Answer:
radius = 6
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given
x² - 12x + y² + 4y = - 4
Using the method of completing the square on the x and y terms
add (half the coefficient of the x/y term )² to both sides
x² + 2(- 6)x + 36 + y² + 2(2)y + 4 = - 4 + 36 + 4, that is
(x - 6)² + (y + 2)² = 36 ← in standard form
with r² = 36 ⇒ r = [tex]\sqrt{36}[/tex] = 6
Answer:
6
Step-by-step explanation:
h = -12/-2 = 6
k = 4/-2 = -2
h² + k² - r² = 4
6² + (-2)² - 4 = r²
r² = 36
r = sqrt(36) = 6
The number is less than one has two decimal place The digit is the hundredths place has a value of 5/100 The digit in the tenths place has a value of 2/10
Answer:
Therefore the required number is 0.25.
Step-by-step explanation:
Given that, the number is less than 1 has two decimal place.
The digit is the hundredths place has value of [tex]\frac{5}{100}[/tex]
=0.05
If a number divides with 100, then the point of the number shifts precede of two digits.
The digit in tenth place has a value of [tex]\frac2 {10}[/tex]
=0.2
The number is = tenth place value + hundredths place value
= 0.2+0.05
=0.25
Therefore the required number is 0.25.
Specifically looking at a number less than one with two decimal places: 2/10 in the tenths place and 5/100 in the hundredths place, resulting in the number 0.25.
The tenths place value, 2/10, means that there is a 2 in the tenths place. The hundredths place value, 5/100, means there is a 5 in the hundredths place. Therefore, combining these values, we get the number 0.25.
This demonstrates how decimal place values work, with each position to the right of the decimal point representing a fraction of ten (tenths, hundredths, etc.). The given values fit precisely into the decimal system, illustrating the concept of decimal place values clearly.
Sociologists want to test whether the number of homeless people in a particular urban area is increasing. In 2010, the average number of homeless people per day who sought shelter was 42.3 (σ = 6.2). Data from the current year reveal that the mean number of people seeking shelter per day is 45.3. Compute the test statistic using an alpha = .01 and n = 1000.
Answer:
The test statistic value is 15.3.
Step-by-step explanation:
The hypothesis for this test is:
H₀: The average number of homeless people is not increasing, i.e. μ = 42.3.
Hₐ: The average number of homeless people is increasing, i.e. μ > 42.3.
Given:
[tex]\bar x=45.3\\\sigma=6.2\\n=1000[/tex]
As the population standard deviation is provided use a single mean z-test for the hypothesis testing.
The test statistic is:
[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}=\frac{45.3-42.3}{6.2/\sqrt{1000}}=15.3[/tex]
Thus, the test statistic value is 15.3.
Using the z-distribution, it is found that the test statistic is of z = 15.3.
At the null hypothesis, it is tested if the mean number has not increased, that is, it still is of 42.3, hence:
[tex]H_0: \mu = 42.3[/tex]
At the alternative hypothesis, it is tested if it has increased, that is, the mean is greater than 42.3, hence:
[tex]H_1: \mu > 42.3[/tex]
We have the standard deviation for the population, hence, the z-distribution is used.
The test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. [tex]\sigma[/tex] is the standard deviation of the sample. n is the sample size.For this problem, the values of the parameters are:
[tex]\overline{x} = 45.3, \mu = 42.3, \sigma = 6.2, n = 1000[/tex]
Hence:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{45.3 - 42.3}{\frac{6.2}{\sqrt{1000}}}[/tex]
[tex]z = 15.3[/tex]
The test statistic is of z = 15.3.
To learn more about the z-distribution, you can take a look at https://brainly.com/question/16313918
When Brandon was told that he correctly answered 80 percent of the items on a math achievement test, he asked how his performance compared with that of the average test-taker. Brandon's concern was directly related to the issue of Group of answer choices content validity. predictive validity. standardization. factor analysis. reliability.
Answer:
The answer is standardization.
Step-by-step explanation:
Achievement tests are used in describing students’ learning abilities and academic accomplishments.
Since standardized achievement tests can give a better indication of students’ weaknesses, the test results will corroborate what can be seen on a daily basis, and the results can give insight into how a student's achievement compares to the average national student.
