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
lina2011 [118]
3 years ago
6

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 8 sin(x

), y = 8 cos(x), 0 ≤ x ≤ π/4; about y = −1

Mathematics
1 answer:
V125BC [204]3 years ago
5 0

Answer with explanation:

The equation of two curves are

y=8 sin x

y=8 cos x

The point of intersection of two curves are

→8 sin x=8 cos x

sinx = cos x

x=\frac{\pi}{4}\\\\y=8\sin\frac{\pi}{4}\\\\y=4\sqrt{2}

When you will look between points , 0 and x=\frac{\pi}{4}\\\\y=8\sin\frac{\pi}{4}\\\\y=4\sqrt{2},the curve obtained is right angled triangle.

Now, rotate the curve that is right angled triangle along the line , y= -1, to obtain a shape similar or resembling with Right triangular prism.

Draw a circular disc in the right triangular prism , having radius =x,and small part on the triangle having length dx.dx varies from 0 to \frac{\pi}{4}.

Required volume of solid obtained

    =\int\limits^{\frac{\pi}{4}}_0 {8 \sin x} \, dx \\\\=|-8\cos x|\left \{ {{x=\frac{\pi}{4}}} \atop {x=0}} \right.\\\\=8-4\sqrt{2}

    =8-4√2 cubic units    

You might be interested in
A company that makes​ hair-care products had 4,000 people try a new shampoo. Of the 4,000 ​people, 28 had a mild allergic reacti
lyudmila [28]

Answer:

0.007%

Step-by-step explanation:

4000/28=0.007%

7 0
3 years ago
PLEASE HELP!!<br> It’s asking for the measure of Arc KL in degrees
barxatty [35]

Answer:

30 degrees

Step-by-step explanation:

5 0
3 years ago
a quart of milk cost 73 cents. a CASE OF 12 QUARTS COSTS $7.68 . how much is saved per quart by buying the milk by the case
Nikitich [7]
12*$.73=$8.76-$7.68=$1.08 So it is $1.08 cheaper to buy it by the case.

Hope that helps.
5 0
3 years ago
If a coin has been altered so that the probability of heads coming up is 3/10, then the probability of tails coming up is also 3
Vadim26 [7]
False. Since the probability of one side of the coin is 3/10, the other must be 7/10.
6 0
3 years ago
Read 2 more answers
What one of the shape has a flat surface
melisa1 [442]

Answer:

Cylinder

Step-by-step explanation:

A cylinder has a 2 flat surfaces.

1 on each side

Answer: Cylinder is the correct answer

Hope this helps.

4 0
3 years ago
Other questions:
  • 0.59 divided by 2.419
    8·2 answers
  • Geoffrey is a lab technician and earns $9.65 per hour and works 40 hours a week. Estimate Geoffrey s annual wages, based on 50 w
    5·1 answer
  • I need help can some one help please . <br><br><br><br> A:$165<br> B:$195<br> C:$230<br> D:$250
    15·1 answer
  • What is the greatest possible error when measuring to the nearest quarter of an inch?
    15·1 answer
  • Helppppppppppppppppppppppppppppppppppp
    14·1 answer
  • HELP PLEASE!!!!
    13·1 answer
  • Suppose that IQ scores in one region are normally distributed with a standard deviation of . Suppose also that exactly of the in
    13·1 answer
  • Are these graphs rational or irrational?
    8·1 answer
  • Someone help (will give brainliest)
    13·1 answer
  • Write an inequality for "x".
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!