(q6) A student wants to find the area of the surface obtained by rotating the curve
, about the x-axis. Which of the following gives the correct area?
Answers
A student wants to find the area of the surface obtained by rotating the curve y = 0 < x < 1, about the x-axis. The correct answer is approximately 0.971π sq. units which gives correct area (rounded to three decimal places), which corresponds to option B.
To find the area of the surface obtained by rotating the curve y = 0 < x < 1 about the x-axis, we can use the method of cylindrical shells.
The formula for the surface area of a solid of revolution using cylindrical shells is given by:
Area = 2π ∫[a, b] y(x) * circumference(x) dx
In this case, the curve is y = x, and we are rotating it about the x-axis from x = 0 to x = 1.
So, the integral becomes:
Area = 2π ∫[0, 1] x * circumference(x) dx
To find the circumference at each point x, we need to consider that the circumference is the same as the height of the cylinder formed by rotating the curve. The height can be calculated as the difference between the y-coordinate of the curve and the x-axis, which is y = x - 0 = x.
Therefore, the circumference at each point x is given by 2πx.
Substituting this into the integral, we have:
Area = 2π ∫[0, 1] x * 2πx dx
= 4π^2 ∫[0, 1] x^2 dx
Evaluating the integral, we get:
Area = 4π^2 * [x^3/3] evaluated from 0 to 1
= 4π^2 * (1/3 - 0)
= 4π^2/3
Simplifying, we find:
Area ≈ 4.189π/3
≈ 1.396π
Therefore, the correct answer is approximately 0.971π sq. units (rounded to three decimal places), which corresponds to option B.
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The probable question could be:
A student wants to find the area of the surface obtained by rotating the curve y = 0 < x < 1, about the x-axis. Which of the following gives the correct area?
A. 1.303π sq. units
B. 0.971π sq. units
C. 0.579π sq. units
D. 0.203π sq. units
Related Questions
What is the slope of the line shown in the graph?
Answers
Answer:
1/2
Step-by-step explanation:
from point to point, you rise by one and run to the right by two
therefore, slope = 1/2
Yuri's homework grades for the 4th six-weeks were as follows: 67, 71, 49, 82, 87, 91, 78 What is the mean (average) of the following set of data? Round your answer to the nearest tenth of a decimal (one decimal place).
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The mean of the data set would be 75.
which criterion is least likely to be used in choosing bins (classes) in a frequency distribution?
Answers
The criterion that is least likely to be used in choosing bins (classes) in a frequency distribution is personal preference or subjective judgment.
When constructing a frequency distribution, it is important to consider objective criteria based on the nature of the data and statistical principles. Common criteria used for choosing bins include the range of the data, the desired number of bins, the shape of the data distribution, and the purpose of the analysis. These criteria help ensure that the bins effectively capture the variation in the data and provide meaningful insights. Personal preference or subjective judgment, on the other hand, may introduce bias and lack objectivity in determining the bin boundaries. It is essential to rely on objective criteria and statistical guidelines to make informed decisions when choosing bins for a frequency distribution.
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You spin the spinner twice what is the probability of landing on a three and then landing on a number greater than three
Answers
Answer:
2/4
Step-by-step explanation:
Some instructions for the time it takes to roast a turkey are: allow 20 minutes for every 450g
How long will it take to roast a turkey that weighs 6.3 kg?
Give your answer in hours and minutes.
