Given the area in the first quadrant bounded by
x^2=8y, the line x=4 and the x-axis. What is the volume generated
when the area is revolved about the line y-axis?
Answers
The volume generated when the given area is revolved about the y-axis is approximately 21.333π cubic units.
To find the volume generated when the given area in the first quadrant is revolved about the y-axis, we can use the method of cylindrical shells.
The given area is bounded by the parabolic curve x^2 = 8y, the line x = 4, and the x-axis. To determine the limits of integration, we need to find the points of intersection between the curve and the line.
Setting x = 4 in the equation \(x^2\) = 8y, we have:
\(4^2\) = 8y
16 = 8y
y = 2
So, the points of intersection are (4, 2) and (0, 0).
Now, let's consider an infinitesimally thin vertical strip of width Δx at a distance x from the y-axis. The height of this strip is given by the equation \(x^2\) = 8y, which can be rearranged as y = (\(1/8)x^2\).
The circumference of the cylindrical shell generated by revolving this strip is given by 2πx, and the height of the shell is Δx. Therefore, the volume of this cylindrical shell is approximately equal to 2πx * (\(1/8)x^2\) * Δx.
To find the total volume, we integrate the expression for the volume over the range of x from 0 to 4:
V = ∫[0 to 4] 2πx * (\(1/8)x^2\) dx
Evaluating the integral, we get:
V = (1/12)π * [\(x^4\) [0 to 4]
V = (1/12)π * (4^4 - 0)
V = (1/12)π * 256
V = 21.333π
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Related Questions
HELP PWEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answers
Answer:
rap music
Step-by-step explanation:
^
Answer:
i’m not sure if these are right or not but
Step-by-step explanation:
the first one is no
i think the second one is no
i think the third one is yes
i think the fourth one is yes
i am not sure and i’m REALLY sorry if its wrong
Solve for x on the diagram below
Answers
The value of x in the angle is 56 degrees
How to detrmine the value of xFrom the question, we have the following parameters that can be used in our computation:
The figure
On the figure, we have teh following equation
64 + x + 60 = 180
The above is by the angle on a straight line theorem
So, we have
124 + x = 180
Evaluate the like terms
x = 56
Hence, the value of x is 56
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Answer:
x = 56
Step-by-step explanation:
64 + x + 60 = 180
124 + x = 180
x = 56
when you make a plot of ln k versus 1/t, what is the slope of the line?
Answers
When you make a plot of ln k versus 1/T, the Slope of the line is -Ea/R, where Ea is the activation energy of the reaction and R is the universal gas constant.
In the context of your question, ln k represents the natural logarithm of the rate constant (k), and 1/T represents the reciprocal of the absolute temperature (T) in Kelvin. When you make a plot of ln k versus 1/T, you are using the Arrhenius equation, which is given by:
k = A * exp(-Ea / (R * T))
Taking the natural logarithm of both sides, we get:
ln k = ln A - (Ea / R) * (1 / T)
This equation represents the equation of a straight line, y = mx + b, where y corresponds to ln k, x corresponds to 1/T, m (the slope) corresponds to -Ea/R, and b (the intercept) corresponds to ln A.
So, when you make a plot of ln k versus 1/T, the slope of the line is -Ea/R, where Ea is the activation energy of the reaction and R is the universal gas constant. This slope helps in determining the activation energy for the given reaction.
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Diff of squares help me out
Answers
Answer:
9
Step-by-step explanation:
9 is the correct answer
8. What are the values of x and y?
X
36
Answers
Select the correct answer.
A charity organization is holding a food drive with a goal to collect at least 1,000 cans of food by the end of the month. It currently has 565 cans from
donations and is having an event where 87 guests will attend and bring cans. Which solution set represents the number of cans each guest must
bring to meet the goal?
OA+
O B.
OC. +
O D.
+
0
O
0
o ++
0
1
+
1
1
1
3
+
3
2
2
+
+2
12
4
3
4
o+
3
4
4
5
5
5
6
+
6
6
7
7
7
5 6 7
8
8
8
8
+
9
9
9
9
10
10
10
10
Answers
The solution set representing the number of cans each guest must bring to meet the goal is {5}.
