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1 year ago

PLEASE HELP ME 1. A different pool had an area that is of the form

Mathematics

1 answer:

arlik [135]1 year ago

6 0

The solutions to the questions are

The number we are using is 5
The perfect square number closest to the area is 1024
The estimated side length is 32

<h3>What are areas?</h3>

The area of a shape is the amount of space on the shape

For most regular quadrilaterals, you multiply the side lengths to determine the area

<h3>The number to use</h3>

The area expression is given as

Area = ▢ × 102 + ▢ × 101 + 6

From the question, we can use any number

However, this number must be positive

Assume the number is 5

So, we have

Area = 5 × 102 + 5 × 101 + 6

<h3>The perfect square number closest to the result</h3>

In (a), we have:

Area = 5 × 102 + 5 × 101 + 6

Evaluate

Area = 1021

The perfect square number closest to this is

Closest = 1024

<h3>The estimated side length</h3>

In (b), we have

Closest = 1024

Rewrite as

Area = 1024

Take the square roots

Length = 32

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3 years ago

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grad f(x, y) = F(x, y)

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∂f/dx = x + 3

∂f/∂y = 6y + 3

Integrating both sides of the first equation with respect to x gives

f = 1/2 x ^2 + 3x + g(y)

Differentiating with respect to y gives

∂f/∂y = dg/dy = 6y + 3

Solving for g gives

g = ∫ (6y + 3) dy = 3y ^2 + 3y + C

and hence

f(x, y) = 1/2 x ^2 + 3x + 3y ^2 + 3y + C

(a) By the fundamental theorem, the integral of F along any path starting at the point P (1, 0) and ending at Q (3, 3) is

∫ F(x, y) • dr = f (3, 3) - f (1, 0) = 99/2 - 7/2 = 46

(b) Now we're talking about a closed path, so the integral is simply 0. We can verify this by checking the integral over the origin-containing paths:

• From the origin to P :

∫ F(x, y) • dr = f (1, 0) - f (0, 0) = 7/2 - 0 = 7/2

• From Q back to the origin:

∫ F(x, y) • dr = f (0, 0) - f (3, 3) = 0 - 99/2 = -99/2

Then the total integral is 7/2 + 46 - 99/2 = 0, as expected.

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