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3 years ago

Let f(x)=−x√3 . What is the average rate of change of f(x) from 8 to 64?

Mathematics

1 answer:

Fed [463]3 years ago

5 0

Average rate of change of the function: $-\sqrt{3}$

Step-by-step explanation:

The average rate of change of a function f(x) can be calculated as:

$r=\frac{f(x_2)-f(x_1)}{x_2-x_1}$

where:

$x_1, x_2$ are the x-values of the interval taken into account to evaluate the rate of change of the function

$f(x_1),f(x_2)$ are the values of the function at those points

In this problem, we have:

$x_1=8\\x_2=64$

The function is $f(x)=-x\sqrt{3}$ , so

$f(x_1)=f(8)=-8\sqrt{3}\\f(x_2)=f(64)=-64\sqrt{3}$

So, the average rate of change in this interval is:

$r=\frac{-64\sqrt{3}-(-8\sqrt{3})}{64-8}=\frac{-56\sqrt{3}}{56}=-\sqrt{3}$

Learn more about rates of change:

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Find the distance between his house

Hunter-Best [27]

Here we are supposed to find the distance between the two points

Suppose A=(-8,-9), B=(-4,-10)

Now As per the distance formula we know that the distance between two points is given by the formula

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\ \\ D= \sqrt{(-4+8)^2+(-10+9)^2}\\ \\ D=\sqrt{(4)^2+(-1)^2}\\ \\ D=\sqrt{16+1}\\ \\ D=\sqrt{17} \ miles$

4 0

3 years ago

The length of a square is 4x-3. Find the area in terms of x

prisoha [69]

Answer:

The area of square in terms of x = 16x² -24x + 9

Step-by-step explanation:

It is stated in the question that the length of a square = 4x - 3

Formula to find the area of the square is

<h2 /><h2>Area = length²</h2><h2 />

Area = ( 4x - 3 )²

<em>by using ( a - b )² = a² + b² - 2ab</em>

here a = 4x and b = -3

So,

(4x)² + (-3)² - 2(4x)(3)

16x² + 9 - 2(12x)

16x² + 9 - 24x

16x² -24x + 9

The area of square in terms of x = 16x² -24x + 9

6 0

3 years ago

The length of a rectangle is 7 ft longer than twice the width. If the perimeter is 92 ft find the length and width of the rectan

user100 [1]

Width of the rectangle is 13 ft and length of the rectangle is 33 ft

<u>Step-by-step explanation:</u>

Step 1:

Given perimeter of the rectangle = 92 ft. Let the width be x, then the length of the rectangle = 2x + 7. Use the formula for perimeter of a rectangle = 2(length + width) to find the dimensions.

92 = 2(2x + 7 + x) = 2(3x + 7) = 6x + 14

⇒ 92 = 6x + 14

⇒ 78 = 6x

⇒ x = 78/6

∴ x = 13 ft

⇒ Width of the rectangle = 13 ft

∴ Length of the rectangle = 2x + 7 = 26 + 7 = 33 ft

4 0

3 years ago

What is an equation for the linear function whose graph contains the points (-1,-2) and (3,10) enter your answers in the boxes

mr Goodwill [35]

The equation for the linear function whose graph contains the points (-1, -2) and (3, 10) is y = 3x + 1

<h3><u>Solution:</u></h3>

Given that linear function whose graph contains the points (-1, -2) and (3, 10)

We have to find the equation of line

Any function of the form f (x) = m x + b, where m is not equal to 0 is called a linear function

So let us use the slope intercept form

<em><u>The slope intercept form is given as:</u></em>

y = mx + c

Where "m" is the slope of line and "c" is the y - intercept

Let us first find slope of line containing points (-1, -2) and (3, 10)

<em><u>The slope of line is given as:</u></em>

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\text {Here } x_{1}=-1 \text { and } y_{1}=-2 \text { and } x_{2}=3 \text { and } y_{2}=10$

$m=\frac{10-(-2)}{3-(-1)}=\frac{12}{4}=3$

Thus the slope of line is "m" = 3

Substitute m = 3 and (x, y) = (-1, -2) in y = mx + c

-2 = 3(-1) + c

-2 = -3 + c

c = -2 + 3 = 1

Now substitute c = 1 and m = 3 in slope intercept form to get equation of line

y = 3x + 1

Thus the equation for the linear function is found out

6 0

4 years ago

Solve through substitution

Talja [164]

Answer:

The above system of equation have NO INTERSECTION POINT.

Step-by-step explanation:

Here, the givens system of equation are:

-3 x + 3 y = 4

and y = x + 3

Now, for the intersection of the equations:

Put y = x + 3 in the given first equation:

-3 x + 3 y = 4 ⇒ -3x + 3 (x+ 3) = 4

or, - 3x + 3x + 9 = 4

⇒ 9 = 4 which gives A CONTRADICTION as 9 ≠ 4

Hence, the above system of equation have NO INTERSECTION POINT.

8 0

3 years ago