What is calculation of given terms?The charity organization is holding a food drive with a goal to collect at least 1,000 cans of food by the end of the month. They have received 565 cans from donations so far. In order to reach their goal, they need to collect more cans. They are having an event where 87 guests will attend and they expect guests to bring cans. In order to achieve the goal, they need to calculate the number of cans each guest should bring. To find this, they need to subtract the number of cans they have already collected from their goal, which is 1,000-565 = 435 cans. Then they will divide this number by the number of guests attending the event, which is 435/87 = 5 cans per guest. So, the solution set representing the number of cans each guest must bring to meet the goal is {5}. This means that each guest should bring at least 5 cans of food to the event in order for the charity organization to meet its goal of collecting 1,000 cans.To learn more more about graph refer
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y= -2/3x + 3 in standard form help :)
Answers
Answer: 2x−3y=−9
Step-by-step explanation:
help if you can id appreciate it
Answers
Less than 14 means
x < 14
Answer:
A. x < 14
Step-by-step explanation:
'<' = "less than"
'=' = "equal to"
'>' = "greater than"
Summer school issues help meeded asap
Answers
Answer:
2.B
Step-by-step explanation:
2.
Henry's container holds milk=200*7/8=175 ml
1) $400 interest is earned on a principal of $2,000 at a simple interest rate of 5%
interest per year. For how many years was the principal invested?
Answers
Answer:
4 years
Step-by-step explanation:
I = $ 400
R = 5%
P =$ 2000
I = Prt
400 = 2000 * \(\frac{5}{100}\) * t
400 = 20 * 5 * t
400 = 100 t
\(\frac{400}{100}=t\)
t = 4 years
Tim has read 30 % of a book. He has 56 more pages to finish. How many pages are there in the book?
Answers
Answer:
80 pagesStep-by-step explanation:
Let the number of pages is xTim has read 30 % of a bookRemaining
100% - 30% = 70%70% of x is 0.7x
0.7x = 56x = 56/0.7x = 80 pagesAnswer:
\( \bf \huge 80 \: pages\)
Step-by-step explanation:
Given that :Tim has read 30 % of a book.He has 56 more pages to finish.to find :How many pages are there in the book ?let us assume :total pages of book is 100•/•explanation :⟼ total book = 100•/•
⟼ Tim has read 30 % of a book.
⟼ 100 - 30 •/• = 70 •/•
⟼ 70 •/• = 56 pages
⟼ 1 •/• = 56 / 70
⟼ 100 •/• = 56 / 70 × 100
⟼ 100 •/• = 56 / 7 × 10
⟼ 100 •/• = 8 × 10
⟼ 100 •/• = 80 pages
∴ tim has 80 total pages in book.
How to simplify 1/2
Somebody help meeeee
Answers
Step-by-step explanation:
1/2 cannot be simplified, however you can solve this question by shading in the other half of the left square, and taking away a shade on the right one :)
Answer:
ok you can not simplify 1/2 but you can make it a higher proportion basically, one square can be one shaded purple of of the two rectangles and the other could be 4 different squares with two shaded purple
A group of friends paid $7 each to play a round of golf . It also cost $ 12 to rent a golf cart. As a group, they paid $ 33 altogether . Determine the number of friends that played golf .
Answers
Answer:
3 friends played golf
Step-by-step explanation:
33-12=21
21/7=3
I need help and its due Friday! If somone help me if will help so much and ty!!!
Answers
All of these have to be estimated using the chart shown^
1- 11% of 507
2-26% of 91
3-34% of 91
4-48% of 124
5-20% of 66
6- 47% of 80
7-48% of 202
8-74% of 39
9-30% of 118
10-20% of 42
11-arnold ate breakfast at a restaurant. The total cost of his food, juice, and coffee was $6.45. If the sales tax rate is 8% and Arnold wants to leave a 20% tip. how much should he pay
12- rodneys weekly gross pay is $91. He must pay 32% of taxes and deductions. estimate rodneys weekly take home after deductions.
Answers
how do you get the top one to the bottom one
Answers
Find the area under the graph of f(x) = x^2 + 6 between x=0 and x=6.
Area = _____
Answers
The area under the graph of f(x) = x^2 + 6 between x = 0 and x = 6 is 144 square units.
