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3 years ago

Augustus ruled the roman empire from 27 BC to AD 14.For how many years did he rule?

Mathematics

1 answer:

Semmy [17]3 years ago

4 0

Answer:

40 years

Step-by-step explanation:

He was also the first Roman Emperor

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Find the following integral

ololo11 [35]

There's nothing preventing us from computing one integral at a time:

$\displaystyle \int_0^{2-x} xyz \,\mathrm dz = \frac12xyz^2\bigg|_{z=0}^{z=2-x} \\\\ = \frac12xy(2-x)^2$

$\displaystyle \int_0^{1-x}\int_0^{2-x}xyz\,\mathrm dz\,\mathrm dy = \frac12\int_0^{1-x}xy(2-x)^2\,\mathrm dy \\\\ = \frac14xy^2(2-x)^2\bigg|_{y=0}^{y=1-x} \\\\= \frac14x(1-x)^2(2-x)^2$

$\displaystyle\int_0^1\int_0^{1-x}\int_0^{2-x}xyz\,\mathrm dz\,\mathrm dy\,\mathrm dx = \frac14\int_0^1x(1-x)^2(2-x)^2\,\mathrm dx$

Expand the integrand completely:

$x(1-x)^2(2-x)^2 = x^5-6x^4+13x^3-12x^2+4x$

Then

$\displaystyle\frac14\int_0^1x(1-x)^2(2-x)^2\,\mathrm dx = \left(\frac16x^6-\frac65x^5+\frac{13}4x^4-4x^3+2x^2\right)\bigg|_{x=0}^{x=1} \\\\ = \boxed{\frac{13}{240}}$

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2 years ago

If the sum of 1 and the product<br> of p and 8 is equal to 62 less than p

Ierofanga [76]

Uhh I think isa carrot

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3 years ago

You flip a coin and then roll a 6-sided number cube (a die).

expeople1 [14]

Answer:

a) No, it does not matter whether you roll the die or flip the coin first, as these two events are <u>independent</u> of each other, which means they do not affect each other.

b) Yes.

Let event 1 be flipping a coin and event 2 be rolling a die.
Let event 1 be rolling a die and event 2 be flipping a coin.

The likelihood that any outcome will occur will not change, as the events are independent.

c) see attached

d) 12 outcomes (H = head, T = tail, numbers represent the value of the die)

H 1 T 1

H 2 T 2

H 3 T 3

H 4 T 4

H 5 T 5

H 6 T 6

$\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}$

$\implies \sf P(even)=\dfrac{1}{6}+\dfrac{1}{6}+\dfrac{1}{6}=\dfrac{3}{6}=\dfrac{1}{2}$

$\implies \sf P(head)=\dfrac{1}{2}$

$\implies \sf P(even)\:and\:P(head)=\dfrac{1}{2} \times \dfrac{1}{2}=\dfrac{1}{4}$

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2 years ago

Can someone help me asap please

Gekata [30.6K]

Answer:

The first one is D

The second one is A

hope this helps :/

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2 years ago

A builder could get 6 sheets of sheetrock for $9. If he bought 12 sheets, how much money would he have spent? sheets 6 12 money

melamori03 [73]

Answer:

$18

Step-by-step explanation:

we proceed by first solving for the unit cost of a sheet

then calculate the cost for any number of sheet

We are told that a builder could buy 6 sheets for the cost of $9

this means that one sheet would cost 9/6= $1.5

Now the builder buys 12 sheets

therefore the cost of 12 sheets will be

12*1.5= $18

3 0

3 years ago

Augustus ruled the roman empire from 27 BC to AD 14.For how many years did he rule?​

Augustus ruled the roman empire from 27 BC to AD 14.For how many years did he rule?