please show work out <3
Answers
Answer:
4 hours and 40 minutes
Step-by-step explanation:
450g = kg
450g = 0.45 kg
We will use ratios:
[tex]\frac{20}{0.45} =\frac{x}{6.3} \\\\0.45x=126\\x=280[/tex]
280 mins =
4 hours and 40 minutes
4(60) + 40
240 + 40
280
What is the point that divides line DC into a ratio of 1:3, starting from point D C (-120, 83) D (156, -64)
Answers
Answer:
Step-by-step explanation:
can someone please answer these
*will give brainliest if you answer all* AND NO LINK
Answers
Answer:
Rectangular Prism → h = 2in
B = 143in
P = 48in
Surface Area = 382in²
Lateral Surface Area = 96in²
Triangular Prism → h = 7in
B = 20in
P = 27in
Surface Area = 229in²
Lateral Surface Area = 189in²
Triangular Prism → h = 10in
B = 120in
P = 60in
Surface Area = 840in²
Lateral Surface Area = 600in²
Step-by-step explanation:
Formulas: Total Surface Area = 2B = Ph
a²+b²=c²
Area = [tex]\frac{1}{2}[/tex]bh
Lateral Area = Ph
PLUG NUMBERS INTO FORMULA. (I'm too lazy to type it all out lol)
Instructions: Write the equation of the line in Point-Slope Form given the information below. Hint: The y-intercept is the
coordinate point (0,b)
Slope= -6/5
Y-Intercept = 2
Point-Slope Form:
Answers
Answer:
y - 2 = -⁶/₅xStep-by-step explanation:
The point-slope form of the equation of the line passing point (x₁, y₁) and with the slope of m is: y - y₁ = m(x - x₁)
m = -⁶/₅
Y-Intercept = 2 ⇒ point (0, 2) ⇒ x₁ = 0, y₁ = 2
Point-Slope Form: y - 2 = -⁶/₅(x - 0)
Need help on this one I really don’t get this
Answers
Please someone help it confusing
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1.false2.false3.true4.true5.true
52 )7,696 with reminder
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have a great day!
The figure shows a tank in the form of a rectangular prism that is 25% full of water. How many more gallons of water will it take to fill the tank? (1 gallon 231 in.)
Answers
Answer:
if it is one gallon then it will take 75 more percent
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
What is the volume of a cylinder with base radius 333 and height 666?
Answers
Answer:
V=πr2h=π·3332·666≈2.32013×108
Step-by-step explanation:
I NEED HELP PLSSSSS I WILL MARK BRAINLEIST <3
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the answer is C...... ....
C. .....
HELP! plz I can't find the aswer
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Explanation: n +8 = adds 8
Multiply by 2 => Doubles the sum of n+8
Necesito un dibujo donde se muestren los ángulos agudos obtusos rectos y llanos
Answers
Answer:
El dibujo se encuentra adjuntado al término de este documento, después de las explicaciones previas.
Step-by-step explanation:
Por Geometría sabemos lo siguiente:
Angulo recto - Dos semirrectas con origen común y cuya medida angular es mayor a 0° y menor a 90°.
Angulo obtuso - Dos semirrectas con origen común y cuya medida angular es mayor a 90° y menor a 180°.
Angulo recto - Dos semirrectas con origen común y cuya medida angular es igual a 90°.
Angulo llano - Dos semirrectas con origen común y cuya medida angular es igual a 180°.
Finalmente, presentamos un dibujo representativo de los cuatro tipos de ángulos.
The school Amina goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.
Answers
Answer:
child = $14
senior = $8
Step-by-step explanation:
3s + c = 38
3s + 2c = 52
52 - 38 = 14
child = $14
3s + 14 = 38
3s = 24
divide by 3
senior = $8
Find the area of the following figure below. Use 3.14 for pie
Answers
Answer: 113.1 i think sorry im bad at pi U_U
Step-by-step explanation:
Answer:
113.04
Step-by-step explanation:
Where rinding area so do the formula
A = Pi×r²
A = 3.14×36
A= 113.04
Sidney has $100 in a savings account. The interest rate is 10% per year and is not
compounded. How much interest will she earn in 3 years?
Answers
Answer:
130 dollars
Step-by-step explanation:
This time I don't think I done messed it up
Have a good day!
Cardania bought a car for $12,000 ten years ago, and it has been depreciating (decreasing in value) at a rate of 8% per year since she drove it off the showroom floor.
How much is the car worth today (10 years after her purchase)?
Answers
Answer:
The car is worth about 5212.66$ 10 years after her purchase.
Step-by-step explanation:
12000(1-0.08)^10=5212.661451
Please answer correctly! I will mark you Brainliest! The pictures go together!
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Answer: the volume of the cone is 21 inches cubed
Step-by-step explanation:
Answer:
65.97 or 65.96
Step-by-step explanation:
follow this picture and i want you to know that sometimes if you look it up and put in the info, it will be 1 or 2 off. sometimes it’s right. the actual formula for finding volume is V= 1/3h(pi)r and to the second power.
now i have no clue if i did this right but i will let you follow your instinct and whatever anyone else says! i’m sorry if this isn’t helpful but i tried by best at describing :)
Someone help plz and make plz make sure it’s right? :)
Answers
ANSWER C
GOOD LUCK
Which sequence is geometric?
