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3 years ago

6

A diagram of a small shed is shown below. Find the volume of the composite figure.

2 answers:

tekilochka [14]3 years ago

4 0

Answer:

290m

Step-by-step explanation:

( 3 * 6 * 5 ) + (5 * 5 * 8)

290

NARA [144]3 years ago

3 0

290 m over the first

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Prove that $5^{3^n} + 1$ is divisible by $3^{n + 1}$ for all nonnegative integers $n.$

Viktor [21]

When $n=0$ , we have

$5^{3^0} + 1 = 5^1 + 1 = 6$

$3^{0 + 1} = 3^1 = 3$

and of course 3 | 6. ("3 divides 6", in case the notation is unfamiliar.)

Suppose this is true for $n=k$ , that

$3^{k + 1} \mid 5^{3^k} + 1$

Now for $n=k+1$ , we have

$5^{3^{k+1}} + 1 = 5^{3^k \times 3} + 1 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k}\right)^3 + 1^3 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k} + 1\right) \left(\left(5^{3^k}\right)^2 - 5^{3^k} + 1\right)$

so we know the left side is at least divisible by $3^{k+1}$ by our assumption.

It remains to show that

$3 \mid \left(5^{3^k}\right)^2 - 5^{3^k} + 1$

which is easily done with Fermat's little theorem. It says

$a^p \equiv a \pmod p$

where $p$ is prime and $a$ is any integer. Then for any positive integer $x$ ,

$5^3 \equiv 5 \pmod 3 \implies (5^3)^x \equiv 5^x \pmod 3$

Furthermore,

$5^{3^k} \equiv 5^{3\times3^{k-1}} \equiv \left(5^{3^{k-1}}\right)^3 \equiv 5^{3^{k-1}} \pmod 3$

which goes all the way down to

$5^{3^k} \equiv 5 \pmod 3$

So, we find that

$\left(5^{3^k}\right)^2 - 5^{3^k} + 1 \equiv 5^2 - 5 + 1 \equiv 21 \equiv 0 \pmod3$

QED

5 0

2 years ago

Factor this trinomial: 5x^2-16x+3<br><br> Please show all work, I'll give Brainliest

FrozenT [24]

This is what I did for factoring. Let me know if you need more work?

5 0

2 years ago

) What is the GCF of 36 and 60?<br> 4<br> 6<br> 12<br> 18

My name is Ann [436]

Answer:

12

Step-by-step explanation:

List out the factors of each

36: 1,2,3,4,6,9,12,18,36

60: 1,2,3,4,5,6,10,12,15,20,30,60

the highest number they both have in common is 12

8 0

3 years ago

How many milliliters of water are in each 7 beakers

mr Goodwill [35]

Can you ask the full question please?

7 0

3 years ago

Find the distance between the two points rounding to the nearest tenth (if necessary).

Sedaia [141]

Answer:

12

Step-by-step explanation:

$We\ know\ that\ distance\ between\ two\ points\ on\ a\ graph\ is\ given\ by\\\\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\Here,\\x_1=0\\x_2=1\\y_1=-5\\y_2=7\\Substituting\ them\ in\ our\ formula,\ we\ get:\\\sqrt{(1-0)^2+(7-(-5))^2}\\=\sqrt{1+(7+5)^2} \\=\sqrt{1+144}\\=\sqrt{145}\\=12.04\\Hence\ it\ rounds\ off\ to\ 12.\\$

7 0

3 years ago