To find the area under the graph of f(x) = x^2 + 6 between x = 0 and x = 6, we need to evaluate the definite integral ∫[0, 6] (x^2 + 6) dx.
Using the power rule of integration, we can integrate each term separately. The integral of x^2 is (1/3)x^3, and the integral of 6 is 6x.
Integrating the function f(x) = x^2 + 6, we have ∫[0, 6] (x^2 + 6) dx = [(1/3)x^3 + 6x] evaluated from 0 to 6.
Substituting the limits, we get [(1/3)(6)^3 + 6(6)] - [(1/3)(0)^3 + 6(0)] = (1/3)(216) + 36 = 72 + 36 = 108.
Therefore, the area under the graph of f(x) = x^2 + 6 between x = 0 and x = 6 is 144 square units.
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PLS HELP ITS URGENT I HAVE LIKE A COUPLE QUESTIONS LEFT IM STUCK ON THIS
Answers
Answer: 3\(i\)
Step-by-step explanation: The reason for this is because \(i\) =
\(\sqrt{-1}\), and when \(\sqrt{-1}\) is multiplied to \(\sqrt{9}\), it becomes \(\sqrt{-9}\). Since \(\sqrt{9}\) can be simplified to 3, we can just multiply \(i\) to 3. This becomes 3\(i\).
Hope this helped!
Answer:
3i
Step-by-step explanation:
8 x -1/4 x -7 cara ngerjain nya bagaimana?
Answers
8*(-1/4)*-7
=2*(-1)*(-7)
=14
Samantha has 22$ To buy one binder and some packages of paper one binder cost 4$ and packages of paper cost 3$
Answers
One binder and six packages of paper can be bought by Samantha with her $22
Since we do not know how many binders and packages of paper she bought. So we assume that she bought b no of binders of p no of packages of paper
It's given that Cost of one binder is $4 and the cost of package of paper is $3
We can set up the algebraic equation:
4b + 3p = 22
4b = 22 - 3p
b = \(\frac{22 - 3p}{4}\)
If we assume that she bought 6 packages of paper, we can put into equation
b = \(\frac{22 - 18}{4}\) = 1 , which means that she bought 1 binder
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please help?!?! i’m so confused i keep getting the same answer i don’t know what i’m doing wrong
Answers
By simplifying the fraction, the value of a is -19 and the value of b is 15
Simplifying fractions: Determining the values of a and bFrom the question, we are to determine the values of a and b.
The given expression is
\(\frac{4x}{x + 3} - \frac{3x - 2}{x - 3} -1\)
\(\frac{4x}{x + 3} - \frac{3x - 2}{x - 3} -\frac{1}{1}\)
\(\frac{4x(x - 3) - [(3x - 2)(x + 3)] - [(x+3)(x-3)]}{(x + 3)(x - 3)}\)
\(\frac{(4x^2 - 12x) - [(3x^2 +9x -2x -6)] - [x^2 - 9]}{(x + 3)(x - 3)}\)
\(\frac{(4x^2 - 12x) - (3x^2 +7x -6) - (x^2 - 9)}{(x + 3)(x - 3)}\)
\(\frac{4x^2 - 12x- 3x^2 -7x +6 - x^2 + 9}{x^{2} -9}\)
Simplify
\(\frac{4x^2 - 3x^2 - x^2-7x - 12x+6 + 9}{x^{2} -9}\)
\(\frac{4x^2 - 4x^2 - 19x+15}{x^{2} -9}\)
\(\frac{ - 19x+15}{x^{2} -9}\)
Compare to \(\frac{ax+b}{x^{2} -9}\)
a = -19, b = 15
Hence, the value of a is -19 and b is 15
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What type of correlation is shown?
х
xx
Х
X
Answers
In a pack of pretzel sticks, one-quarter of the total number of pretzel sticks is 14.
how many are in the bag
Answers
Answer:
6 lol have a good day
Answer:
I got 56.
Step-by-step explanation:
Well if 1/4 of the bag is 14, then multiply it by 4. Sorry if this is wrong!
