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2 years ago

Error Analysis A classmate says that the system consisting of x=0, y=0, and z=0 has no solution. Explain the student's error.

Mathematics

1 answer:

harina [27]2 years ago

3 0

The system can't have only zeros .
It will be only one answer or there will be no answer.
Hence one variable at least not equal to zero for proper system.

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Prove that for any natural n the number 3^(n+4)−3^n is divisible by 16.

gtnhenbr [62]

Answer:

Proved (See Explanation)

Step-by-step explanation:

Show that 3ⁿ⁺⁴ - 3ⁿ is divisible by 16.

This is done as follows

$\frac{3^{n+4} - 3^n}{16}$

From laws of indices;

aᵐ⁺ⁿ = aᵐ * aⁿ.

So, 3ⁿ⁺⁴ can be written as 3ⁿ * 3⁴.

$\frac{3^{n+4} - 3^n}{16}$ becomes

$\frac{3^n * 3^4 - 3^n}{16}$

Factorize

$\frac{3^n(3^4 - 1)}{16}$

$\frac{3^n(81 - 1)}{16}$

$\frac{3^n(80)}{16}$

3ⁿ * 5

5(3ⁿ)

<em>The expression can not be further simplified.</em>

<em>However, we can conclude that when 3ⁿ⁺⁴ - 3ⁿ is divisible by 16, because 5(3ⁿ) is a natural whole number as long as n is a natural whole number.</em>

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Error Analysis A classmate says that the system consisting of x=0, y=0, and z=0 has no solution. Explain the student's error.​

Error Analysis A classmate says that the system consisting of x=0, y=0, and z=0 has no solution. Explain the student's error.