O 5, 15, 25, 35, ...
O 5, 10, 20, 40, ... *
O 6, 12, 18, 24, ...
O 7, 14, 21, 28, ...
Answers
Answer:
0, 5, 10, 20, 40, ... *
Step-by-step explanation:
geometric sequences require a common ration and the only sequence with a common ratio is B. common ratio is 2
(h + 1) cm 6 cm A Write and solve an equation to find the value of h Include all of your work in your answer. B. In two or more complete sentences, verify your answer using mental math. 2
Answers
Answer:
See belowStep-by-step explanation:
we are given opposite and adjacent if the given right angle triangle
we want to make an equation with the given information
Part-1:notice that adjacent is greater than opposite so we can only take 30° as our angle
hence,
using trigonometric property
our equation is
[tex] \displaystyle \: \tan( {30}^{ \circ} ) = \frac{h + 1}{6} [/tex]
we took tangent function because we know that tangent function is the ratio of opposite and adjacent
now let's solve the equation
recall unit circle:
[tex] \displaystyle \: \frac{ \sqrt[]{3} }{3} = \frac{h + 1}{6} [/tex]
cross multiplication:
[tex]3(h + 1) = 6 \sqrt{3} [/tex]
divide both sides by 3:
[tex]h + 1 = 2 \sqrt{3} [/tex]
cancel 1 from both sides:
[tex] \therefore \: h = 2 \sqrt{3} - 1[/tex]
Part-2:by using mental math
The angle of elevation at the top of a tower at a point on the ground is 30° at a distance of 6 metre from the foot and the height of the tower is h+1. find h
now this question verifies the equation
because we are given a right angle triangle where the opposite is less than the adjacent so we took 30° as our angle
by solving the equation we'll again get our answer
How to find the arc length (geometry)
Answers
Answer:
94.2
Step-by-step explanation:
Arc length is basically circumference.
Circumference formula: 2πr
All we need is the radius.
Radius = r
15 x 2 = 30 (diameter)
Then we are going to multiply by pi.
Arc length = 30π OR 94.2
If a square had a area of 49cm^2 then what would be the perimeter?
Answers
What is the area of the rectangle below?
5/6 m H
2/3 m L
Answers
Answer:
5/9
Step-by-step explanation:
Answer:
A = 0.55 or 5/9
Step-by-step explanation:
Area = HL
A = (5/6)(2/3)
A = 0.55 or 5/9
Eric needs $10 to buy a book. He has $6 already. How much more money does Eric
need?
Answers
He needs 4 more dollars
Answer: $4
Step-by-step explanation: Since he needs 10 dollars and he already has 6 dollars, we can subtract to find the remaining amount, which is 4 dollars.
A spinner used in a board game is divided into 12 equally sized sectors. Seven of these sectors indicate that the player should move his token forward on the board, three of these sectors indicate that the player should move his token backward, and the remaining sectors award the player bonus points but do not move his token on the board.
The total area of the sectors that do not allow the player to move his token is 45. 1 inches squared.
What is the radius of the spinner?
Enter your answer, rounded to the nearest tenth of an inch, in the box
Answers
Answer:
The radius is 9.28 inches.
Step-by-step explanation:
Since there are 7 Move Ahead zones, and 3 Go Backwards zones on the spinner, there must be 2 other zones (the Freeze! +Bonus pts)
2 out of 12 zones are Freeze! +Bonus pts. That is 1/6 of the spinner. They said the area of the the Freeze!+Bonus pts is 45.1 inches squared.
45.1 × 6
= 270.6
The entire spinner has the area 270.6
The area of a circle is:
A = pi•r^2
We are looking for r. Thats the radius they asked for in the question.
270.6 = pi•r^2
pi is a number, I'm using the pi button on the calculator bc it is most exact.
270.6 = pi•r^2
Divide both sides by pi.
86.134655 = r^2
square root both sides.
9.28 = r
The radius is 9.28 inches.
true or false inequalities have many solutions and equations have one solution
Answers
Answer:
Step-by-step explanation:
Like systems of equations, system of inequalities can have zero, one, or infinite solutions.
Answer:
Yes this is true..............................................................................................................................