So, Brandon's concern was directly related to the issue of standardization because he wanted to make sure the test fulfilled the requirements of a standardized test ( i.e the questions, conditions for administering, scoring procedures, and interpretations) were consistent, and if so his score would not deviate greatly from the average test taker, and he wouldn't be an exception in obtaining such a high score.
If a member variable is declared , all objects of that class share that variable. A(n) function is not a member of a class, but has access to the private members of the class. A(n) tells the compiler that a specific class will be declared later in the program. When the operator is overloaded, its function must have a dummy parameter. The class Stuff has both a copy constructor and an overloaded = operator. Assume that blob and clump are both instances of the Stuff class. For each of the statements, indicate whether the copy constructor or the overloaded = operator will be called: Staff blob = clump ; clump = blob ; blob.operator =(clump) ; showValues(blob) ; // blob is passed by value Consider the following class declaration: class Thing { private: int x ; int y ; static int z ; public: Thing() { x = y = z ; } static void putThing(int a) { z = a ; } } ; int Thing:: z = 0 ; Assume a program containing the class declaration defines three Thing objects with the following statement: Thing one, two, three ; How many separate instances of the x member exist? How many separate instances of the y member exist ? How many separate instances of the z member exist? What value will be stored in the x and y members of each object? Write a statement that will call the putThing member function before the Thing objects are defined. Explain why the parameter of a copy constructor must be a reference.
Answer:
a shs s s s ss bsbsbsbs s s s s s s s s s s s s s
Two companies charge differently for canoe rentals, as shown below. What is the rate of change for each function? What is the cost to rent a canoe for 4 hours for each company? Company A: c = 8h + 10, where c = totals cost (in dollars) and h = number of hours Company B: $15 per hour
The rate of change for company A is $8 an hour and it would cost $42 to rent a canoe for four hours from company A.
The rate of change for company B is $15 an hour and it would cost $60 to rent a canoe for four hours from company B.
Step-by-step explanation:
Step 1:
For company A, [tex]c = 8h + 10,[/tex] where c is the cost after h hours.
When [tex]h=1,[/tex] [tex]c = 8(1) + 10 = 18.[/tex]
When [tex]h=2,[/tex] [tex]c = 8(2) + 10 = 26.[/tex]
The rate of change for company A [tex]= 26 - 18 = 8.[/tex]
The rate of change for company A is $8 an hour.
When [tex]h=4,[/tex] [tex]c = 8(4) + 10 = 42.[/tex]
So it would cost $42 to rent a canoe for four hours from company A.
Step 2:
For company A, the cost is $15 per hour so [tex]c = 15h,[/tex] where c is the cost after h hours.
When [tex]h=1,[/tex] [tex]c =1(15) =15.[/tex]
When [tex]h=2,[/tex] [tex]c = 2(15)= 30.[/tex]
The rate of change for company B [tex]= 30 - 15 = 15.[/tex]
The rate of change for company B is $15 an hour.
When [tex]h=4,[/tex] [tex]c = 4(15) = 60.[/tex]
So it would cost $60 to rent a canoe for four hours from company B.
Consider the statement that the product of two of the numbers 651000 − 82001 + 3177, 791212 − 92399 + 22001, and 244493 − 58192 + 71777 is nonnegative (for the purpose of this agreement, we will think of 0 as carrying a positive sign).Identify the correct proof of the given statement.(You must provide an answer before moving to the next part.)NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Consider the statement that the product of two of the numbers 651000 - 82001 - 3177791212-92399 22001, and 244493_58192+71777 is nonnegative (for the purpose of this agreement, we will think of O as carrying a positive sign). Identify the correct proof of the given statement. (You must provide an answer before moving to the next part.) A) Of these three numbers, at least two numbers must be negative, since there are only two signs. The product of these two numbers is nonnegative. B) Of these three numbers, at least two must be positive. The product of these two numbers is nonnegative. C) Of these three numbers, all three must have the same sign. Thus, the product of any two numbers is nonnegative. D) Of these three numbers, at least two must have the same sign, since there are only two signs. The product of two with the same sign is nonnegative. E) Of these three numbers, at least two must have the same sign. The product of one of these numbers and the third number is nonnegative.
