sunshine over the previous twenty years for 250 women. And estimated the total number of hours that each woman had been exposed to sunshine in the previous twenty years.
Then the researcher compares the amount of exposure to sunshine for the two groups.
Thus, the type of observational study describer here is retrospective study.
A student walk 60m on a bearing
of 028 degree and then 180m
due east. How is she from her
starting point, correct to the
nearest whole number?
Answer:
d = 234.6 m
Step-by-step explanation:
You can consider a system of coordinates with its origin at the beginning of the walk of the student.
When she start to walk, she is at (0,0)m. After her first walk, her coordinates are calculated by using the information about the incline and the distance that she traveled:
[tex]x_1=60cos28\°=52.97m\\\\y_1=60sin28\°=28.16m[/tex]
she is at the coordinates (52.97 , 28.16)m.
Next, when she walks 180m to the east, her coordinates are:
(52.97+180 , 28.16)m = (232.97 , 28.16)m
To calculate the distance from the final point of the student to the starting point you use the Pythagoras generalization for the distance between two points:
[tex]d=\sqrt{(x-x_o)^2+(y-y_o)^2}\\\\x=232.97\\\\x_o=0\\\\y=28.16\\\\y_o=0\\\\d=\sqrt{(232.97-0)^2+(28.16-0)^2}m=234.6m[/tex]
The displacement of the student on her complete trajectory was of 234.6m
In 2003, a school population was 903. By 2007 the population had grown to 1311. How much did the population grow between the year 2003 and 2007? How long did it take the population to grow feom 903 students to 1311 students? What is the average population growth per year?
Answer:
The average population growth per year is 102.
Step-by-step explanation:
From the given data, we can find the slope which will give us the average rate of change. Our points are:
[tex](2003, 903)\quad and \quad (2007, 1311)[/tex]
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}=\frac{1311-903}{2007-2003}\\\\m=102[/tex]
Best Regards!
The probability that a machine works on a given day is based on whether it was working in the previous day. If the machine was working yesterday, then the probability it will work today is 0.76. Of the machine was broken yesterday, then the probability it will be broken today is 0.33. Of the machine is broken today, what is the likelihood that it will be working two days from now
Answer:
73.03% probability that it will be working two days from now
Step-by-step explanation:
The machine is broken today.
If the machine is broken on a day, the following day, it has a 1-0.33 = 0.67 probability of working on the next day.
Otherwise, if it is works correctly on a day, it has a 0.76 probability of working on the next day.
Uf the machine is broken today, what is the likelihood that it will be working two days from now
Either of these outcomes are acceptable:
Tomorrow - 2 days from now
Not working - working
Working - Working
Not working - working
Today, it does not work. So tomorrow the probability of not working correctly is 0.33. Then, if tomorrow does not work, 0.67 probability of working correctly two days from now
0.33*0.67 = 0.2211
Working - Working
Today, it does not work. So tomorrow the probability of working correctly is 0.67. Then, if tomorrow works, 0.76 probability of working correctly two days from now
0.67*0.76 = 0.5092
Total
0.2211 + 0.5092 = 0.7303
73.03% probability that it will be working two days from now
The caller times at a customer service center has an exponential distribution with an average of 22 seconds. Find the probability that a randomly selected call time will be less than 30 seconds? (Round to 4 decimal places.)
Answer:
The probability that a randomly selected call time will be less than 30 seconds is 0.7443.
Step-by-step explanation:
We are given that the caller times at a customer service center has an exponential distribution with an average of 22 seconds.
Let X = caller times at a customer service center
The probability distribution (pdf) of the exponential distribution is given by;
[tex]f(x) = \lambda e^{-\lambda x} ; x > 0[/tex]
Here, [tex]\lambda[/tex] = exponential parameter
Now, the mean of the exponential distribution is given by;
Mean = [tex]\frac{1}{\lambda}[/tex]
So, [tex]22=\frac{1}{\lambda}[/tex] ⇒ [tex]\lambda=\frac{1}{22}[/tex]
SO, X ~ Exp([tex]\lambda=\frac{1}{22}[/tex])
To find the given probability we will use cumulative distribution function (cdf) of the exponential distribution, i.e;
[tex]P(X\leq x) = 1 - e^{-\lambda x}[/tex] ; x > 0
Now, the probability that a randomly selected call time will be less than 30 seconds is given by = P(X < 30 seconds)
P(X < 30) = [tex]1 - e^{-\frac{1}{22} \times 30}[/tex]
= 1 - 0.2557
= 0.7443
Pls help on this question
To collect data on the signal strengths in a neighborhood, Briana must drive from house to house
and take readings. She has a graduate student, Henry, to assist her. Briana figures it would take her
12 hours to complete the task working alone, and that it would take Henry 18 hours if he completed
the task by himself.
