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castortr0y [4]
3 years ago
12

College calculus: volume of a solid

Mathematics
1 answer:
Oliga [24]3 years ago
3 0
First, start by graphing the given region.
You should get a parabolic shape with min at (0,6) and end points intersecting with y=7.
When you rotate this around y=5, it will look like a vertical doughnut.
The cross-section of a doughnut is circular and looks like a washer.

Hence, we will use the 'washer method'
V = \pi  \int\limits^a_b {R^2 - r^2} \, dx
R is radius of outer ring from center which is y=5. The max value of region is y=7, giving a distance of 2 for our radius.
R = 2
'r' is radius of inner ring, this is point along curve f(x)=5+sec(x).
The distance from y=5 would be f(x) - 5.
r = sec(x)

V = \pi  \int\limits^{\pi/3}_{-\pi/3} {4 - sec^2 (x)} \, dx  \\  \\  \\ V = \pi |_{-\pi/3}^{\pi/3}(4x - tan x) \\  \\  \\ V = \frac{8\pi^2}{3} - 2\sqrt{3} \pi
You might be interested in
If a,b,c,d, and e are non negative such that x^6-289x^4-x^2+289=(x-a)(x+b)(x_c)(x+d)(x^2+ex+1), what is the value of a+b+c+d+e?
Irina18 [472]

Answer:

36

Step-by-step explanation:

Hello,

If X=x^2 it becomes

X^3-289X^2-X+289=(X^2-1)(X-289)

and 289=17^2

X^2-1=(X-1)(X+1)=(x^2-1)(x^2+1)=(x+1)(x-1)(x^2+1) \\\\x^2-289=x^2-17^2=(x-17)(x+17)

So,

x^6-289x^4-x^2+289=(x^2-1)(x^2+1)(x^2-289)=(x-1)(x+1)(x+17)(x-17)(x^2+1)

a = 1

b = 1

c = 17

d = 17

e = 0

Then a + b + c + d + e = 36

Thanks

3 0
2 years ago
Please help lot of points at stake- and will give brainly.
Veronika [31]

Answer:

a)1400 + 300x ≤ 5000

b) x ≤ 12 days

Step-by-step explanation:

a) Since the grocery store owner wants to stay within budget then, this means he would be spending at most $5,000

The word at most is represented by the inequality sign ≤ = Less than or equal to

Let x = Number of days

Hence,

Our inequality equation is

$1400 + 300× x ≤ $5000

1400 + 300x ≤ 5000

b) Solving for x

1400 + 300x ≤ 5000

300x ≤ 5000 - 1400

300x ≤ 3600

x ≤ 3600/300

x ≤ 12 days

3 0
2 years ago
Use the quadratic formula to find both solutions to the quadratic equation given below. 3x^2-x+4=0
Nuetrik [128]

Answer:

B. and D.

Step-by-step explanation:

4 0
3 years ago
a submarine is moving at a 35 km/h. It can say underwater for another 4.5 hours. If it speeds a steady, how long will it take a
dedylja [7]

Answer:

1 hour 24 minutes

Step-by-step explanation:

49/35=1.4

8 0
3 years ago
Leah's house has a media room with a large flat-screen television to watch movies. The media room television has a width of 8 fe
Naddik [55]
The Answer Would Be 64 because if you divide 8/4.5 its equal to 64/36.
8 0
3 years ago
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