(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
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Step-by-step explanation:
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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°.
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What is the slope of the line shown in the graph?
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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
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the answer is C...... ....
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Answer:
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Answer:
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Step-by-step explanation:
Arc length is basically circumference.
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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 =
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240 + 40
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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:
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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
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Lateral Surface Area = 96in²
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P = 27in
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Lateral Surface Area = 189in²
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P = 60in
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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
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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
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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
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A = pi•r^2
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270.6 = pi•r^2
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86.134655 = r^2
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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1.false2.false3.true4.true5.true
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ANSWER C
GOOD LUCK
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
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Answers
Answer:
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Step-by-step explanation:
Answer:
A = 0.55 or 5/9
Step-by-step explanation:
Area = HL
A = (5/6)(2/3)
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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
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hence,
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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
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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.
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?
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Answer:
130 dollars
Step-by-step explanation:
This time I don't think I done messed it up
Have a good day!
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:
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
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Point-Slope Form: y - 2 = -⁶/₅(x - 0)
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.
To know more about frequency distributions here: brainly.com/question/30625605
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HELP! plz I can't find the aswer
Answers
Explanation: n +8 = adds 8
Multiply by 2 => Doubles the sum of n+8
52 )7,696 with reminder
Answers
have a great day!
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