All categories

2 years ago

Need help finding constant rate of change!

Mathematics

1 answer:

Salsk061 [2.6K]2 years ago

7 0

Answer:

$m = \frac{4}{7}\\$

Step-by-step explanation:

Given

The attached graph

Required

The constant rate of change (m)

This is calculated as:

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

From the graph, we have:

$(x_1,y_1) = (3,4)$

$(x_2,y_2) = (10,8)$

So, the formula becomes:

$m = \frac{8-4}{10 - 3}$

$m = \frac{4}{7}\\$

You might be interested in

Use the drawing below to answer the questions that follow.

zhannawk [14.2K]

you have to multiple 16 i think

8 0

1 year ago

Read 2 more answers

Consider the following function. f(x) = 2x3 + 9x2 − 24x (a) Find the critical numbers of f. (Enter your answers as a comma-separ

viktelen [127]

Answer:

(a) The critical number of $f(x)$ are $x=-4, 1$

(b)

Increasing for $(-\infty, -4)$
Decreasing for $(-4, 1)$
Increasing for $(1, \infty)$

(c)

relative maximum $(-4, 112)$
relative minimum $(1, -13)$

Step-by-step explanation:

(a) The critical numbers of a function are given by finding the roots of the first derivative of the function or the values where the first derivative does not exist. Since the function is a polynomial, its domain and the domain of its derivatives is $(-\infty, \infty)$ . Thus:

$\frac{df(x)}{dx} = \frac{d(2x^3+9x^2-24x)}{dx} =6 x^2+18x -24\\6 x^2+18x -24=0\\\boxed{x=-4, x=1}$

(b)

A function $f(x)$ defined on an interval is monotone increasing on $(a, b)$ if for every $x_1, x_2 \in (a, b): x_1$ implies $f(x_1)$

A function $f(x)$ defined on an interval is monotone decreasing on $(a, b)$ if for every $x_1, x_2 \in (a, b): x_1$ implies $f(x_1)>f(x_2)$

Combining the domain $(-\infty, \infty)$ with the critical numbers we have the intervals $(-\infty, -4)$ , $(-4, 1)$ and $(1, \infty)$ . Note that any of the points are included, in the case of the infinity it is by definition and the critical number are never included because the function monotony is not defined in the critical points, i.e. it is not monotone increasing or decreasing. Now, let's check for the monotony in each interval, for this, we check for the sign of the first derivative in each interval. Evaluating in each interval the first derivative (one point is enough), we obtain the monotony of the function to be:

Increasing for $(-\infty, -4)$
Decreasing for $(-4, 1)$
Increasing for $(1, \infty)$

(c) From the values obtained in (a) so the relative extremum are the points $(-4, 112)$ and $(1, -13)$ . The $y$ -values are found by evaluating the critical numbers in the original function. Since the first derivative decreases after passing through $x=-4$ and increases after passing through the point $x=1$ we have:

relative maximum $(-4, 112)$
relative minimum $(1, -13)$

3 0

2 years ago

Which expression correctly represents eight times the difference of 4 and a number

expeople1 [14]

Answer:

The expression for two times the difference of 4 and a number is

$8(4-d)$

Step-by-step explanation:

To Find:

Write an expression for Eight times the difference of 4 and a number.

Solution:

Let the Unknown number be 'd'

Difference of 4 and d = ( 4 - d )

So One Time Difference of 4 and d = 1× ( 4 - d )

∴ Two Times Difference of 4 and d = 2× ( 4 - d )

∴ Eight Times Difference of 4 and d = 8× ( 4 - d )

The expression for Eight times the difference of 4 and d. will be

$8(4-d)$

The expression for Eight times the difference of 4 and a number is

$8(4-d)$

6 0

2 years ago

This year the winner of the new york marathon ran the 8 kilometer event in 24 mins. What is the runners unit rate

Nataliya [291]

3km / 1 min because 24/8 =3

6 0

2 years ago

Plz help ...........

bogdanovich [222]

Step-by-step explanation:

Given c = longest of triange = 15m

Given b = short side of triangle = 9m

By pythagoras' Theorem,

${c}^{2} = {a}^{2} + {b}^{2} \\ {a}^{2} + {b}^{2} = {c}^{2} \\ {a}^{2} + {(9)}^{2} = {(15)}^{2} \\ {a}^{2} + 81 = 225 \\ {a}^{2} = 225 - 81 \\ {a}^{2} = 144 \\ a = \sqrt{144} \\ = 12m$

6 0

2 years ago