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3 years ago

Find the average rate of change of f(x)=2x-1 from x=-1 to x=2

Mathematics

1 answer:

MrMuchimi3 years ago

3 0

The average rate of change from x = -1 to x = 2 is 2

Solution:

Given function is:

f(x) = 2x - 1

We have to find the average rate of change from x = -1 to x = 2

The average rate of change is given as:

$\text {Average rate of change}=\frac{f(b)-f(a)}{b-a}$

The average rate of change from x = -1 to x = 2 is given by formula:

$\text {Average rate of change}=\frac{f(2)-f(-1)}{2-(-1)}\\\\\text {Average rate of change}=\frac{f(2)-f(-1)}{3}$

Find f(2) and f( - 1)

Substitute x = 2 in given function

f(2) = 2(2) - 1 = 4 - 1 = 3

Substitute x = -1 in given function

f( - 1) = 2(-1) - 1 = -2 - 1 = -3

Substitute the values in above formula,

$\text {Average rate of change}=\frac{3-(-3)}{3}=\frac{6}{3}=2$

Thus average rate of change from x = -1 to x = 2 is 2

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Given B(17,5), C(11, -3), D-1, 2), and E(x, -6), find the value of x so that BC || DE.

son4ous [18]

Answer:

$x=-7$

Step-by-step explanation:

Remember that:

Two lines are parallel if their slopes are the same.
Two lines are perpendicular if their slopes are negative reciprocals.
And two lines are neither (a.k.a intersecting) if they are neither parallel nor perpendicular.

We want to find the value of x such that $\overline{BC}\parallel\overline{DE}$ .

Therefore, the slopes of BC and DE must be equivalent.

So, let's find the slope of BC first.

BC)

We can use the slope formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Let B(17, 5) be (x₁, y₁) and let C(11, -3) be (x₂, y₂). Substitute:

$m=\frac{-3-5}{11-17}$

Subtract:

$m=-8/-6=4/3$

So, the slope of BC is 4/3.

DE)

Let D(-1, 2) be (x₁, y₁) and let E(x, -6) be (x, y₂). Substitute:

$m=\frac{-6-2}{x-(-1)}$

We know that the two slopes must be equal. So, the slope of DE must also be 4/3. Substitute 4/3 for m:

$\frac{4}{3}=\frac{-6-2}{x-(-1)}$

Solve for x. Simplify the right:

$\frac{4}{3}=\frac{-8}{x+1}$

Cross multiply:

$4(x+1)=-8(3)$

Multiply on the right:

$4(x+1)=-24$

Divide both sides by 4:

$x+1=-6$

Subtract 1 from both sides:

$x=-7$

So, the value of x is -7.

And we're done!

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3 years ago

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Answer:

Richter scale is a good way to talk about how strong an earthquake is. It is also easy to compare two earthquakes using the Richter scale.

Generally, earthquakes are estimated to be under

on the Richter scale.

Below is the formula for comparing two earthquakes.

M2-M1=log(I2-I1)

You can check out how this formula is derived.

Compute the magnitude of an earthquake

Given the intensity of two earthquakes and the magnitude of one of them, we can find the magnitude of the other earthquake. For example:

Earthquake

times stronger than earthquake

. Earthquake

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on the Richter scale?

M_A-M_B=log(I_A/I_B)

M_A-2.3=log(15)

M_A=log(15)+3.5

M_A=3.5

How much stronger is this earthquake comparing to that?

When given the magnitudes of

earthquakes, we can figure out how much stronger one earthquake is comparing to the other one. For example:

On the Richter scale, earthquake

is estimated to be

and earthquake

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1.5

How much stronger is earthquake

times

Step-by-step explanation:

The picture is the explanation......

And please comment if it helps you

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3 years ago