Express the number as a ratio of integers. 3.469 = 3.469469469

1 answer:

6 0

If you're looking for a fractional representation of the non-terminating decimal,
3.469469469....
then:

Let x=3.469469469.....
then
1000x-x=(3469.469469469...) - (3.469469469....)
999x = 3466
x=3466 / 999
= 3+469/999
$=3\frac{469}{999}$

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Hi! I need help with the attached question in calc. Thank you:)

Elena L [17]

Answer:

3π square units.

Step-by-step explanation:

We can use the disk method.

Since we are revolving around AB, we have a vertical axis of revolution.

So, our representative rectangle will be horizontal.

R₁ is bounded by y = 9x.

So, x = y/9.

Our radius since our axis is AB will be 1 - x or 1 - y/9.

And we are integrating from y = 0 to y = 9.

By the disk method (for a vertical axis of revolution):

$\displaystyle V=\pi \int_a^b [R(y)]^2\, dy$

So:

$\displaystyle V=\pi\int_0^9\Big(1-\frac{y}{9}\Big)^2\, dy$

Simplify:

$\displaystyle V=\pi\int_0^9(1-\frac{2y}{9}+\frac{y^2}{81})\, dy$

Integrate:

$\displaystyle V=\pi\Big[y-\frac{1}{9}y^2+\frac{1}{243}y^3\Big|_0^9\Big]$

Evaluate (I ignored the 0):

$\displaystyle V=\pi[9-\frac{1}{9}(9)^2+\frac{1}{243}(9^3)]=3\pi$

The volume of the solid is 3π square units.

Note:

You can do this without calculus. Notice that R₁ revolved around AB is simply a right cone with radius 1 and height 9. Then by the volume for a cone formula:

$\displaystyle V=\frac{1}{3}\pi(1)^2(9)=3\pi$

We acquire the exact same answer.

8 0

2 years ago

Find three prime numbers that add up to another prime number.

Illusion [34]

5+7+11=23
3+11+53=67
3+11+61=71
are some examples

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3 years ago

Read 2 more answers

what are the lengths of the legs of a right triangle in which one acute angle measures 19° and the hypotensue is 15 units long?

givi [52]

Refer to the diagram shown below.

Given:
m∠A = 19°
c = 15

By definition,
sin A = a/c
Therefore
a = c*sin A = 15*sin(19°) = 4.8835

cos A = b/c
Therefore
b = c*cos A = 15*cos(19°) =14.1828

Answer:
The lengths are 4.88, 14.18, and 15.00 (nearest hundredth)