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3 years ago

Is 0.135135135135 rational or irrational

Mathematics

1 answer:

nadya68 [22]3 years ago

5 0

It is rational because it is a repeating decimal. it repeats .135

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A pencil cup is a cylinder made of plastic with one base missing. The cup is 5 inches tall and has a radius of 1.75 inches. Appr

wariber [46]

Answer:

74.22

Step-by-step explanation:

a pencil cup is like a cylinder

A=2πrh+2πr2=2·π·1.75·5+2·π·1.752≈74.22013

hope this helps

correct me if this is wrong

3 0

3 years ago

How do I solve this?

Gelneren [198K]

I hope this helps you!

8 0

3 years ago

G find the area of the surface over the given region. use a computer algebra system to verify your results. the sphere r(u,v) =

Svetach [21]

Presumably you should be doing this using calculus methods, namely computing the surface integral along $\mathbf r(u,v)$ .

But since $\mathbf r(u,v)$ describes a sphere, we can simply recall that the surface area of a sphere of radius $a$ is $4\pi a^2$ .

In calculus terms, we would first find an expression for the surface element, which is given by

$\displaystyle\iint_S\mathrm dS=\iint_S\left\|\frac{\partial\mathbf r}{\partial u}\times\frac{\partial\mathbf r}{\partial v}\right\|\,\mathrm du\,\mathrm dv$

$\dfrac{\partial\mathbf r}{\partial u}=a\cos u\cos v\,\mathbf i+a\cos u\sin v\,\mathbf j-a\sin u\,\mathbf k$
$\dfrac{\partial\mathbf r}{\partial v}=-a\sin u\sin v\,\mathbf i+a\sin u\cos v\,\mathbf j$
$\implies\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}=a^2\sin^2u\cos v\,\mathbf i+a^2\sin^2u\sin v\,\mathbf j+a^2\sin u\cos u\,\mathbf k$
$\implies\left\|\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}\right\|=a^2\sin u$

So the area of the surface is

$\displaystyle\iint_S\mathrm dS=\int_{u=0}^{u=\pi}\int_{v=0}^{v=2\pi}a^2\sin u\,\mathrm dv\,\mathrm du=2\pi a^2\int_{u=0}^{u=\pi}\sin u$
$=-2\pi a^2(\cos\pi-\cos 0)$
$=-2\pi a^2(-1-1)$
$=4\pi a^2$

as expected.

6 0

3 years ago

In Europe, 53% of the flowers of the Rewardless Orchid, Dactylorhiza sambucina, are yellow, whereas the remaining flowers are pu

stich3 [128]

Answer:

a. The probability of taking out a purple flower is 0.47.

b. The probability that out of a sample of 5 flowers at least 3 flowers are yellow 0.56.

c. The standard deviation of the distribution for proportion of yellow flowers is 0.22.

d. The probability that out of the 263 samples, at most 150 of them are yellow is 0.90.

Step-by-step explanation:

7 0

3 years ago

what is the y-intercept of the equation of the line that is perpendicular to the line y=3/5x+10 and passes through the point (15

ohaa [14]

The slope of the given line is the coefficient of x, 3/5. The slope of the perpendicular line will be the negative reciprocal of that: -1/(3/5) = -5/3.

The point-slope form of the equation for a line of slope m through point (h, k) can be written ...

... y = m(x -h) +k

For your point and the slope found above, this becomes

... y = (-5/3)(x -15) -5

When x=0, this is

... y = (-5/3)(-15) -5 = 20

The y-intercept is 20.

3 0

3 years ago