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tatyana61 [14]
3 years ago
14

The squares are identical. What is the area of each square?

Mathematics
1 answer:
Nastasia [14]3 years ago
6 0

Answer:

A = 256 units^2

Step-by-step explanation:

If the squares are identical, then the side lengths are identical

3x+7 = 5x+1

Subtract 3x from each side

3x+7-3x = 5x-3x+1

7 = 2x+1

Subtract 1

7-1 =2x+1-1

6 = 2x

Divide by 2

6/2 =2x/2

3 =x

The side length is 3x+7 = 3*3 +7 = 9+7 = 16

The area is

A = s^2 where s is the side length

A = 16^2

A = 256 units^2

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We have to find a funtion f such that its gradient is (ycos(xy), x(cos(xy)-ze^(yz), -ye^(yz)). In other words:

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we can find the value of f using integration over each separate, variable. For example, if we integrate ycos(x,y) over the x variable (assuming y and z as constants), we should obtain any function like f plus a function h(y,z). We will use the substitution method. We call u(x) = xy. The derivate of u (in respect to x) is y, hence

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Where, again, the constant of integration depends on Z.

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if we derivate f over z, we obtain

f_z(x,y,z) = -ye^{yz} + d/dz K(z)

That should be equal to -ye^(yz), hence the derivate of K(z) is 0 and, as a consecuence, K can be any constant. We can take K = 0. We obtain, therefore, that f(x,y,z) = cos(xy) - e^(yz)

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