(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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Step-by-step explanation:
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the answer is C...... ....
C. .....
(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
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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
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by solving the equation we'll again get our answer
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
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Answer:
Step-by-step explanation:
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
Someone help plz and make plz make sure it’s right? :)
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ANSWER C
GOOD LUCK
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
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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)
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.
Please someone help it confusing
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1.false2.false3.true4.true5.true
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Answer:
Step-by-step explanation:
Like systems of equations, system of inequalities can have zero, one, or infinite solutions.
Answer:
Yes this is true..............................................................................................................................
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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°.
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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have a great day!
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Answers
Answer:
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Step-by-step explanation:
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
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Step-by-step explanation:
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3s + 2c = 52
52 - 38 = 14
child = $14
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Answers
Answer:
94.2
Step-by-step explanation:
Arc length is basically circumference.
Circumference formula: 2πr
All we need is the radius.
Radius = r
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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
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Answers
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Which sequence is geometric?
O 5, 15, 25, 35, ...
O 5, 10, 20, 40, ... *
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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
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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!
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
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PLUG NUMBERS INTO FORMULA. (I'm too lazy to type it all out lol)
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Answers
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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
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A= 113.04
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).
Answers
The mean of the data set would be 75.
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 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