Answer: Working together, they can complete the task in 7 hours and 12 minutes.
Step-by-step explanation:
Ok, Briana needs 12 hours to complete the task.
Then we can find the ratio of work over time as:
1 task/12hours = 1/12 task per hour.
This means that she can complete 1/12 of the task per hour.
Henry needs 18 hours to complete the task, then his ratio is:
1 task/18 hours = 1/18 task per hour.
This means that he can complete 1/18 of the task in one hour.
If they work together, then the ratios can be added:
R = 1/12 + 1/18 = 18/(12*18) + 12/(18*12) = 30/216
we can reduce it to:
R = 15/108 = 5/36
So, working together, in one hour they can complete 5/36 of the task, now we can find the number of hours needed to complete the task as:
(5/36)*x = 1 task
x = 36/5 hours = 7.2 hours
knowing that an hour is 60 minutes, then 0.2 of an hour is 60*0.2 = 12 minutes.
then x = 7 hours and 12 minutes.
Check all of the points that are solutions to the system of inequalities.
y> 4x + 2
y< 4x + 5
Someone help me ASAP
Answer:
It is only (5,24).
Step-by-step explanation:
You are correct.
Sometimes, check all options means there could be just one option.
According to statcounter, Google Chrome browser controls 62.8% of the market share worldwide. A random sample of 70 users was selected. What is the probability that 35 or more from this sample used Google Chrome as their browser
Answer:
The probability that 35 or more from this sample used Google Chrome as their browser is 0.9838.
Step-by-step explanation:
We are given that according to Statcounter, the Google Chrome browser controls 62.8% of the market share worldwide.
A random sample of 70 users was selected.
Let [tex]\hat p[/tex] = sample proportion of users who used Google Chrome as their browser.
The z-score probability distribution for the sample proportion is given by;
Z = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion = [tex]\frac{35}{70}[/tex] = 0.50
p = population proportion = 62.8%
n = sample of users = 70
Now, the probability that 35 or more from this sample used Google Chrome as their browser is given by = P( [tex]\hat p[/tex] [tex]\geq[/tex] 0.50)
P( [tex]\hat p[/tex] [tex]\geq[/tex] 0.50) = P( [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] [tex]\geq[/tex] [tex]\frac{0.50-0.628}{\sqrt{\frac{0.50(1-0.50)}{70} } }[/tex] ) = P(Z [tex]\geq[/tex] -2.14)
= P(Z [tex]\leq[/tex] 2.14) = 0.9838
The above probability is calculated by looking at the value of x = 2.14 in the z table which has an area of 0.9838.
A diagnostic test has a 95% probability of giving a positive result when given to a person who has a certain disease. It has a 10% probability of giving a (false) positive result when given to a person who doesn’t have the disease. It is estimated that 15% of the population suffers from this disease.
(a) What is the probability that a test result is positive?
(b) A person recieves a positive test result. What is the probability that this person actually has the disease? (probability of a true positive)
(c) A person recieves a positive test result. What is the probability that this person doesn’t actually have the disease? (probability of a false negative)
Answer:
a)0.2275 b)95/105=19/21 c)10/105= 2/21
Step-by-step explanation:
a) The case "The test result is positive" consists in 2 parts.
The 1st one is "The person has the desease (15%=0.15) and the test's result is positive (95%=0.95)
The probability of that is P(desease, positive) = 0.15*0.95=0.1425
The 2nd one is "The person has no the desease (100%-15%=85%=0.85). However the test result is positive (10%=0.1)
The probability of that is P(not desease, positive)=0.85*0.1=0.085
The total probability that test is positive is the sum of 1st and 2-nd parts of the case: P(pos) = 0.1425+0.085=0.2275
b) As it has been shown in a) The test result can be positive in case that the person is really has the desease (95%) and in case the person has no the desease (10%). This actually means that 95 persons from 105 having positive test result are really has the desease.
