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Gnoma [55]
2 years ago
11

A grasshopper sits on the first square of a 1×N board. He can jump over one or two squares and land on the next square. The gras

shopper can jump forward or back but he must stay on the board. Find the least number n such that for any N ≥ n the grasshopper can land on each square exactly once. 100 PTS PLS HELP. Can someone answer this genuinely and not just take the points?!!? Thank you
Mathematics
2 answers:
Neko [114]2 years ago
6 0

Answer:

n=N-1

Step-by-step explanation:

Helga [31]2 years ago
4 0

Answer:

n=N-1

Step-by-step explanation:

You can start by imagining this scenario on a small scale, say 5 squares.

Assuming it starts on the first square, the grasshopper can cover the full 5 squares in 2 ways; either it can jump one square at a time, or it can jump all the way to the end and then backtrack. If it jumps one square at a time, it will take 4 hops to cover all 5 squares. If it jumps two squares at a time and then backtracks, it will take 2 jumps to cover the full 5 squares and then 2 to cover the 2 it missed, which is also 4. It will always be one less than the total amount of squares, since it begins on the first square and must touch the rest exactly once. Therefore, the smallest amount n is N-1. Hope this helps!

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irinina [24]
Sorry for the hand writing. But you want to factor out a 4y^2 which will result in (9y^2-1). Then you will factor out the equation in parentheses to (3y-1)(3y+1). Don’t forget to put the 4y^2 out front!

8 0
3 years ago
Read 2 more answers
Can someone please please answer this and explain it? my math teacher didn’t :( will give brainliest points for explanation!!! (
AnnZ [28]

Answer:

QR = 1

Step-by-step explanation:

PR = PQ + QR

PR = x + 19

PQ = 9

So now put what you know in the equation above.

PR = 9 + 2x + 19

PR also equals x + 19

so

x + 19 = 9 + 2x + 19

x + 19 = 2x + 28

19 - 28 + x = 2x

-9 + x = 2x

-9 = 2x - x

-9 = x

===================

QR = 2x + 19

QR = 2*-9 + 19

QR = -18 + 19

QR = 1

This really is kind of a nasty question. You don't expect to get a minus number of x.

8 0
3 years ago
The ratio of boys to girls in Mr. Hoda's art
SOVA2 [1]

Answer:

15:10

Step-by-step explanation:

Method 1: 5 lots of 3:2 →5 × (3:2) = (5×3) : (5×2) = 15:10

Method 2: 3/2 × 1 → 3/2 ×5/5 = 3×5 2×5= 15:10

boys: 15

girls: 10

3 0
3 years ago
Is 2/5 - (-5/6) positive,negative, or zero
malfutka [58]
It is positive.

Hope this helped.
6 0
3 years ago
Wilmer went up a hill for x minutes at a speed of y kilometers per minutes. Then he went down the same path at a speed of z kilo
dedylja [7]

Answer:

xy=wz

Step-by-step explanation:

Given that:

Speed of Wilmer up the hill = y km/min

Time taken up the hill = x minutes

Speed of Wilmer down the hill = z  km/min

Time taken up the hill = w minutes

Distance can be calculated by multiplying the Speed with Time i.e.

The formula for distance is given as:

Distance = Speed \times Time

Distance up the hill = y\times x =xy\ kilometers

Distance down the hill = z\times w =wz\ kilometers

It is well known that, the distance up the hill and down the hill will be same.

Putting both the values equal, we get:

xy=wz

4 0
2 years ago
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