A ball is dropped and bounces to a height of 5 feet. The ball rebounds to 70% of its previous height after each bounce The function that could be used to model the nth term in the sequence of heights of the ball after the initial drop is

Answers

Answer 1

Answer:

Answer:

$T_n = 7.143(0.7^n)$

Step-by-step explanation:

If a ball bounces to a height of 5feet, the initial drop = 5feet

If the ball rebounds to 70% of its previous height after each bounce, the next height after rebouncing will be expressed as;

= 70% of 5

= 70/100 * 5

= 0.7*5

= 3.5 feet

The next height will be 0.7*3.75 = 2.45 and so on

The heights wil form a sequence as thus;

5, 3.5, 2.45...

This sequence forms a geometric progression.

To get the function that could be used to model the nth term in the sequence of heights of the ball after the initial drop, w will find the nth term of the sequence

$T_n = ar^(n-1)$

a is the first term of the sequence

n is the number of terms

r is the common ratio

From the sequence:

a = 5

$r = (3.5)/(5) = (2.75)/(3.5) = 0.7$

Substitute the given values into the formula

$T_n = 5(0.7)^(n-1)\nT_n = 5((0.7^n)/(0.7^1) )\nT_n = (5)/(0.7)* 0.7^n \nT_n = 7.143(0.7^n)$

The nth tern=m required is $T_n = 7.143(0.7^n)$

Answer 2

Answer:

The function that models the nth term in the sequence of heights of the ball after the initial drop is an = 5 * 0.7(n-1)

The sequence of heights of the ball can be modeled using a geometric sequence, since the ball rebounds to 70% of its previous height after each bounce. The formula for a geometric sequence is:

an = a1 × r(n-1)

where an represents the nth term in the sequence, a1 is the initial term (in this case, the height of the first bounce), and r is the common ratio (in this case, 0.7). So, the function that could be used to model the nth term in the sequence of heights of the ball after the initial drop is:

an = 5 × 0.7(n-1)

Learn more about Geometric sequence here:

brainly.com/question/34246122

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Find the value of A in the equation 5/a+3=3/A-2

Answers

If you would like to find the value of a in the equation 5/a + 3 = 3/a - 2, you can do this using the following steps:

5/a + 3 = 3/a - 2 /*a
5 + 3a = 3 - 2a
3a + 2a = 3 - 5
5a = -2
a = -2/5

The correct result would be -2/5.

5+3a = 3-2a
So
5a = -2
a=-2/5=-0.4

(-3/5, 7/5) and (2/5, 6/5) A. The equation of the line in slope-intercept form is ?
B. Standard Form
Please help

Answers

First, let's find the slope of the line using the formula $(y_2 - y_1)/(x_2 - x_1)$ , where $(x_1, y_1)$ and $(x_2, y_2)$ are points on the line.

The equation for the slope of this line would be:

$((7)/(5) - (6)/(5))/(-(3)/(5) - (2)/(5)) = ((1)/(5))/(-1) = -(1)/(5)$

Now, let's find use the point-slope equation to find an equation for our line, which is $(y - y_1) = m(x - x_1)$ , where $(x_1, y_1)$ is a point on the line and $m$ is the slope. The point-slope equation for our line would be:

$(y - (6)/(5)) = -(1)/(5)(x - (2)/(5))$

$y - (6)/(5) = -(1)/(5)x + (2)/(25)$

$y = -(1)/(5)x + (32)/(25)$

The slope-intercept form of the line would be y = -x/5 + 32/25.

Now, we can use operations to convert this equation into standard form:

$25y = -5x + 32$

$5x + 25y = 32$

The standard form of the line would be 5x + 25y = 32.

Jambalaya is a Cajun dish made from chicken, sausage, and rice. Simone is making a large pot of jambalaya for a party. Chicken costs $6 per pound, sausage costs $3 per pound, and rice costs $1 per pound. She spends $42 on 13.5 pounds of food. She buys twice as much rice as sausage. How much chicken, sausage, and rice will she use in her dish?Can someone please show me how to make this into 3 algebraic equations. I should be good from there. I would really appreciate it.

Answers

$x- amount\ of\ chicken-\ cost\ 6\$\ per\ pound\n y-amount\ of sausage\ - cost\ 3\$\ per\ pound\n z-amount\ of rice-\ cost\ 1\$\ per\ pound \n\n x+y+z=13,5\ and\n 6*x+3*y+1z=42 \ and\n z=2y\n\n First\ substitude\ z=2y\ to \ both\ equations:\n \left \{ {{x+y+2y=13,5} \atop {6x+3y+2y=42}} \right. \n\n \left \{ {{x+3y=13,5} \atop {6x+5y=42}} \right. |First\ equation\ multiply\ by\ -6\n\n \left \{ {{-6x-18y=-81 } \atop {6x+5y=42}} \right.|Adding\ equations\n \+\ -\ -\ -\ -\ -\ -\- \n -13y=-39|:-13$ $y=3\n x+3y=13,5\n x+3*3=13,5\n x=13,5-9=4,5\n x=4,5\n z=2y\n z=2*3=6\n She\ will \ use \ 4,5\ pounds\ of\ chicken, \ 3\ pounds\ of\ sausage\n and\ 6\ pounds\ of \ rice$

Need help worth 34 points!

Answers

x + y = 3
- x - x
y = -x + 3

y - y₁ = m(x - x₁)
y - (-1) = -1[x - (-1)]
y + 1 = -1(x + 1)
y + 1 = -1(x) - 1(1)
y + 1 = -x - 1
- 1 - 1
y = -x - 2

The answer is B.

Answer:

the answer is b

Step-by-step explanation:

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