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What is the density of a brick

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1 answer:

Dahasolnce [82]3 years ago

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While fire clay bricks have a density of 2400 kg/m3, for common red bricks it is 1900 kg/m3 . [

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Given:

Consider the given function is:

$f(x)=x^2-8x+13$

To find:

The average rate of change of the function over the interval $-1\leq x\leq 6$ .

Solution:

The average rate of change of the function f(x) over the interval [a,b] is:

$m=\dfrac{f(x_2)-f(x_1)}{x_2-x_1}$

We have,

$f(x)=x^2-8x+13$

At $x=-1$ ,

$f(-1)=(-1)^2-8(-1)+13$

$f(-1)=1+8+13$

$f(-1)=22$

At $x=6$ ,

$f(6)=(6)^2-8(6)+13$

$f(6)=36-48+13$

$f(6)=1$

Now, the average rate of change of the function f(x) over the interval $-1\leq x\leq 6$ is:

$m=\dfrac{f(6)-f(-1)}{6-(-1)}$

$m=\dfrac{1-22}{7}$

$m=\dfrac{-21}{7}$

$m=-3$

Therefore, the average rate of change of the function f(x) over the interval $-1\leq x\leq 6$ is -3.

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