Ask question

Ask question

All categories

3 years ago

7

Calculate the average rate of change for the given function, from x = 2 to x = 7.

1 answer:

Marina86 [1]3 years ago

5 0

$\bf slope = m = \cfrac{rise}{run} \implies 
\cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby 
\begin{array}{llll}
average~rate\\
of~change
\end{array}\\\\
-------------------------------\\\\

\begin{array}{ccll}
x&f(x)\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
-2&0\\2&15\\7&30
\end{array}
\qquad 
\begin{cases}
x_1=2\\
x_2=7
\end{cases}\implies \cfrac{f(7)-f(2)}{7-2}\implies \cfrac{30-15}{5}
\\\\\\
\cfrac{15}{5}\implies 3$

You might be interested in

Find the total number of sides (y)

riadik2000 [5.3K]

Answer:

There are 24 sides.

Step-by-step explanation:

There are 6 figures and in each figure there are 4 sides

So,

4 × 6 = 24

Thus, There are 24 sides.

<u>-TheUnknownScientist</u><u> 72</u>

6 0

2 years ago

The sum of the exterior angles of any polygon is 360°. True or False

Semenov [28]

That answer has to be true

7 0

3 years ago

A toy rocket is launched from a platform that is 48 ft high. The rocket height above the ground is modeled by h=-16t^2+32t+48. a

Komok [63]

Answer:

a) 64 feet

b) 3 seconds

Step-by-step explanation:

a)

The maximum height of $h=h(t)$ can be bound by finding the y-coordinate of the vertex of $y=-16x^2+32x+48$ .

Compare this equation to $y=ax^2+bx+c$ to find the values of $a,b,\text{ and } c$ .

$a=-16$

$b=32$

$c=48$ .

The x-coordinate of the vertex can be found by evaluating:

$\frac{-b}{2a}=\frac{-32}{2(-16)$

$\frac{-b}{2a}=\frac{-32}{-32}$

$\frac{-b}{2a}=1$

So the x-coordinate of the vertex is 1.

The y-coordinate can be found be evaluating $y=-16x^2+32x+48$ at $x=1$ :

$y=-16(1)^2+32(1)+48$

$y=-16+32+48$

$y=16+48$

$y=64$

So the maximum height of the rocket is 64 ft high.

b)

When the rocket hit's the ground the height that the rocket will be from the ground is 0 ft.

So we are trying to find the second t such that:

$0=-16t^2+32t+48$

I'm going to divide both sides by -16:

$0=t^2-2t-3$

Now we need to find two numbers that multiply to be -3 and add to be -2.

Those numbers are -3 and 1 since (-3)(1)=-3 and (-3)+(1)=-2.

$0=(t-3)(t+1)$

This implies we have either $t-3=0$ or $t+1=0$

The first equation can be solved by adding 3 on both sides: $t=3$ .

The second equation can be solved by subtracting 1 on both sides: $t=-1$ .

So when $t=3$ seconds, is when the rocket has hit the ground.

5 0

3 years ago

Help with this question

larisa [96]

Answer:

-2

Step-by-step explanation:

2x + y = 10 Subtract 2x from both sides.

2x-2x + y = 10 - 2x Combine the left.

y = 10 - 2x

The slope is the number in front of the x -- in this case - 2

The answer is - 2

4 0

2 years ago

Can anyone solve 3m-5n=15 for N

Kazeer [188]

I hope this helps you

7 0

3 years ago