So the probability that the test result is positive and person has the desease is P (desease/positive)= 95/105
c) It's clearly seen that the sum of probabilities of b) and c) equal 1.
Both events make full group of events.
If the test result is positive the person can have the desease or can have not the desease. So ( no desease/positive)= 1-95/105=10/105
Divide: (y2−4y+6)÷(y+1).
Answer:
Step-by-step explanation:
hello
[tex]y^2-4y+6= (y+1)^2-2y-1-4y+6=(y+1)^2-6y+5=(y+1)^2-6(y+1)+11[/tex]
so
[tex]\dfrac{y^2-4y+6}{y+1}=y+1-6+\dfrac{11}{y+1}=y-5+\dfrac{11}{y+1}[/tex]
hope this helps
The box plots show Devonte’s scores in Spanish and in French. Devonte inferred that his French scores have less variability than his Spanish scores. Which explains whether Devonte’s inference is correct?
Devonte is correct because the range is greater for French.
Devonte is correct because the interquartile range is less for French. Devonte is not correct because his highest grade is in Spanish.
Devonte is not correct because the interquartile range is less for Spanish.
Answer:
Devonte is correct because the interquartile range is less for French
Step-by-step explanation:
The first box plot at the top shows scores in Spanish, while the second box plot below it shows French scores.
Variability can be ascertain by finding out the interquartile range of a data set.
The higher the value of the IQR, the more the variability, while the lower the IQR, the less the variability.
IQR = Q3 - Q1
IQR for Spanish score = 85 - 60 = 25
IQR for French score = 80 - 65 = 20
From the above, we can say that Spanish scores has more variability when compared to French scores.
Therefore, Devonte is correct because the interquartile range is less for French, which shows that the variability in French scores is lesser than that of Devonte's Spanish scores.
Answer:
Devonte is correct because the interquartile range is less for French.
Step-by-step explanation:
The scoring range indicates the deviance from the standard values. It can only be inferred that the interquartile range is very narrow. In other words, there is less variability in the scores. Thus, a smaller quartile range means that there is less variability in the quantity being measured. The interqurtile range is the difference in the values of the the 75th percentile and the 25th percentile of a cumulative frequency distribution curve.
What is the value of AC?
Answer:
0.637
Step-by-step explanation:
The average value of a whole sinusoidal waveform over one complete cycle is zero as the two halves cancel each other out
Solve the equation x^3 + 2x^2 - 11x -12 = 0
Answer: there are 4 solutions
x = -2
x = -1/2 = -0.500
x =(3-√5)/2= 0.382
x =(3+√5)/2= 2.618
Step-by-step explanation:
The table below shows the number of students who attend various after-school activities.Which does the ratio 17:44 represent?
Answer:
The part-to-part relationship between homework help and sports
Step-by-step explanation:
Assume the table is like the one below.
[tex]\begin{array}{lcl}\textbf{Activity}& \textbf{Students} \\\text{Spanish} & 19 \\\text{Basketball} & 24 \\\text{Drama} & 15\\\text{Homework help} & 17 \\\text{Soccer} & 20 \\\end{array}[/tex]
17 students participated in homework help.
44 students participated in basketball (24) and soccer (20), i.e. sports
Both sports and homework help are parts of the whole group of all activities.
Thus, 17:44 represents the part-to-part relationship between homework help and sports.
Explanation: Please show table.
Please answer this correctly
Answer:
6,4,4,4,5,7
Step-by-step explanation:
Answer: 31-40 6 bracelets, 41-50 4 bracelets, 51-60 4 bracelets, 61-70 4 bracelets, 71-80 5 bracelets, 81-90 7 bracelets
Step-by-step explanation:
6 given numbers within 31-40
4 given numbers within 41-50
4 given numbers within 51-60
4 given numbers within 61-70
5 given numbers within 71-80
7 given numbers within 81-90
insert a digit to make numbers that are divisible by 24 if it is possible 38_36
Answer:
ge
Step-by-step explanation:
ge
The top figure in the composite figure is called a . And What is the volume?