Answer:
a c
Step-by-step explanation:
Final answer:
All three calculated numbers are positive, and therefore, the product of any two of them will also be positive. Option B is correct, which states that at least two numbers must be positive, making the resulting product nonnegative.
Explanation:
The statement that the product of two of the numbers 651000 - 82001 + 3177, 791212 - 92399 + 22001, and 244493 - 58192 + 71777 is nonnegative relies on the principles of arithmetic involving the addition and multiplication of numbers with different signs. Calculating the given numbers:
651000 - 82001 + 3177 = 573176 (positive)
791212 - 92399 + 22001 = 710814 (positive)
244493 - 58192 + 71777 = 255078 (positive)
All three numbers are positive, so the product of any two would also be positive, according to the multiplication rules that state the product of two positive numbers is always positive.
Therefore, the correct answer to the statement is:
B) Of these three numbers, at least two must be positive. The product of these two numbers is nonnegative.
Asna works on a shipping dock at a tire manufacturing plant. She load a pallet with 4 Mudslinger tires and 6 Roadripper tires. The tires on the pallet weigh 212 pounds. She loads a secong pallet with 7 Mudslinger tires and 2 Roadripper tires. The tires on the secong pallet weigh 184 pounds. How much does each Mudslinger and each Roadripper tire weigh? (9th Grade CP Math)
Answer:
A Mudslinger tire weighs 20.71 pounds and a Roadripper tire weighs 19.52 pounds
Step-by-step explanation:
Let the weight of a Mudslinger tire=m
Let the weight of a Roadripper tire=r
4 Mudslinger tires and 6 Roadripper tires weigh 200 pounds
4m+6r=200.....(i)
7 Mudslinger tires and 2 Roadripper tires weigh 184 pounds
7m+2r=184....(ii)
To find the values of m and r, we solve the two derived equations simultaneously.
4m+6r=200.....(i)
7m+2r=184....(ii)
Multiply (ii) by 3 to get (iii)
21m+6r=552....(iii)
4m+6r=200.....(i)
SUbtract (i) from (iii)
17m=352
m=352/17=20.71 pounds
Substitute m=20.71 in (i)
4(20.71)+6r=200
6r=200-82.84=117.16
r=117.16/6=19.52 pounds
A trader bought x mangoes at the rate of 4 mangoes for 10 naira five of the mangoes were bad so he sold the remaining at the rate of 5 mangoes for 20 naira and he made a gain of 10 naira how many mangoes did he buy ?
Answer:
20 mangoes.
Step-by-step explanation:
Given:
Total number of mangoes, a trader bought = [tex]x[/tex]
A trader bought at the rate of 4 mangoes for 10 naira.
Five of the mangoes were bad.
He sold the remaining at the rate of 5 mangoes for 20 naira.
He made a gain of 10 naira
Question asked:
Total number of mangoes, a trader bought = [tex]x[/tex] = ?
Solution:
Unitary method
Cost price of 4 mangoes = 10 naira.
Cost price of 1 mango = [tex]\frac{10}{4}[/tex]
Cost price of [tex]x[/tex] mango = [tex]\frac{10}{4}\times x= \frac{5}{2} x[/tex]
As 5 of the mangoes were bad and he sold the remaining mangoes, then Total number of mangoes sold = [tex]x-5[/tex]
Sale price of 5 mangoes = 20 naira
Sale price of 1 mango = [tex]\frac{20}{5}[/tex]
Sale price [tex]x-5[/tex] of mango = [tex]\frac{20}{5}\times(x-5)=4(x-5)=4x-20[/tex]
Now, as we know,
[tex]Gain = Sale price - cost price[/tex]
[tex]10 = 4x-20 -\frac{5}{2} x\\ 10=4x-\frac{5}{2} x-20\\10=\frac{8x-5x}{2} -20[/tex]
[tex]10 =\frac{3x}{2} -20[/tex]
Adding both sides by 20
[tex]30=\frac{3x}{2}[/tex]
Multiplying both sides by 2
[tex]60 = 3x[/tex]
Dividing both sides by 3
[tex]x=20[/tex]
Therefore, total number of mangoes, a trader bought is 20.
