Is 2.67034165508… rational or unrational?

The table shows the values of a function f(x).

Inessa [10]

Answer:

-4

Step-by-step explanation:

The average rate of change of a function f(x) between two points x = a and x=b is given by,

$f(x)=\frac{f(b)-f(a)}{b-a}$

This can be understood with a simpler example, the straight line.

In this case, the rate of change of the 'function' is given by the slope,

$m=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}$ ;

$(x_{1},f(x_{1})),(x_{2},f(x_{2}))$ being two points on the straight line.

So, for the given problem,

a = -2

b = 2

Hence, average rate of change of $f(x)=\frac{f(2)-f(-2)}{2-(-2)} =\frac{9-25}{2+2} =\frac{-16}{4} =-4$

6 0

4 years ago

Read 2 more answers

A rocket is launched from atop a 104-foot cliff with an initial velocity of 110 ft/s. A. Substitute the values into the vertical

miv72 [106K]

Answer:

7.68 s

Step-by-step explanation:

The vertical motion formula is:

$h_{t} = h_{0} + v_{0}t - \frac{gt^{2}}{2}$

<u>Where:</u>

h(t): is the final height = 0

h(0): is the height of the cliff = 104 foot

v(0): is the initial velocity = 110 ft/s

g: is the gravity = 9.8 m/s² = 32.15 ft/s²

Hence, from the vertical motion formula we can find the time that will take the rocket to hit the ground:

$0 = 104 + 110*t - \frac{32.15t^{2}}{2}$

$0 = 104 + t(110 - 16.08t)$

We have two solutions:

t₁= -0.84 s

t₂ = 7.68 s

We will take the positive value, thus the time that will take the rocket to hit the ground is 7.68 s.

I hope it helps you!

4 0

3 years ago

Frank practiced basketball on 4 different days last week for 1 3/4 hours each time. How many hours did he practice last week?

GrogVix [38]

4 3/4 hours he practiced last week

3 0

3 years ago

A pair of fair dice is cast. What is the probability that the sum of the numbers falling uppermost is less than 4, if it is know

mestny [16]

<span>The ways to make a 7 with 2 die is:
(1) 6 and 1
(2) 1 and 6
(3) 2 and 5
(4) 5 and 2
(5) 3 and 4
(6) 4 and 3
There are 6 ways to make a 7 with the 2 die,
but there is only 1 way to make 7 if the 1st
die comes up 6.
The probability of getting
(1) 6 and 1 is 1/6</span>

8 0

4 years ago

A circle is centered at $O$ and has an area of $48 \pi.$ Let $Q$ and $R$ be points on the circle, and let $P$ be the circumcente

nikklg [1K]

Answer:

Area of Triangle QRP = 3 $\sqrt{3}$