Find the range of the function shown on the grid. "Brainliest only if correct"

The height h(n) of a bouncing ball is an exponential function of the number n of bounces.

Digiron [165]

Answer:

The height of a bouncing ball is defined by $h(n) = 6\cdot \left(\frac{4}{6} \right)^{n-1}$ .

Step-by-step explanation:

According to this statement, we need to derive the expression of the height of a bouncing ball, that is, a function of the number of bounces. The exponential expression of the bouncing ball is of the form:

$h = h_{o}\cdot r^{n-1}$ , $n \in \mathbb{N}$ , $0 < r < 1$ (1)

Where:

$h_{o}$ - Height reached by the ball on the first bounce, measured in feet.

$r$ - Decrease rate, no unit.

$n$ - Number of bounces, no unit.

$h$ - Height reached by the ball on the n-th bounce, measured in feet.

The decrease rate is the ratio between heights of two consecutive bounces, that is:

$r = \frac{h_{1}}{h_{o}}$ (2)

Where $h_{1}$ is the height reached by the ball on the second bounce, measured in feet.

If we know that $h_{o} = 6\,ft$ and $h_{1} = 4\,ft$ , then the expression for the height of the bouncing ball is:

$h(n) = 6\cdot \left(\frac{4}{6} \right)^{n-1}$

The height of a bouncing ball is defined by $h(n) = 6\cdot \left(\frac{4}{6} \right)^{n-1}$ .

5 0

3 years ago

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Two cooling fans are installed in some laptop computers. Suppose the reliability of each cooling fan is 0.92. What percent impro

wlad13 [49]

Answer:

8%

Step-by-step explanation:

Given that:

Reliability of each = 0.92

r = 0.92

1 - (1 - r)(1 - r) = 1 - (0.08)(0.08) = 1 - 0.0064 = 0.9936

Percentage improvement :

1 - (0.9936) / r

1 - (0.9936 / 0.92)

1 - 1.08

= - 0.08

= 0.08 / 100 = 8%

5 0

2 years ago

Please help Factor completely. Show your work (as much work as possible, including a list of factors if

defon

Answer:

1. x =0; x = -7

2. x = -3; x = 10

3. x = -5; x = -4

Step-by-step explanation:

(1). 6x² + 42x = 0

6x (x + 7) = 0

6x = 0. OR. x + 7 = 0

x = 0/6. x = 0 - 7

x = 0. x = -7

x = 0

x = -7

(2). x² - 7x - 30 = 0

The factors here are (3, -10)

x² - 10x + 3x - 30 = 0

x ( x - 10) + 3 ( x - 10) = 0

(x + 3) ( x - 10) = 0

x + 3 = 0 OR. x - 10 = 0

x = 0-3. x = 0 + 10

x = -3. x = 10

x = -3

x = 10

(3). x² + 9x + 20 = 0

The factors are ( 4, 5)

x² + 4x + 5x + 20 = 0

x ( x + 4) + 5 ( x + 4) = 0

(x + 5) (x + 4) = 0

x + 5 = 0 . OR. x + 4 = 0

x = 0-5. x = 0 - 4

x = -5. x = -4

x = -5

x = -4

6 0

3 years ago

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HELP^^ LOOK AT THE PICTURE. this is algebra in & out tables ?

s2008m [1.1K]

Answer:

a= 1 , b = 1/16 , c = 1/256 , d= 3/2 , e=4/9 , f= 16/81

Step-by-step explanation:

The first table is given as;

x 4⁻ˣ

-1 4

0 1

2 1/16

4 1/256

a= 1 , b = 1/16 , c = 1/256

The second table is given as;

x {2/3}^x

-1 3/2

0 1

2 4/9

4 16/81

d= 3/2 , e=4/9 , f= 16/81

5 0

3 years ago

Which of these is a binomial? O A. x + 2y2 - 7 O B. ab O C. 5xy O D. 2x3 - 7y3

Lemur [1.5K]

Answer:

D

Step-by-step explanation:

2 terms

8 0

2 years ago