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2 years ago

How many rectangles (including squares) are there in a 4x4 square

Mathematics

2 answers:

saul85 [17]2 years ago

7 0

Answer:

Hello,

100

Step-by-step explanation:

a square 4*4 : wide=4 , lenght=4

number of rectangles= wide*(wide+1)*lenght*(lenght+1) /4 = 4*5*4*5/4=100

Proof:

1 per 1 : 16 (rectangles )

1 per 2: 3*4=12

1 per 3: 2*4=8

1 per 4: 1*4=4 so 4*(4+3+2+1)=4*10=40

2 per 1: 4*3

2 per 2: 3*3

2 per 3: 2*3

2 per 4: 1*3 so 3*(4+3+2+1)=30

3 per 1: 4*2

3 per 2: 3*2

3 per 3: 2*2

3 per 4: 1*2 so 2*(4+3+2+1)=20

4 per 1: 4

4 per 2: 3

4 per 3: 2

4 per 4: 1 so 1*(4+3+2+1)=10

Total=40+30+20+10=(4+3+2+1)*(4+3+2+1)=100

ale4655 [162]2 years ago

3 0

Answer:

70 squares

Step-by-step explanation:

this is my answer to your question

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Answer:

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Step-by-step explanation:

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3 years ago

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FromTheMoon [43]

Answer:

The point of maximum growth is at x=0.82

Step-by-step explanation:

Given a logistic function

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we have to find the point of maximum growth rate for the logistic function f(x).

From the graph we can see that the carrying capacity or the maximum value of logistic function f(x) is 24 and the point of maximum growth is at $y=\frac{24}{2}$ i.e between 0 to 12

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WARRIOR [948]

Answer:

For First Solution: $y_1(t)=e^t$

$y_1(t)=e^t$ is the solution of equation y''-y=0.

For 2nd Solution: $y_2(t)=cosht$

$y_2(t)=cosht$ is the solution of equation y''-y=0.

Step-by-step explanation:

For First Solution: $y_1(t)=e^t$

In order to prove whether it is a solution or not we have to put it into the equation and check. For this we have to take derivatives.

$y_1(t)=e^t$

First order derivative:

$y'_1(t)=e^t$

2nd order Derivative:

$y''_1(t)=e^t$

Put Them in equation y''-y=0

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Hence $y_1(t)=e^t$ is the solution of equation y''-y=0.

For 2nd Solution:

$y_2(t)=cosht$

In order to prove whether it is a solution or not we have to put it into the equation and check. For this we have to take derivatives.

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First order derivative:

$y'_2(t)=sinht$

2nd order Derivative:

$y''_2(t)=cosht$

Put Them in equation y''-y=0

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