Which other expression has the same value as (-14) - 8? Explain your reasoning.
a. (-14) +8
b. 14- (-8)
c. 14+(-8)
d. (-14) + (-8)
Answers
The answer is D. (-14) + (-8) because (-14) + (-8) = -22
Please help fast its really important ;-; The base of a 15 foot ladder is 9 feet from a building. The top of the leaning ladder reaches and makes contact with the building's roof. On the corner of the building, a 6 foot flagpole is erected on the roof. What is the height from the base of the building to the top of the flagpole?
Answers
Answer:
18 ft
Step-by-step explanation:
Given that:
Length of ladder = 15 ft
Distance of ladder's foot from the building = 9 ft
Height of flagpole erected on the roof = 6 ft
To find:
Height of the top of flagpole from the base of the building?
Solution:
The given situation can be represented from the figure as attached in the answer area.
We have to find the length of \(BD\).
There is a right angle \(\triangle ABC\), right angled at point \(B\\\).
We can use Pythagorean theorem here to find the side \(BA\).
As per Pythagorean theorem:
\(\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow AC^{2} = BC^{2} + AB^{2}\\\Rightarrow 15^2 = 9^2+AB^2\\\Rightarrow AB^2 = 225-81\\\Rightarrow AB = \sqrt {144}\\\Rightarrow AB =12\ ft\)
\(BD = BA + AD\\\Rightarrow BD = 12 + 6\\\Rightarrow BD = \bold{18\ ft}\)
f the slope of a line is positive, the line is falling (or going down) from left to right , true or false
Answers
Step-by-step explanation:
Note that when a line has a positive slope it rises up left to right. Note that when a line has a negative slope it falls left to right. Note that when a line is horizontal the slope is 0. Note that when the line is vertical the slope is undefined
Answer:
False
explanation:When the slope is positive, the y-value increases as x increases which means that the line would move upward as it goes to the right side of the graph. The opposite is true when the slope is negative. The line would fall down as the x-value increases. This means that as x increases, y decreases when moving to the right side of the graph. When you go to the right, x-value increases.
Please please help me on this it’s due soon!!!!
Answers
Answer:
1 cup of milk = 3cups of brown sugar
Answer:
It's 3
Step-by-step explanation:
Because...
When we see the table we can find that it is given 2×3=6, 6×3=18, .... and so on so if we multiply 3 with 1 cup of milk then
3×1=3
So from this the answer is 3
Hope you understood!!
Select the correct answer.
To bake one cake, Drew uses 18 ounces of flour. He has 850 ounces of flour. Let y represent the ounces of flour left and x represent the number of cakes he has baked. When the situation is modeled on a graph, what are the slope and the y-intercept of the line representing this situation?
A.
slope = 850 and y-intercept = 18
B.
slope = 18 and y-intercept = 850
C.
slope = -18 and y-intercept = 850
D.
slope = 850 and y-intercept = -18
Answers
Answer:
The answer is C, hope that helps:)
Step-by-step explanation:
A scatterplot shows a set of data points that fit very loosely around a line that slopes down to the right. Which of the following values would be closet to the correlation for these data?
A.) 0.75
B.) 0.35
C.) -0.75
D.) -0.35
Answers
The value closest to the correlation for the given scatterplot would be C.) -0.75.
Which option is the closest value to the correlation for the loosely scattered data points with a downward sloping line?In a scatterplot, the correlation coefficient measures the strength and direction of the linear relationship between two variables. A value of -0.75 indicates a strong negative correlation. Since the data points fit loosely around a line that slopes down to the right, it suggests a negative correlation. The closer the correlation coefficient is to -1, the stronger the negative correlation. Option C.) -0.75 is the value closest to -1 and represents a stronger negative correlation compared to the other options.
To determine the precise correlation coefficient, statistical calculations or software can be used. These calculations involve measuring the covariance and standard deviations of the variables. However, based on the given description, it is apparent that the data points exhibit a loose fit around a downward-sloping line, indicating a strong negative correlation.
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The measures of the angles of △ABC are given by the expressions in the table.
Angle Measure
A (4x−13)°
B 15°
C (x+18)∘
What is the measure of ∠A and ∠C?
Answers
Answer:
A=82
C=83
X+y=60
X=30+50+80
X=80