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
Vesna [10]
2 years ago
11

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x, y =

0, x = 5, x = 7; about x = 1
Mathematics
1 answer:
miss Akunina [59]2 years ago
6 0

Answer:

381.18 cubic units

Step-by-step explanation:

Graph the region:

desmos.com/calculator/iwvreqjz2m

The region is a trapezoid.  When we rotate it about x = 1, we get a hollow cylinder shape.  We can either use washer method or shell method to find the volume.

If we find the volume using washer method, we'll have to use two integrals, one for the triangular part of the trapezoid and one for rectangular part.  If we use shell method, we only need one integral.  So let's use shell method.

Cut a thin, vertical slice of the region.  The width of this slice is dx.  The height of the slice is y₂ − y₁ = x − 0 = x.  The radius of the shell is x − 1.

The volume of the shell is:

dV = 2π (x − 1) (x) dx

dV = 2π (x² − x) dx

The total volume is the sum of all the shells from x=5 to x=7.

V = ∫ dV

V = ∫₅⁷ 2π (x² − x) dx

V = 2π ∫₅⁷ (x² − x) dx

V = 2π (⅓ x³ − ½ x² + C) |₅⁷

V = 2π [(⅓ 7³ − ½ 7² + C) − (⅓ 5³ − ½ 5² + C)]

V = 2π [⅓ 7³ − ½ 7² − ⅓ 5³ + ½ 5²]

V = 2π [⅓ (7³ − 5³) + ½ (5² − 7²)]

V = 2π [⅓ (218) + ½ (-24)]

V = 2π (72⅔ − 12)

V = 121⅓ π

V ≈ 381.18

The volume is approximately 381.18 cubic units.

You might be interested in
Determine the period.
vagabundo [1.1K]

Answer:

the period is the to top points of the highest points on top of the crests

7 0
2 years ago
Read 2 more answers
HELP ME PLS ASAP <br><br> a and b
morpeh [17]

Answer:

A.  

1. 5cm

2. 10cm

3. 20cm

4. 40 cm

Step-by-step explanation:

I think you need to double the area of the scaled factor.

6 0
3 years ago
Solve by quadratic formula:<br> 3x^2 - 10x - 20= 0
Arlecino [84]

this is your answer, i hope this helps you

5 0
3 years ago
Rewrite each pair of fractions using the least common denominator 5/6 2/5
Ivanshal [37]

Answer:

25/30 and 12/30

Step-by-step explanation:

6 and 5 have a least common multiple of 30

6*5 = 30

5/6 * 5/5 = 25/30

2/5 *6/6 = 12/30

5 0
3 years ago
Read 2 more answers
Nathan bought a video game for $60. Target is having a sale for 20% off all
anastassius [24]
$60 because he already bought the game but for other game $48
8 0
2 years ago
Other questions:
  • Which equation has the solution x = 9?<br><br><br> Select each correct answer.
    5·2 answers
  • List all subsets of the set S = {a,b}
    12·1 answer
  • If 2x-4(3-x)=18, then x=_____? Can someone please help me with this problem
    10·1 answer
  • Parallel to the line y= -6 containing points (2, 7)
    15·1 answer
  • Define a variable, then write and solve an inequality: Alex and his mother spent at least $130 while shopping for new clothes. A
    7·1 answer
  • PLEASE ANSWER ASAP! I WILL GIVE BRAINLIEST ANSWER !!!
    10·1 answer
  • Anybody Know This. ?
    15·1 answer
  • Find the slope of the line. Use the "/" to make a fraction if needed. Reduce your answer.
    9·1 answer
  • Use the distributive property to write an equivalent expression to -4(p+ 4) that
    7·1 answer
  • WILL GIVE BRAINLIEST
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!