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2 years ago

What is the geometric mean of 30 and 6

Mathematics

2 answers:

sladkih [1.3K]2 years ago

8 0

Square root (30 x 6)=
Square root 180=
Square root ( 13 x 13)+11=
13 square root of 11 = 13.41640786

Alik [6]2 years ago

6 0

Since we have 2 numbers, we'll be square rooting.

All we have to do to find the mean is multiply & square root the products.

30 × 6 = 180

$\sqrt{180} = 13.42$

You can use the same process and check my answer if you'd like; I rounded the square root, so you may get a different answer.

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1. What are the solutions (coordinate points) to the system of equations?

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The given system of equations is:

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Another solution is (-2,0)

The solutions are; (0,6) and (-2,0)

Question 2:

The function is

$f(x) = {x}^{6} - {x}^{4}$

Let us put x=-x,

$f( - x) = {( - x)}^{6} - {( - x)}^{4}$

This gives:

$f( - x) = {x}^{6} - {x}^{4}$

We can observe that:

$f(x) = f( - x)$

This is the property of an even function.

Question 3:

The given function is

$f(x) = {x}^{2} + 3x - 2$

The average rate of change of f(x) from x=a to x=b is given as:

$\frac{f(b) - f(a)}{b - a}$

This is the slope of the secant line connecting the two points on f(x)

From x=2 to x=6, the average rate of change

$= \frac{f(6) - f(2)}{6 - 2} \\ = \frac{ {6}^{2} + 3 \times 6 - 2 - {2}^{2} - 3 \times 2 + 2 }{4} \\ = \frac{36 + 18 - 4 - 6}{4} \\ = \frac{44}{4} \\ = 11$

The average rate of change is 11

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