Answer:
Triangular Prism
volume 748
In the fall semester of 2009, the average Graduate Management Admission Test (GMAT) of the students at a certain university was 500 with a standard deviation of 90. In the fall of 2010, the average GMAT was 570 with a standard deviation of 85.5. Which year's GMAT scores show a more dispersed distribution
Answer:
Due to the higher coefficient of variation, 2009's GMAT scores show a more dispersed distribution
Step-by-step explanation:
To verify how dispersed a distribution is, we find it's coefficient of variation.
Coefficient of variation:
Mean of [tex]\mu[/tex], standard deviation of [tex]\sigma[/tex]. The coefficient is:
[tex]CV = \frac{\sigma}{\mu}[/tex]
Which year's GMAT scores show a more dispersed distribution
Whichever year has the highest coefficient.
2009:
Mean of 500, standard deviation of 90. So
[tex]CV = \frac{90}{500} = 0.18[/tex]
2010:
Mean of 570, standard deviation of 85.5. So
[tex]CV = \frac{85.5}{570} = 0.15[/tex]
Due to the higher coefficient of variation, 2009's GMAT scores show a more dispersed distribution
2009's GMAT scores show a more dispersed distribution.
Given that in 2009: Mean = 500 and standard deviation = 90.
In 2010: Mean = 570 and standard deviation = 85.5.
If the standard deviation is higher then the scores will be more dispersed.
Note that: 90 > 85.5. And 90 corresponds to 2009.
So, 2009's GMAT scores show a more dispersed distribution.
Learn more: https://brainly.com/question/11231804
Simplify 18 - 2[x + (x - 5)]. 28 - 4 x 8 - 4 x 28 - 2 x
Answer:
[tex]-4x+28[/tex]
Step-by-step explanation:
[tex]18-2(x+x-5)[/tex]
[tex]18+(-2)(x)+(-2)(x)+(-2)(-5)[/tex]
[tex]18+-2x+-2x+10[/tex]
[tex]-2x-2x+10+18[/tex]
[tex]=-4x+28[/tex]
Which statement describes the behavior of the function f (x) = StartFraction 2 x Over 1 minus x squared EndFraction? f (x) = StartFraction 2 x Over 1 minus x squared EndFraction
Answer:
B. The graph approaches 0 as x approaches infinity.
Step-by-step explanation:
The function f(x) is:
f(x) = (2x)/(1-x^2)
When x approach infinity the term x² grows rapidly (more rapid than x), thus 1 - x², which is in the denominator will decrease, become a large negative more rapid than the x in the numerator. Thus you can expect that the function approaches zero.
Answer:
The left hand end behavior is decreasing and approaching 0, while the right hand end behavior is increasing and approaching 0.
Step-by-step explanation:
Assuming your fraction is [tex]\frac{2x}{1-x^{2} }[/tex], start by finding patterns. Since the denominator is 1-[tex]x^{2}[/tex], we can see that any number that is not between 0 and 1 results in a negative denominator. The numerator is 2x, so when x>1, the function is negative, and when x<1, the function is positive.
The denominator can never equal 0 - that results in 1/0, which is an UNDEFINED number.
SO, x can never be -1 or 1.
There is a vertical asymptote where the denominator is 0, so z = -1 and zxx = 1 are vertical asymptotes.
As the denominator becomes larger, the number approaches 0.
The left hand end behavior is decreasing and approaching 0, while the right hand end behavior is increasing and approaching 0.
An easier way to determine end behavior in a shorter time frame is to substitute in large numbers and estimate... like estimating in 300 or 900
A bucket that weighs 4 lb and a rope of negligible weight are used to draw water from a well that is 60 ft deep. The bucket is filled with 42 lb of water and is pulled up at a rate of 1.5 ft/s, but water leaks out of a hole in the bucket at a rate of 0.15 lb/s. Find the work done in pulling the bucket to the top of the well. Show how to approximate the required work by a Riemann sum. (Let x be the height in feet above the bottom of the well. Enter xi* as xi.)
