1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Llana [10]
3 years ago
13

CALCULUS: Which of the following represents the volume of the solid formed by revolving the region bounded by the graphs of y =

img src="https://tex.z-dn.net/?f=x%5E%7B3%7D" id="TexFormula1" title="x^{3}" alt="x^{3}" align="absmiddle" class="latex-formula">, y = 1, and x = 3, about the line x = 3?
A. π * [27,1]∫ (3-∛y)² dy
B. π * ∛\int\limits^3_1 {(3-\sqrt[3]{y})^{2} } \, dy
C. None of these
Mathematics
2 answers:
Mademuasel [1]3 years ago
6 0

Answer:

π * [27,1]∫ (3-∛y)² dy

Step-by-step explanation:

Assoli18 [71]3 years ago
4 0

Disk method it is, since both given options integrate with respect to <em>y</em>.

First find where the boundaries of the region intersect.

• <em>y</em> = <em>x</em> ³ and <em>y</em> = 1 intersect at (1, 1)

• <em>y</em> = <em>x</em> ³ and <em>x</em> = 3 intersect at (3, 27)

• <em>y</em> = 1 and <em>x</em> = 3 intersect at (1, 3)

So the bounded region is the set of points

{ (<em>x</em>, <em>y</em>) | 1 ≤ <em>x</em> ≤ 3 and 1 ≤ <em>y</em> ≤ <em>x</em> ³ }

But since we're integrating with respect to <em>y</em>, rewrite this set so that <em>y</em> has constant limits:

{ (<em>x</em>, <em>y</em>) | ∛<em>y</em> ≤ <em>x</em> ≤ 3 and 1 ≤ <em>y</em> ≤ 27 }

Pick some point <em>y</em> in the interval [1, 27] and construct a disk centered at the given axis of revolution (<em>x</em> = 3). Such a disk will have radius 3 - ∛<em>y </em>because <em>x</em> = ∛<em>y</em> is the horizontal distance from the <em>y</em>-axis to the curve <em>y</em> = <em>x</em> ³ and <em>x</em> = 3 is itself 3 units away from the <em>y</em>-axis. Its height will be some small change in <em>y</em>, call it ∆<em>y</em>. Then the volume of this disk is

<em>π</em> (3 - ∛<em>y</em> )² ∆<em>y</em>

Now do the same thing for every <em>y</em> in [1, 27] - infinitely many of them! - and make ∆<em>y</em> very small, such that ∆<em>y</em> → d<em>y</em>. The volume of the solid is the sum total of the volumes of these infinitely many disks, given by the integral

\displaystyle\pi\int_1^{27}\left(3-\sqrt[3]{y}\right)^2\,\mathrm dy

and so the answer is A (assuming the limits of integration are listed from upper to lower).

You might be interested in
Researchers found a linear relationship between tail-feather length (in mm) and weight (in g) in a random sample of 20 male long
Dafna11 [192]

Answer:

   

Step-by-step explanation:

As far as I know, this question is not correct. I have the searched the internet and found a similar question which makes sense. In the correct question, 95% Confidence Interval is already given calculated from the software and

<em>95% prediction interval is asked (PI) for the weight of one male long tailed finch weighing 20 g.</em>

We have this data given in the correct question found on internet. And they have calculated this data using software:

New Obs = 20

Fit = 92.34

SE Fit = 5.26

95% Confidence Interval = (81.29, 103.38)

95% Prediction Interval = (67.61, 117.06)

Now, Just look at the prediction interval:

Now the formula for Prediction Interval = Point Estimate ± Margin of Error

Upper limit for prediction interval = 117.06

lower limit = 67.61

Formula for point estimate = (Upper + Lower)/2

Point Estimate = (117.06 + 67.61)/2

Point Estimate = 92.34

Formula for margin of error = (Upper - Lower)/2

Margin of Error = (117.06 - 67.61)/2

Margin of Error = 24.72

Formula for Prediction Interval = Point Estimate ± Margin of Error

PI = 92.34 ± 24.72

4 0
3 years ago
Please help quickly
Crank

Answer:25 m

Step-by-step explanation:

3 0
3 years ago
Jackson played a video game for 1/6 for hour. Hailey played a video game for 1/3 hour. Who played the video game for a greater a
viva [34]

Answer:

hailey played the game longer (1/3 hour).

Step-by-step explanation:

You are deciding which is greater: 1/6 or 1/3.in this case, a smaller denominator (such as 3) produces a greater value.1/3 has a smaller denom. than does 1/6, so 1/3 is greater than 1/6.hailey played the game longer (1/3 hour).

5 0
3 years ago
What is the range of the exponential function f(x)=2•7x
sergeinik [125]

f(x) cannot be 0 or less than zero, but can approach+ infinity

Answer is (0, ∞)

5 0
3 years ago
7(x+5)=-7(x+5) solving equations with variable on both sides​
sergij07 [2.7K]

Answer:

Step-by-step explanation:

7x+5=7x+5

-7x. -7x

Answer is 5=5

3 0
3 years ago
Other questions:
  • If a person walks 1/2 mile in 20 minutes, how far will that person walk in one hour?
    14·2 answers
  • Given: FKLM is a trapezoid, KL = 26 FM = 49, FK = 10, m∠F = 48º Find: Area of FKLM
    11·1 answer
  • Find the area of a parallelogram with a base of 10cm and height of 5cm. Write the area first and show your work.
    6·1 answer
  • F(5)= 3.14r^{2} <br><br> pls help
    15·1 answer
  • Negative n divided by 10
    14·2 answers
  • Given: m∠A = m∠C = 90° AB ║ DC Prove: ∆ABD ≅ ∆CBD
    9·1 answer
  • Can someone plz help me with these problems!!!
    8·2 answers
  • I am ranked 48th out of 326 in my class. What rank would I be considered? Top 1%, top 5%, top 10%, top 20%, etc. (this is for co
    6·2 answers
  • Help me pleaseeeee :(
    14·2 answers
  • A circular disc has circumference 250 cm.<br> Calculate the radius of the disc.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!