Mathematics, 04.03.2021 22:20 SpittingFatLama

Renae has been playing Tower of Hanoi and has noticed that the minimum number of moves it takes to defeat the game is related to the number of disks she must move. She has recorded her observations below. Write an equation that describes this pattern. Show your work. Number of Disks in the Tower ║Minimum Number of Moves

1 ║1

2║ 3

3 ║7

4 ║15

5 ║31

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Answer from: manlyman31

y = 2^x - 1

Step-by-step explanation:

Let the number of disks be x and the minimum number of moves be y.

y = 2^x - 1

When x = 1: y = 1

y = 1 = 2 - 1 = 2^1 - 1

When x = 2: y = 3

y = 3 = 4 - 1 = 2^2 - 1

When x = 3: y = 7

y = 7 = 8 - 1 = 2^3 - 1

When x=4: y = 15

y = 15 = 16 - 1 = 2^4 - 1

When x = 5: y = 31

y = 31 = 32 - 1 = 2^5 - 1

Notice that for each derived expression of y, the exponent of 2 is being replaced by the value of x.

The general equation is: y = 2^x - 1

Answer from: Quest

mr. flanders’ class sold 47 doughnuts and mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations:

$\left\{\begin{array}{l}x+y=85\\1.35x+1.08y=104.49\end{array}\right.\rightarrow \left\{\begin{array}{l}x=85-y\\1.35(85-y)+1.08y=104.49\end{array}\right.$

$114.75-1.35y+1.08y=104.49,\\ \\114.75-104.49=1.35y-1.08y,\\ \\10.26=0.27y,\\ \\y=38,\\ \\x=85-38=47.$

Answer from: Quest

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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