All categories

3 years ago

What is the average rate of change between f (1) and f (5) in the function f (x) = x2 - x - 6 ?

Mathematics

1 answer:

NISA [10]3 years ago

5 0

Answer:

${ \tt{average = \frac{f(1) + f(5)}{2} }} \\ \\ = { \tt{ \frac{( {1}^{2} - 1 - 6) + ( {5}^{2} - 5 - 6) }{2} }} \\ = \frac{ - 6 + 14}{2} \\ \\ = { \tt{4}}$

You might be interested in

Help asap

ZanzabumX [31]

Your fruit punch recipe can be composed of 4 juice containers of lemonade, 2 juice containers of orange juice, 2 juice containers of grape juice, 2 juice containers of apple juice, 2 juice containers of cranberry juice, and 2 juice containers of pineapple juice.

<h3>Unit conversion</h3>

Unit conversion is a tool very useful to solve some questions. For this exercise, you should know that 1 liter (l) = 1000 milliliters (ml).

The question asks you a design your own fruit punch recipe with exactly 5 liters of punch and includes at least three of the juice.

You have several options, an alternative is to use all juices.

Step 1 - Convert the units for each given juice containers

250 milliliters of lemonade = 0.250 l of lemonade juice

500 milliliters of orange juice = 0.500 l of orange juice

250 milliliters of grape juice = 0.250 l of grape juice

250 milliliters of apple juice= 0.250 l of apple juice

500 milliliters of cranberry juice = 0.500 l of cranberry juice

500 milliliter’s of pineapple juice = 0.500 l of pineapple juice

Step 2 -Design your own fruit punch recipe with exactly 5 liters

4 juice containers of lemonade = 4* 0.250 l = 1 l of lemonade

2 juice containers of orange juice= 2* 0.500 l = 1 l of orange juice

2 juice containers of grape juice= 2* 0.250 l = 0.500 l of grape juice

2 juice containers of apple juice= 2* 0.250 l = 0.500 l of apple juice

2 juice containers of cranberry juice= 2* 0.500 l = 1 l of cranberry juice

2 juice containers of pineapple juice= 2* 0.500 l = 1 l pineapple juice

Thus, your own fruit punch recipe is composed of: 4 juice containers of lemonade, 2 juice containers of orange juice, 2 juice containers of grape juice, 2 juice containers of apple juice, 2 juice containers of cranberry juice, and 2 juice containers of pineapple juice.

Read more about the unit conversion for capacity here:

brainly.com/question/14965845

4 0

2 years ago

If the sum of the interior angle of a polygon is 1800 how many sides does it have

Verdich [7]

Answer: 12 sides

Step-by-step explanation:

The sum of the interior angles of a polygon is 180(n-2), where n is the number of sides

$180(n-2)=1800\\\\n-2=10\\\\n=12$

6 0

2 years ago

MATH HELP ASAP!!! MAKING BRAINLIST

Ulleksa [173]

Answer:

22.86

Step-by-step explanation:

2.54 x 9 will give you the answer.

7 0

2 years ago

Read 2 more answers

Five plus one multiplied by ten eaquals 5 1x10=

faust18 [17]

By order of operation
5+1x10
5+10
15

By normal solving
5+1x10
6x10
60

3 0

3 years ago

Y''+y'+y=0, y(0)=1, y'(0)=0

mars1129 [50]

Answer:

$y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+\frac{1}{\sqrt{3}}\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

Step-by-step explanation:

A second order linear , homogeneous ordinary differential equation has form $ay''+by'+cy=0$ .

Given: $y''+y'+y=0$

Let $y=e^{rt}$ be it's solution.

We get,

$\left ( r^2+r+1 \right )e^{rt}=0$

Since $e^{rt}\neq 0$ , $r^2+r+1=0$

{ we know that for equation $ax^2+bx+c=0$ , roots are of form $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ }

We get,

$y=\frac{-1\pm \sqrt{1^2-4}}{2}=\frac{-1\pm \sqrt{3}i}{2}$

For two complex roots $r_1=\alpha +i\beta \,,\,r_2=\alpha -i\beta$ , the general solution is of form $y=e^{\alpha t}\left ( c_1\cos \beta t+c_2\sin \beta t \right )$

i.e $y=e^{\frac{-t}{2}}\left ( c_1\cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

Applying conditions y(0)=1 on $e^{\frac{-t}{2}}\left ( c_1\cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$ , $c_1=1$

So, equation becomes $y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

On differentiating with respect to t, we get

$y'=\frac{-1}{2}e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )+e^{\frac{-t}{2}}\left ( \frac{-\sqrt{3}}{2} \sin \left ( \frac{\sqrt{3}t}{2} \right )+c_2\frac{\sqrt{3}}{2}\cos\left ( \frac{\sqrt{3}t}{2} \right )\right )$

Applying condition: y'(0)=0, we get $0=\frac{-1}{2}+\frac{\sqrt{3}}{2}c_2\Rightarrow c_2=\frac{1}{\sqrt{3}}$

Therefore,

$y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+\frac{1}{\sqrt{3}}\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

3 0

3 years ago