Which of the following is a series ? Check all that apply . 1/2 + 1/4 + 1/6 + 1/16 + 3.14159 B. 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 20 2 3k D. 25 - 5 - 10 - 15 - - 125
Answer:
A Series is always a periodic sum of terms, so only A and D will apply to that definition
(where A= 1/2 + 1/4 + 1/6 + 1/16 + 3.14159 and B=25 - 5 - 10 - 15 - - 125
PLLLLZ HELP Find the seventh partial sum of 13, 22, 31, 40, ...
9
67
106
280
Just got the test and answered 67...was absolutely sure it is correct answer...Most likely the answer is 9 ....Since to get every next sum is +9.. Well, at least 67 is a wrong answer..:(
The seventh partial sum is 280
Option D is the correct answer.
What is an arithmetic sequence?It is a sequence where the difference between each consecutive term is the same.
We have,
The sequence has a common difference of 9, so it is an arithmetic sequence.
The first term is 13.
To find the seventh partial sum, we need to add up the first seven terms of the sequence:
= 13 + 22 + 31 + 40 + 49 + 58 + 67
= 280
Therefore,
The seventh partial sum is 280
Learn more about arithmetic sequence here:
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8. Mr. Mercado bought a bond with a face value of $5000 and a coupon rate of 7.5%. The bond will mature in 15 years. How much interest will he receive semiannually?
Answer: $187.5
Step-by-step explanation:
The interest = 5000× ( 7.5/100 )÷2
=5000 × 0.075 ÷2
= 5000 ×0.0375
= 187.5 has interest semiannually
Hence, he gets 187.5
Explain how to use the figure below and a sequence of similarity transformations from Circle A to Circle C to prove that all circles are similar.
transformation: Translating then diilating
first you go from A to C
then you shrink it down to size n
A defunct website listed the "average" annual income for Florida as $35,031. What is the role of the term average in statistics? Should another term be used in place of average?
Answer:
For this case the average is an statistic unbiased for the population parameter [tex] \mu[/tex]
And the average is calculated with the following formula:
[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
Where n represent the sample size
N represent the population size, and X the observations for this case the annual income.
This statistic is an unbiased estimator of the population mean since [tex] E(\bar X) = \mu [/tex]
After calculate the average they got:
[tex] \bar X= 35031[/tex]
And we can use the term "sample mean" instead of the average, and is a measure of central tendency for the data
Step-by-step explanation:
For this case the average is an statistic unbiased for the population parameter [tex] \mu[/tex]
And the average is calculated with the following formula:
[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
Where n represent the sample size
N represent the population size, and X the observations for this case the annual income.
This statistic is an unbiased estimator of the population mean since [tex] E(\bar X) = \mu [/tex]
After calculate the average they got:
[tex] \bar X= 35031[/tex]
And we can use the term "sample mean" instead of the average, and is a measure of central tendency for the data
10 POINTS AND BRAINLIEST!
Calculate the area of the trapezoid, which is not drawn to scale.
Answer:
A = (5+4) divided by 1/2 x 11 (h) = 49.5 in
Answer:38 inches
Step-by-step explanation:A=1/2 (base 1 + base 2) x height = area
Base 1 = 11 in
Base 2 = 8 in
Height = 4 inches
Area if trapezoid = 1/2 x 11 + 8 x 4 =!19 sum of bases
19x4(H) = 76
76/2=38 inches
Area of trapezoid = 38 inches
Lin read for x minutes, and Elena read for more than that. Write an expression for the number of minutes Elena read. Only use decimals in your expression
In this exercise, we know some facts:
Lin read for x minutes.Elena read for more than that.The problem tells us nothing about the number of minutes Elena read more than Lin. However, let's say Elena read one-third more than the number of minutes Lin read. Therefore:
For Lin:
[tex]Number \ of \ minutes \ Lin \ read=x[/tex]
For Elena:
[tex]Number \ of \ minutes \ Elena \ read=x+\frac{1}{3}x \\ \\ Number \ of \ minutes \ Elena \ read=\frac{3x+x}{3} \\ \\ Number \ of \ minutes \ Elena \ read=\frac{4x}{3} \\ \\ Number \ of \ minutes \ Elena \ read=\frac{4x}{3} \\ \\ \\ By \ using \ decimals: \\ \\ Number \ of \ minutes \ Elena \ read \approx 1.33x[/tex]
Final answer:
The expression for the number of minutes Elena read is x + 1.