Answer:
2580 ft-lb
Step-by-step explanation:
Water leaks out of the bucket at a rate of [tex]\frac{0.15 \mathrm{lb} / \mathrm{s}}{1.5 \mathrm{ft} / \mathrm{s}}=0.1 \mathrm{lb} / \mathrm{ft}[/tex]
Work done required to pull the bucket to the top of the well is given by integral
[tex]W=\int_{a}^{b} F(x) dx[/tex]
Here, function [tex]F(x)[/tex] is the total weight of the bucket and water [tex]x[/tex] feet above the bottom of the well. That is,
[tex]F(x)=4+(42-0.1 x)[/tex]
[tex]=46-0.1x[/tex]
[tex]a[/tex] is the initial height and [tex]b[/tex] is the maximum height of well. That is,
[tex]a=0 \text { and } b=60[/tex]
Find the work done as,
[tex]W=\int_{a}^{b} F(x) d x[/tex]
[tex]=\int_{0}^{60}(46-0.1 x) dx[/tex]
[tex]&\left.=46x-0.05 x^{2}\right]_{0}^{60}[/tex]
[tex]=(2760-180)-0[[/tex]
[tex]=2580 \mathrm{ft}-\mathrm{lb} [/tex]
Hence, the work done required to pull the bucket to the top of the well is [tex]2580 \mathrm{ft}- \mathrm{lb}[/tex]
eight less than fout times a number is less than 56. what are the possible values of that number
Answer:
x<16
Step-by-step explanation:
number n
eight less than four times a number ... 4 x n - 8
is less than 56 ... < 56
4 x n - 8 < 56
4 x n < 56 + 8
4 x n < 64/4
n < 64 / 4
n < 16
Answer:
Step-by-step explanation:
Let the number be x
Four times the number : 4x
Eight less than four times a number: 4x - 8
4x - 8 < 56
Now add 8 to both sides,
4x < 56+8
4x < 64
Divide both sides by 4,
x < 64/4
x < 16
Possible values of number = Value less than 16
Mary is running a marathon which is a total of 26 miles. She is running at a pace of 7.5 miles per hour and
has already run 8 miles. If she stays at the same pace, how much time in hours does she have left?
Answer:
2.4 hours
Step-by-step explanation:
If Mary is running 26 miles at a pace of 7.5 miles per hour, it will take her 3.47 hours to run the full course.
26/7.5 = 3.466666...
If she has run 8 miles, 1.07 hours have passed.
8/7.5 = 1.06666666...
Subtract the total time from the time that has already passed to find the time left.
3.47 - 1.07 = 2.4
Mary has 2.4 hours left.
Consider the graph of the line of best fit, y = 0.5x + 1, and the given data points. A graph shows the horizontal axis numbered negative 4 to positive 4 and the vertical axis numbered negative 4 to positive 4. Points show an upward trend. Which is the residual value when x = 2? –2 –1 1 2
Answer
its -1
Step-by-step explanation:
ED 2020 boiiiii
The residual value of the line of the best fit when x = 2 is -1
How to determine the residual value?The equation of the line is given as:
y = 0.5x + 1
When x = 2, we have:
y = 0.5 * 2 + 1
Evaluate
y = 2
The residual is the difference between the actual value and the predicted value.
From the complete graph, the actual value is 1.
So, we have:
Residual = 1 - 2
Evaluate
Residual = -1
Hence, the residual value when x = 2 is -1
Read more about residuals at:
https://brainly.com/question/1168961
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The measure of angle O is 600°. The polnt (x, y) corresponding to on the unit circle is?
Answer:
[tex](\frac{-1}{2} , \frac{-\sqrt{3} }{2} )[/tex]
Step-by-step explanation:
Memorize your unit circle.
Step 1: Subtract 360 from 600 degrees to find rotation
600° - 360° = 240°
Step 2: Either find coordinates from unit circle or convert to radians
240° = 4π/3
Step 3: Find coordinates
Leah has 28 more marbles than Dan. 1/3 of Leah’s marbles are equal in number to 4/5 of Dan’s marbles. Find the number of marbles Leah has.
Answer:
48
Step-by-step explanation:
L = D + 28
⅓L = ⅘D
Solve the system of equations using elimination or substitution. Using substitution:
⅓L = ⅘(L − 28)
Multiply both sides by 15:
5L = 12(L − 28)
Distribute:
5L = 12L − 336
Combine like terms:
336 = 7L
Divide:
L = 48
2ft/sec is how many mph?
Answer:
1.36364
Step-by-step explanation:
I calculated the solution on a calculator
So the answer to 1 d.p is 1.4