Determine if 0.59136363636363636... is rational or irrational and give a reason for your answer

Mathematics

1 answer:

Reil [10]1 year ago

7 0

The number 0.59136363636363636... is an irrational numbers

<h3>How to determine the number type?</h3>

The number is given as:

Number = 0.59136363636363636...

The three dots at the end of the number implies that the numbe is a non-terminating decimal

All non-terminating decimal are irrational numbers

Hence, the number 0.59136363636363636... is an irrational numbers

Read more about irrational numbers at

brainly.com/question/11919233

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A town in east Texas recieved 10 inches of rain in two weeks. If it kept raining at this rate for a 31-day month, how much rain

Gelneren [198K]

The best way to approach this problem is to find out how much fell in week. As you know what two weeks is, you simply have to halve this, giving you that one week is 5 inches of rain. One you have this, you can multiply this by 4 (as this will give you 4 weeks, or 28 days), and this gives you 20 inches in 28 days. You should then find the odd three days. If you divide 5 by 7, this will give you the rain fall in one day. 5/7= 0.8 inches per day. You then have top multiply this by 3 (as you've got three odd days), and this gives you 2.4. You then have to add together 2.4 and 20, giving you 22.4
Therefore, if the rain continued to fall at the same rate for 31 days, it would receive 22.4 inches of rain.
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2 years ago

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2 years ago

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. A right cylindrical drum is to hold 7.35 cubic feet of liquid. Find the dimensions (radius of the base and height) of the drum

Drupady [299]

Answer:

$r=1.05\ \text{ft}$

$h=2.12\ \text{ft}$

$20.91\ \text{ft}^3$

Step-by-step explanation:

r = Radius

h = Height

Volume of cylinder = $7.35\ \text{ft}^3$

$V=\pi r^2h\\\Rightarrow h=\dfrac{V}{\pi r^2}\\\Rightarrow h=\dfrac{7.35}{\pi r^2}$

Surface area is given by

$A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi r^2+2\pi r\dfrac{7.35}{\pi r^2}\\\Rightarrow A=2\pi r^2+\dfrac{14.7}{r}$

Differentiating with respect to radius we get

$\dfrac{dA}{dr}=4\pi r-\dfrac{14.7}{r^2}$

Equating with zero we get

$0=4\pi r-\dfrac{14.7}{r^2}\\\Rightarrow 4\pi r=\dfrac{14.7}{r^2}\\\Rightarrow r^3=\dfrac{14.7}{4\pi}\\\Rightarrow r=(\dfrac{14.7}{4\pi})^{\dfrac{1}{3}}\\\Rightarrow r=1.05$

$\dfrac{d^2A}{dr^2}=4\pi-2\times \dfrac{14.7}{r^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=4\pi+2\times \dfrac{14.7}{1.05^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=37.96>0$