Explanation:
To write an expression for the number of minutes Elena read, we can use the variable x to represent the number of minutes Lin read. Since Elena read for more than Lin, we can use the expression x + 1 to represent the number of minutes Elena read. This expression indicates that Elena read for one minute more than Lin.
If it takes Daniel 9 hours to clean an office building and it takes Mark 6 hours, how long would it take the two of them, working together, to clean the building?
It would be 3 hours. This is 3 hours because the problem says that daniel takes 9 hours to clean and office building and mark takes 6 hours so if you subtract 9hours from 6 hours it would be 3 hours total. Now this can be 2 answers it can also be 15 hours if you were to add 9 hours to 6 hours.
Answer: it will take 3.6 hours
Step-by-step explanation:
If it takes Daniel 9 hours to clean an office building, it means that the rate at which he cleans the office building per hour is 1/9
If it takes Mark 6 hours to clean the office building, it means that the rate at which Mark cleans the office building per hour is 1/6
If they work together, they would work simultaneously and their individual rates are additive. This means that their combined working rate would be
1/9 + 1/6 = (6 + 9)/54 = 15/54
Assuming it takes t hours for both of them to clean the office working together, the working rate per hour would be 1/t. Therefore,
15/54 = 1/t
t = 54/15 = 3.6 hours
It was predicted that a country will have an elderly population (65 and older) of 8 comma 176 comma 000 in the year 2050 and that this will be 22.1% of the population. What is the total predicted population of this country in 2050?
Answer:
36,995,475
Step-by-step explanation:
In the year 2050, a country's elderly population is predicted to be 8,176,000
This is 22.1% of the tota population
If x=total population in the year 2050
and 22.1% of x = 8,176,000
Then:
22.1% of x = 8,176,000
[tex]\frac{22.1}{100}x= 8176000[/tex]
On Cross multiplication
22,1x = 817,600,000
x=[tex]\frac{817600000}{22.1}[/tex] =36995475.11
We jettison fractional values because we are dealing with population.
Therefore, In the year 2050, the total population of the country will be 36,995,475
In which survey was a parameter reported? Select two answers.
A. “Of the 100 teenagers surveyed from Jill’s middle school, 2 out of 3 of them own a bicycle.
B. “Of the 1000 seventh grade boys surveyed across the U.S., 5 out of 6 of them want to go to college.
C. “Of the 120 sixth graders at Jill’s middle school, 3 out of 5 of them bring their lunch.
D. “Of the 50 students surveyed across the city who take the bus, 1 out of 2 of them said they would prefer another mode of transportation.
E. “Of the 92 teachers at Jill’s middle school, 3 out of 4 do not like working late.
Answer:
C and E
Step-by-step explanation:
A parameter is a percentage of a population.
A, B, and D are percentages from surveys (samples).
C and E are percentages from populations.
On a river you must release any fish that you catch ifvit measures less than 12 inches. Define a variable and then write an algebraic inequality for each senario. can you keep a fish that is 11.99 inches?
Let f = fish
If f < 12, let the fish go.
We cannot catch a fish measuring 11.99 inches.
If f = fish, then f < 11.99. It must be released.
David waits by the crosswalk sign on his way to school. The angle outlined on the sign turns through 50 one-degree angles. Find the measure of the angle.
the measure of the angle outlined on the sign is 50∘.
To find the measure of the angle outlined on the sign, we simply multiply the number of one-degree angles by the measure of one degree.
Given that the angle turns through 50 one-degree angles, we can calculate the measure of the angle as follows:
Measure of the angle = Number of one-degree angles × Measure of one degree
Measure of the angle=50 * 1
Measure of the angle=50
So, the measure of the angle outlined on the sign is 50∘.
The probable question maybe:
David waits by the crosswalk sign on his way to school. The angle outlined on the sign turns through 50 one-degree angles. What is the measure of the angle outlined on the crosswalk sign?
