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3 years ago

The equation y = 1/4x represents a proportional relationship. What is the constant of proportionality?

Mathematics

1 answer:

Andrew [12]3 years ago

4 0

Answer:

[see below]

Step-by-step explanation:

The equation is in the form:

y = kx

Where k is the constant of proportionality.

Since 1/4 is in k's spot, the constant of proportionality should be '1/4'.

Hope this helps.

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3 years ago

To begin a bacteria study, a petri dish had 2800 bacteria cells. Each hour since, the number of cells has increased by 7.2%. Let

Rudiy27

The function that models exponential growth is:

P(t) = P0*(1 + r)^t, where

P0 = P(0) is the initial value of P

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The same exponential function written using y and t is:

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3 years ago

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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3 years ago