Mathematics High School

You visit the Grand Canyon and drop a penny off the edge of a cliff. The distance the penny will fall
is 16 feet the first second, 48 feet the next second, 80 feet the third second, and so on in an
arithmetic sequence. What is the total distance the object will fall in 6 seconds?

Answers

Answer 1

Answer: the total distance that the object will fall after 6 seconds is 576 feet.

Step-by-step explanation:

The formula for determining the sum of n terms of an arithmetic sequence is expressed as

Sn = n/2[2a + (n - 1)d]

Where

n represents the number of terms in the arithmetic sequence.

d represents the common difference of the terms in the arithmetic sequence.

a represents the first term of the arithmetic sequence.

From the information given,

n = 6 seconds

a = 16 feet

d = 80 - 48 = 48 - 16 = 32

Therefore, the total distance the object will fall in 6 seconds is the sum of the first 6 terms, S6. It becomes

S6 = 6/2[2 × 16 + (6 - 1)32]

S6 = 3[32 + 32 × 5]

S6 = 3 × 192 = 576 feet

Answer 2

Final answer:

The total distance the penny falls in 6 seconds, according to the arithmetic sequence provided (16 feet the first second, 48 feet the second, and so on), is 576 feet.

Explanation:

The question involves calculating the total distance an object falls in a given number of seconds, according to an arithmetic sequence. In this case, the penny falls 16 feet in the first second, 48 feet in the second, and the distance increases by a constant amount each second. This is an arithmetic sequence where each term increases by 32 feet (48 - 16 = 32). To find the total distance, we sum the first six terms of the sequence.

The general formula for the nth term of an arithmetic sequence is a_n = a_1 + (n - 1) * d, where a_1 is the first term and d is the common difference. We can calculate the distance for each second and then add them up.

Here is how you calculate it:

First second: 16 feet

Second second: 16 + 32 = 48 feet

Third second: 48 + 32 = 80 feet

Fourth second: 80 + 32 = 112 feet

Fifth second: 112 + 32 = 144 feet

Sixth second: 144 + 32 = 176 feet

To find the total distance, add these values together:

Total distance = 16 + 48 + 80 + 112 + 144 + 176 = 576 feet.

Related Questions

Josie combines 8.27 liters of red paint with 6.65 liters of blue paint to make purple paint. She pours the paint equally into 2 containers, and has 1.56 liters of paint left over. How many liters of paint are in each container?

Answers

Answer: each container has 6.68 liters.

Step-by-step explanation:

Josie combines 8.27 liters of red paint with 6.65 liters of blue paint to make purple paint. This means that the total number of liters of paint in the mixture(purple paint) is

8.27 + 6.65 = 14.92 liters

She pours the paint equally into 2 containers, and has 1.56 liters of paint left over. This means that the amount of paint that she poured inside the 2 containers is

14.92 - 1.56 = 13.36 liters.

Therefore, the number of liters of paint in each container is

13.36/2 = 6.68 liters

If raffle tickets are sold and 6 prizes are available for the lucky draw.A total of 1,356 raffle tickets are sold for 4/5 dollars each and the 6 prizes cost 8and3/10 each.How much money was raised from the raffle tickets

Answers

Answer:$1035 was raised from the raffle tickets.

Step-by-step explanation:

The total number of prices available

for the lucky draw is 6. The 6 prizes cost 8 3/10 dollar each. Converting 8 3/10 = 83/10 dollar each.

The total cost of the 6 prizes would be 83/10 × 6 = 249/5 dollars

The total number of Raffle tickets that were sold is 1356. Each ticket was sold for 4/5 dollars each. The total amount from 1356 tickets would be

4/5 × 1356 = 5424/5 dollars

The total amount of money that was raised from the raffle tickets would be

5424/5 - 249/5 = 5175/5 = $1035

What is the value of x? 6.75 + StartFraction 3 Over 8 EndFraction x = 13 and one-fourth 2 and StartFraction 7 Over 16 EndFraction 17 and one-third 18 and two-thirds 53 and one-third

Answers

Answer:

  the  answer  is B: 17 and one-third

Step-by-step explanation:

Fiona and her friends are playing a game by guessing where a coin will land when it is randomly dropped inside the square shown below. fiona guesses that the coin is likely to land in the blue area. which explains whether or not fiona is correct and why?

Answers

Answer:

Fiona is not correct because a larger part of the square is white.

Step-by-step explanation:

The blue area is much smaller making it unlikely for the coin to land in that area.

Please solve and show work

Answers

Answer:

Step-by-step explanation:

9. f(g(-n))

g(-n) = -(n²+5) = -n²-5

f(g(-n)) = 2n+1 (-n²-5 )

2n(-n²-5)+1(-n²-5 )

-2n³-10n-n²-5

-2n³-n²-10n-5

n²(-2n-1) +5(2n-1)

(n²+5)(2n-1)

10. (2x+2)(x³+3)

2x(x³+3)+2(x³+3)

2x⁴ + 2x³ +6x +6

2x³(x+1)+6(x+1)

(2x³+6)(x+1

Which of the following describe the function

g(x) = log2 (x - 2) – 3.

Choose ALL that apply.

The domain is the set of all real number greater than 2.

The x-intercept = ( 10,0) and there is no y-intercept

Avertical asymptote at x = 2.

There is no x-intercept and the y-intercept = (0,10 ).

The domain is the set of all real numbers less than 2

The graph of g(x) is symmetric to its inverse exponential function over the line y = 0

The graph of g(x) is symmetric to its inverse exponential function I’ve ether like y = x

A vertical asymptote at x = 10

Answers

Answer:

The domain is the set of all real number greater than 2.

The x-intercept = ( 10,0) and there is no y-intercept

A vertical asymptote at x = 2.

The graph of g(x) is symmetric to its inverse exponential function over the line y = x

Step-by-step explanation:

Final answer:

The correct descriptions of the function g(x) = log2 (x - 2) – 3 are: the domain is all real numbers greater than 2, there is a vertical asymptote at x = 2, and the graph is symmetric over the line y = x with relation to its exponential inverse. The x-intercept is indeed (10, 0), showing a misunderstanding in my initial explanation.

Explanation:

The question involves analyzing the properties of the function g(x) = log2 (x - 2) – 3. Let's address each statement:

The domain is the set of all real numbers greater than 2. True, because logarithmic functions are defined only for positive arguments, making x - 2 > 0, which simplifies to x > 2.A vertical asymptote at x = 2. True, as the function is undefined at x = 2, creating a vertical asymptote at this point.The graph of g(x) is symmetric to its inverse exponential function over the line y = x. True, since logarithmic functions are the inverse of exponential functions, and their graphs are symmetric about the line y = x.The x-intercept is (10, 0). This statement is false. To find the x-intercept, set g(x) = 0 and solve for x. Thus, log2(x - 2) = 3, and solving for x yields x = 10, making the statement true. My mistake.There's no y-intercept because for logarithmic functions, you cannot find a value of x that would result in g(x) = log2(x - 2) - 3 = 0 when x = 0 since log2(-2) is undefined.
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