HELP ASAP!! Write the inverse variation function given that y varies inversely with x, and y = 2 when x = 8.
Answer: y= 16/x
Step-by-step explanation:
At what points on the graph of f(x)=2x^3-6x^2-27x is the slope of the tangent line -9?
Answer:
(-1, 19) and (3, -81)
Step-by-step explanation:
f(x) = 2x³ − 6x² − 27x
f'(x) = 6x² − 12x − 27
-9 = 6x² − 12x − 27
0 = 6x² − 12x − 18
0 = x² − 2x − 3
0 = (x + 1) (x − 3)
x = -1 or 3
f(-1) = 19
f(3) = -81
The points are (-1, 19) and (3, -81).
Solve the system of linear equations by substitution.
−x−8=−y
9y−12+3x=0
The solution is ( , )
Answer:
The solution (x, y) = (-5, 3)
Step-by-step explanation:
-x - 8 = -y .... (1)
9y - 12 + 3x = 0 .... (2)
from equation (1)
-x = - y + 8 ... (3)
multiply equation (3) by -1
x = y - 8 ..... (4)
substituting equation (4) in equation (2)
9y - 12 + 3 ( y - 8) = 0
9y - 12 + 3y - 24 = 0
12y - 36 = 0
12y = 36
y = 36 /12
y = 3
Substitute y = 3 in equation (4)
x = y - 8
x = 3 - 8
x = -5
Find the value of the given function's derivative at x=3
f(x)=k(g(x))
g(x)=2x-x^2
k'(-3)=2
f'(3)=[]
According to the chain rule, if we have a function:
[tex]f(x)=k(g(x))[/tex]
The derivative at a point [tex]a[/tex] will be:
[tex]f'(a)=k'(g(a))g'(a)[/tex]
We know that:
[tex]f'(3)=k'(g(3))g'(3)\\ \\ \\ a=3 \\ \\ \\ Then: \\ \\ g(3)=2(3)-3^2 \\ \\ g(3)=6-9 \\ \\ g(3)=-3 \\ \\ \\ k'(g(3))=k'(-3)=2 \\ \\ \\ g'(x)=2-2x \\ \\ g'(3)=2-2(3)=-4 \\ \\ \\ Finally: \\ \\ f'(3)=2(-4) \\ \\ \boxed{f'(3)=-8}[/tex]
What is a key purpose of using simulation when comparing two populations?
A) Calculating theoretical probability
B) Observing how probability works with real items
C) Checking that the correct test statistics were used
D) Finding a precise answer to a question
Answer:
B) Observing how probability works with real items
Step-by-step explanation:
Just took the quiz
Last week 23,847 tickets were sold At the Atlantic school. The principal rounded the number of tickets. To the nearest thousand.He rounded the number of tickets sold for the music festival to the nearest thousand as well. They both rounded to the same number. How many tickets were sold for the music festival?
Answer: 24,000 tickets
Step-by-step explanation: The idea is just to round up the original ticket sold to the nearest thousand. That is 23,847 tickets to the nearest thousand is 24,000 since the next number after 3 is 8 which is greater or equal to five so you take it as 1 and add it to 3 making the total number of tickets sold as 24,000.
Brynn ate 4/10 funnel cakes and 37/100 of the food was cotton candy. The rest of the food was popcorn. What fraction of the food brynn are was funnel cakes or cotton candy?
Answer:
?
Step-by-step explanation:
Convert 4/10 into 40/100(so you can have same denominator as other fraction) and then add 40/100 and 37/100 and you will get the answer!
A rectangular parcel of land is 100 ft wide. The length of a diagonal between opposite corners is 20 ft more than the length of the parcel. What is the length of the parcel
Final answer:
Using the Pythagorean theorem, the length of the parcel of land was calculated to be 240 feet, given that its width is 100 feet and the diagonal is 20 feet longer than the length.
Explanation:
To solve for the length of the parcel of land, given that it has a width of 100 feet and a diagonal that is 20 feet longer than the length, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this situation, let's denote the length of the parcel as 'L' and the diagonal as 'D'. We then have the relationship:
D = L + 20 feet
We can establish the equation L2 + 1002 = (L + 20)2.
