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2 years ago

Find The Surface Area Of The Pyramid

Mathematics

2 answers:

Travka [436]2 years ago

7 0

75
the formula is
=12pl+B

Salsk061 [2.6K]2 years ago

7 0

Answer is 75 i hope this helps you

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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

Whats the slope of (2,-5),(-6,5)

Makovka662 [10]

The slope of the line with the points (2,-5) and (-6,5) is 5/-4 (or 10/-8).

3 0

3 years ago

Can u please help me please. Please

jonny [76]

The answer is
C = 4 ÷ 1/5

6 0

3 years ago

This has two answers so ya give um to me

alexandr1967 [171]

Let's separate this absolute value equation into two different equations.

x + 1 = 3.

Subtract 1 from each side

x = 2.

x + 1 = -3

Subtract 1 from each side

x = -4

The two solutions are x = 2 and x = -4

5 0

3 years ago

Find the equation of this linear model

kompoz [17]

Answer:

Is there a diagram to this question?

Step-by-step explanation:

7 0

2 years ago