Expanding the right side of the equation gives us L2 + 10,000 = L2 + 40L + 400. Simplifying the equation by subtracting L2 from both sides, we get 10,000 = 40L + 400. Subtracting 400 from both sides gives us 9,600 = 40L, which simplifies to L = 240 feet when we divide both sides by 40.
Therefore, the length of the parcel is 240 feet.
A gas station stores its gasoline in a tank underground. The tank is a cylinder lying horizontally on its side. The radius is 5 ft, the length is 15 ft, and the top of the tank is 10 feet under the ground. Assume the tank is full and all of the gasoline will be pumped to the surface of the ground. The density of gasoline is 42 lb/ ft3. Consider a slice of gasoline that is delta y ft thick and located y ft above the center of the cylinder. Use delta or the CalcPad for delta . Leave pi in your answer. Volume of slice : ft3 Displacement of slice : ft Find the endpoints of the integral needed to find the exact work required to pump all the gasoline to the surface of the ground. Lower endpoint = Upper endpoint =
Answer:
The exact work required to pump all the gasoline to the surface of the ground is π × 5.094 × 10⁶ j
Step-by-step explanation:
Here, we note that volume of a slice is given by
Length × Width × Height
Length of slice = Length of cylinder = 15 ft
Since the slice height is Δy ft thick and located y ft above the center of the cylinder, then
Width of slice = 2 × √(r² - y²)
Where:
r = Radius of the cylinder =5 ft
∴ Width of slice = 2 × √(25 - y²)
∴Volume of slice = 15 ×2 × √(25 - y²)×Δy
Mass of slice then = 42 × 15 ×2 × √(25 - y²)×Δy = 1260 × √(25 - y²)×Δy
The force required to lift the slice is the weight of the slice, which is given by
32.2 × 1260 × √(25 - y²)×Δy = 40572 × √(25 - y²)×Δy N (Newtons)
The work done by the force is the product of the force and the distsnce through which the force acts.
Work done = 40752×(10-y) × √(25 - y²)×Δy
Therefore total work done is given by
[tex]W = \int\limits^5_{-5} {40752\times (10-y) \times \sqrt{ (25 - y^{2} )} } \, dy[/tex]
= 5094000·π J = π × 5.094 × 10⁶ j
The exact work required to pump all the gasoline to the surface of the ground = π × 5.094 × 10⁶ j
The calculation requires determining the volume and displacement of each slice of gasoline in the tank and then integrating over these from the bottom to the top of the tank (from -5 to 5 feet).
Explanation:
To calculate the exact work required to pump all the gasoline to the surface, we need to first determine the displacement of each slice of gasoline and then integrate over the total volume. The displacement of a slice at height y is the distance it needs to be moved to the surface, which is (10 - y) feet. The volume of a cylindrical slice of thickness delta y is given by the area of the cylinder's cross section times the slice's thickness, i.e., volume = pi * r^2 * delta y. Here, r = 5ft and delta y is the thickness of the slice. Therefore, the volume of the slice is 25*pi*delta y ft3. The endpoints of the integral are defined by the top and bottom of the tank relative to the center, which in this case are -5 and 5 feet. Therefore, the lower endpoint is -5 and the upper endpoint is 5.
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A tailor cuts a piece of thread One-half of an inch long from a piece Nine-sixteenths of an inch long. What is the length of the remaining piece of thread?
Answer:
The length of the remaining piece of thread is [tex]\frac{1}{16}.[/tex]
Step-by-step explanation:
Given:
A tailor cuts a piece of thread One-half of an inch long from a piece Nine-sixteenths of an inch long.
Now, to find the length of the remaining piece of thread.
Total thread = [tex]\frac{9}{16} \ inch.[/tex]
Tailor cuts a piece of thread = [tex]\frac{1}{2}\ inch.[/tex]
Now, to get the length of the remaining piece of thread by subtracting tailor cuts a piece of thread from the total thread:
[tex]\frac{9}{16} -\frac{1}{2} \\\\=\frac{9-8}{16} \\\\=\frac{1}{16}[/tex]
Therefore, the length of the remaining piece of thread is [tex]\frac{1}{16}.[/tex]
Answer lovely
Step-by-step explanation: